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Unit 3
Classification of Elements and Periodicity in Properties
After studying this Unit, you will be able to • appreciate how the concept of grouping elements in accordance to their properties led to the development of Periodic Table
• understand the Periodic Law; • understand the significance of atomic number and electronic configuration as the basis for periodic classification; • name the elements with Z >100 according to IUPAC nomenclature; • classify elements into s, p, d, f blocks and learn their main characteristics; • recognise the periodic trends in physical and chemical properties of elements; • compare the reactivity of elements and correlate it with their occurrence in nature; • explain the relationship between ionization enthalpy and metallic character; • use scientific vocabulary appropriately to communicate ideas related to certain important properties of atoms e.g., atomic/ ionic radii, ionization enthalpy, electron gain enthalpy, electronegativity, valence of elements.
The Periodic Table is arguably the most important concept in chemistry, both in principle and in practice
It is the everyday support for students, it suggests new avenues of research to professionals, and it provides a succinct organization of the whole of chemistry
It is a remarkable demonstration of the fact that the chemical elements are not a random cluster of entities but instead display trends and lie together in families
An awareness of the Periodic Table is essential to anyone who wishes to disentangle the world and see how it is built up from the fundamental building blocks of the chemistry, the chemical elements
Glenn T
Seaborg In this Unit, we will study the historical development of the Periodic Table as it stands today and the Modern Periodic Law
We will also learn how the periodic classification follows as a logical consequence of the electronic configuration of atoms
Finally, we shall examine some of the periodic trends in the physical and chemical properties of the elements
3.1 WHY DO WE NEED TO CLASSIFY ELEMENTS ? We know by now that the elements are the basic units of all types of matter
In 1800, only 31 elements were known
By 1865, the number of identified elements had more than doubled to 63
At present 114 elements are known
Of them, the recently discovered elements are man-made
Efforts to synthesise new elements are continuing
With such a large number of elements it is very difficult to study individually the chemistry of all these elements and their innumerable compounds individually
To ease out this problem, scientists searched for a systematic way to organise their knowledge by classifying the elements
Not only that it would rationalize known chemical facts about elements, but even predict new ones for undertaking further study. 3.2 GENESIS OF PERIODIC CLASSIFICATION Classification of elements into groups and development of Periodic Law and Periodic Table are the consequences of systematising the knowledge gained by a number of scientists through their observations and experiments
The German chemist, Johann Dobereiner in early 1800’s was the first to consider the idea of trends among properties of elements
By 1829 he noted a similarity among the physical and chemical properties of several groups of three elements (Triads)
In each case, he noticed that the middle element of each of the Triads had an atomic weight about half way between the atomic weights of the other two (Table 3.1)
Also the properties of the middle element were in between those of the other two members
Since Dobereiner’s relationship, referred to as the Law of Triads, seemed to work only for a few elements, it was dismissed as coincidence
The next reported attempt to classify elements was made by a French geologist, A.E.B
de Chancourtois in 1862
He arranged the then known elements in order of increasing atomic weights and made a cylindrical table of elements to display the periodic recurrence of properties
This also did not attract much attention
The English chemist, John Alexander Newlands in 1865 profounded the Law of Octaves
He arranged the elements in increasing order of their atomic weights and noted that every eighth element had properties similar to the first element (Table 3.2)
The relationship was just like every eighth note that resembles the first in octaves of music
Newlands’s Law of Octaves seemed to be true only for elements up to calcium
Although his idea was not widely accepted at that time, he, for his work, was later awarded Davy Medal in 1887 by the Royal Society, London
Table 3.1 Dobereiner’s Triads
The Periodic Law, as we know it today owes its development to the Russian chemist, Dmitri Mendeleev (1834-1907) and the German chemist, Lothar Meyer (1830-1895)
Working independently, both the chemists in 1869 proposed that on arranging elements in the increasing order of their atomic weights, similarities appear in physical and chemical properties at regular intervals
Lothar Meyer plotted the physical properties such as atomic volume, melting point and boiling point against atomic weight and obtained a periodically repeated pattern
Unlike Newlands, Lothar Meyer observed a change in length of that repeating pattern
By 1868, Lothar Meyer had developed a table of the elements that closely resembles the Modern Periodic Table
However, his work was not published until after the work of Dmitri Mendeleev, the scientist who is generally credited with the development of the Modern Periodic Table.
Table 3.2 Newlands’ Octaves
While Dobereiner initiated the study of periodic relationship, it was Mendeleev who was responsible for publishing the Periodic Law for the first time
It states as follows : The properties of the elements are a periodic function of their atomic weights
Mendeleev arranged elements in horizontal rows and vertical columns of a table in order of their increasing atomic weights in such a way that the elements with similar properties occupied the same vertical column or group
Mendeleev’s system of classifying elements was more elaborate than that of Lothar Meyer’s
He fully recognized the significance of periodicity and used broader range of physical and chemical properties to classify the elements
In particular, Mendeleev relied on the similarities in the empirical formulas and properties of the compounds formed by the elements
He realized that some of the elements did not fit in with his scheme of classification if the order of atomic weight was strictly followed
He ignored the order of atomic weights, thinking that the atomic measurements might be incorrect, and placed the elements with similar properties together
For example, iodine with lower atomic weight than that of tellurium (Group VI) was placed in Group VII along with fluorine, chlorine, bromine because of similarities in properties
At the same time, keeping his primary aim of arranging the elements of similar properties in the same group, he proposed that some of the elements were still undiscovered and, therefore, left several gaps in the table
For example, both gallium and germanium were unknown at the time Mendeleev published his Periodic Table
He left the gap under aluminium and a gap under silicon, and called these elements Eka-Aluminium and Eka-Silicon
Mendeleev predicted not only the existence of gallium and germanium, but also described some of their general physical properties
These elements were discovered later
Some of the properties predicted by Mendeleev for these elements and those found experimentally are listed in Table 3.3.
Table 3.3 Mendeleev’s Predictions for the Elements Eka-aluminium (Gallium) and Eka-silicon (Germanium)
The boldness of Mendeleev’s quantitative predictions and their eventual success made him and his Periodic Table famous
Mendeleev’s Periodic Table published in 1905 is shown in .
PERIODIC SYSTEM OF THE ELEMENTS IN GROUPS AND SERIES
3.3 MODERN PERIODIC LAW AND THE PRESENT FORM OF THE PERIODIC TABLE We must bear in mind that when Mendeleev developed his Periodic Table, chemists knew nothing about the internal structure of atom
However, the beginning of the 20th century witnessed profound developments in theories about sub-atomic particles
In 1913, the English physicist, Henry Moseley observed regularities in the characteristic X-ray spectra of the elements
A plot of (whereis frequency of X-rays emitted) against atomic number (Z ) gave a straight line and not the plot of vs atomic mass
He thereby showed that the atomic number is a more fundamental property of an element than its atomic mass
Mendeleev’s Periodic Law was, therefore, accordingly modified
This is known as the Modern Periodic Law and can be stated as : The physical and chemical properties of the elements are periodic functions of their atomic numbers
The Periodic Law revealed important analogies among the 94 naturally occurring elements (neptunium and plutonium like actinium and protoactinium are also found in pitch blende – an ore of uranium)
It stimulated renewed interest in Inorganic Chemistry and has carried into the present with the creation of artificially produced short-lived elements
You may recall that the atomic number is equal to the nuclear charge (i.e., number of protons) or the number of electrons in a neutral atom
It is then easy to visualize the significance of quantum numbers and electronic configurations in periodicity of elements
In fact, it is now recognized that the Periodic Law is essentially the consequence of the periodic variation in electronic configurations, which indeed determine the physical and chemical properties of elements and their compounds
Numerous forms of Periodic Table have been devised from time to time
Some forms emphasise chemical reactions and valence, whereas others stress the electronic configuration of elements
A modern version, the so-called “long form” of the Periodic Table of the elements , is the most convenient and widely used
The horizontal rows (which Mendeleev called series) are called periods and the vertical columns, groups
Elements having similar outer electronic configurations in their atoms are arranged in vertical columns, referred to as groups or families
According to the recommendation of International Union of Pure and Applied Chemistry (IUPAC), the groups are numbered from 1 to 18 replacing the older notation of groups IA … VIIA, VIII, IB … VIIB and 0
There are altogether seven periods
The period number corresponds to the highest principal quantum number (n) of the elements in the period
The first period contains 2 elements
The subsequent periods consists of 8, 8, 18, 18 and 32 elements, respectively
The seventh period is incomplete and like the sixth period would have a theoretical maximum (on the basis of quantum numbers) of 32 elements
In this form of the Periodic Table, 14 elements of both sixth and seventh periods (lanthanoids and actinoids, respectively) are placed in separate panels at the bottom*.
3.4 NOMENCLATURE OF ELEMENTS WITH ATOMIC NUMBERS > 100 The naming of the new elements had been traditionally the privilege of the discoverer (or discoverers) and the suggested name was ratified by the IUPAC
In recent years this has led to some controversy
The new elements with very high atomic numbers are so unstable that only minute quantities, sometimes only a few atoms of them are obtained
Their synthesis and characterisation, therefore, require highly sophisticated costly equipment and laboratory
Such work is carried out with competitive spirit only in some laboratories in the world
Scientists, before collecting the reliable data on the new element, at times get tempted to claim for its discovery
For example, both American and Soviet scientists claimed credit for discovering element 104
The Americans named it Rutherfordium whereas Soviets named it Kurchatovium
To avoid such problems, the IUPAC has made recommendation that until a new element’s discovery is proved, and its name is officially recognised, a systematic nomenclature be derived directly from the atomic number of the element using the numerical roots for 0 and numbers 1-9
These are shown in Table 3.4
The roots are put together in order of digits which make up the atomic number and “ium” is added at the end
The IUPAC names for elements with Z above 100 are shown in Table 3.5.
* Glenn T
Seaborg’s work in the middle of the 20th century starting with the discovery of plutonium in 1940, followed by those of all the transuranium elements from 94 to 102 led to reconfiguration of the periodic table placing the actinoids below the lanthanoids
In 1951, Seaborg was awarded the Nobel Prize in chemistry for his work
Element 106 has been named Seaborgium (Sg) in his honour.
Table 3.4 Notation for IUPAC Nomenclature of Elements
Table 3.5 Nomenclature of Elements with Atomic Number Above 100
Thus, the new element first gets a temporary name, with symbol consisting of three letters
Later permanent name and symbol are given by a vote of IUPAC representatives from each country
The permanent name might reflect the country (or state of the country) in which the element was discovered, or pay tribute to a notable scientist
As of now, elements with atomic numbers up to 118 have been discovered
Official names of all elements have been announced by IUPAC.
Problem 3.1 What would be the IUPAC name and symbol for the element with atomic number 120? Solution From Table 3.4, the roots for 1, 2 and 0 are un, bi and nil, respectively
Hence, the symbol and the name respectively are Ubn and unbinilium
3.5 ELECTRONIC CONFIGURATIONS OF ELEMENTS AND THE PERIODIC TABLE In the preceding unit we have learnt that an electron in an atom is characterised by a set of four quantum numbers, and the principal quantum number (n ) defines the main energy level known as shell
We have also studied about the filling of electrons into different subshells, also referred to as orbitals (s, p, d, f) in an atom
The distribution of electrons into orbitals of an atom is called its electronic configuration
An element’s location in the Periodic Table reflects the quantum numbers of the last orbital filled
In this section we will observe a direct connection between the electronic configurations of the elements and the long form of the Periodic Table
(a) Electronic Configurations in Periods The period indicates the value of n for the outermost or valence shell
In other words, successive period in the Periodic Table is associated with the filling of the next higher principal energy level (n = 1, n = 2, etc.)
It can be readily seen that the number of elements in each period is twice the number of atomic orbitals available in the energy level that is being filled
The first period (n = 1) starts with the filling of the lowest level (1s) and therefore has two elements — hydrogen (ls1) and helium (ls2) when the first shell (K) is completed
The second period (n = 2) starts with lithium and the third electron enters the 2s orbital
The next element, beryllium has four electrons and has the electronic configuration 1s22s2
Starting from the next element boron, the 2p orbitals are filled with electrons when the L shell is completed at neon (2s22p6)
Thus there are 8 elements in the second period
The third period (n = 3) begins at sodium, and the added electron enters a 3s orbital
Successive filling of 3s and 3p orbitals gives rise to the third period of 8 elements from sodium to argon
The fourth period (n = 4) starts at potassium, and the added electrons fill up the 4s orbital
Now you may note that before the 4p orbital is filled, filling up of 3d orbitals becomes energetically favourable and we come across the so called 3d transition series of elements
This starts from scandium (Z = 21) which has the electronic configuration 3d14s2
The 3d orbitals are filled at zinc (Z=30) with electronic configuration 3d104s2
The fourth period ends at krypton with the filling up of the 4p orbitals
Altogether we have 18 elements in this fourth period
The fifth period (n = 5) beginning with rubidium is similar to the fourth period and contains the 4d transition series starting at yttrium (Z = 39)
This period ends at xenon with the filling up of the 5p orbitals
The sixth period (n = 6) contains 32 elements and successive electrons enter 6s, 4f, 5d and 6p orbitals, in the order — filling up of the 4f orbitals begins with cerium (Z = 58) and ends at lutetium (Z = 71) to give the 4f-inner transition series which is called the lanthanoid series
The seventh period (n = 7) is similar to the sixth period with the successive filling up of the 7s, 5f, 6d and 7p orbitals and includes most of the man-made radioactive elements
This period will end at the element with atomic number 118 which would belong to the noble gas family
Filling up of the 5f orbitals after actinium (Z = 89) gives the 5f-inner transition series known as the actinoid series
The 4f- and 5f-inner transition series of elements are placed separately in the Periodic Table to maintain its structure and to preserve the principle of classification by keeping elements with similar properties in a single column.
Problem 3.2 How would you justify the presence of 18 elements in the 5th period of the Periodic Table? Solution When n = 5, l = 0, 1, 2, 3
The order in which the energy of the available orbitals 4d, 5s and 5p increases is 5s < 4d < 5p
The total number of orbitals available are 9
The maximum number of electrons that can be accommodated is 18; and therefore 18 elements are there in the 5th period.
(b) Groupwise Electronic Configurations Elements in the same vertical column or group have similar valence shell electronic configurations, the same number of electrons in the outer orbitals, and similar properties
For example, the Group 1 elements (alkali metals) all have ns1 valence shell electronic configuration as shown below
Thus it can be seen that the properties of an element have periodic dependence upon its atomic number and not on relative atomic mass
3.6 ELECTRONIC CONFIGURATIONS AND TYPES OF ELEMENTS: s-, p-, d-, f- BLOCKS The aufbau (build up) principle and the electronic configuration of atoms provide a theoretical foundation for the periodic classification
The elements in a vertical column of the Periodic Table constitute a group or family and exhibit similar chemical behaviour
This similarity arises because these elements have the same number and same distribution of electrons in their outermost orbitals
We can classify the elements into four blocks viz., s-block, p-block, d-block and f-block depending on the type of atomic orbitals that are being filled with electrons
This is illustrated in
We notice two exceptions to this categorisation
Strictly, helium belongs to the s-block but its positioning in the p-block along with other group 18 elements is justified because it has a completely filled valence shell (1s2) and as a result, exhibits properties characteristic of other noble gases
The other exception is hydrogen
It has only one s-electron and hence can be placed in group 1 (alkali metals)
It can also gain an electron to achieve a noble gas arrangement and hence it can behave similar to a group 17 (halogen family) elements
Because it is a special case, we shall place hydrogen separately at the top of the Periodic Table as shown in and
We will briefly discuss the salient features of the four types of elements marked in the Periodic Table
More about these elements will be discussed later
During the description of their features certain terminology has been used which has been classified in section 3.7.
3.6.1 The s-Block Elements
The elements of Group 1 (alkali metals) and Group 2 (alkaline earth metals) which have ns1 and ns2 outermost electronic configuration belong to the s-Block Elements
They are all reactive metals with low ionization enthalpies
They lose the outermost electron(s) readily to form 1+ ion (in the case of alkali metals) or 2+ ion (in the case of alkaline earth metals)
The metallic character and the reactivity increase as we go down the group
Because of high reactivity they are never found pure in nature
The compounds of the s-block elements, with the exception of those of lithium and beryllium are predominantly ionic
3.6.2 The p-Block Elements The p-Block Elements comprise those belonging to Group 13 to 18 and these together with the s-Block Elements are called the Representative Elements or Main Group Elements
The outermost electronic configuration varies from ns2np1 to ns2np6 in each period
At the end of each period is a noble gas element with a closed valence shell ns2np6 configuration
All the orbitals in the valence shell of the noble gases are completely filled by electrons and it is very difficult to alter this stable arrangement by the addition or removal of electrons
The noble gases thus exhibit very low chemical reactivity
Preceding the noble gas family are two chemically important groups of non-metals
They are the halogens (Group 17) and the chalcogens (Group 16)
These two groups of elements have highly negative electron gain enthalpies and readily add one or two electrons respectively to attain the stable noble gas configuration
The non-metallic character increases as we move from left to right across a period and metallic character increases as we go down the group
3.6.3 The d-Block Elements (Transition Elements) These are the elements of Group 3 to 12 in the centre of the Periodic Table
These are characterised by the filling of inner d orbitals by electrons and are therefore referred to as d-Block Elements
These elements have the general outer electronic configuration (n-1) d1-10ns0-2
They are all metals
They mostly form coloured ions, exhibit variable valence (oxidation states), paramagnetism and oftenly used as catalysts
However, Zn, Cd and Hg which have the electronic configuration, (n-1) d10ns2 do not show most of the properties of transition elements
In a way, transition metals form a bridge between the chemically active metals of s-block elements and the less active elements of Groups 13 and 14 and thus take their familiar name “Transition Elements”
3.6.4 The f-Block Elements (Inner-Transition Elements) The two rows of elements at the bottom of the Periodic Table, called the Lanthanoids, Ce(Z = 58) – Lu(Z = 71) and Actinoids, Th (Z = 90) – Lr (Z = 103) are characterised by the outer electronic configuration (n-2)f1-14 (n-1)d0–1ns2
The last electron added to each element is filled in f- orbital
These two series of elements are hence called the Inner-Transition Elements (f-Block Elements)
They are all metals
Within each series, the properties of the elements are quite similar
The chemistry of the early actinoids is more complicated than the corresponding lanthanoids, due to the large number of oxidation states possible for these actinoid elements
Actinoid elements are radioactive
Many of the actinoid elements have been made only in nanogram quantities or even less by nuclear reactions and their chemistry is not fully studied
The elements after uranium are called Transuranium Elements.
Problem 3.3 The elements Z = 117 and 120 have not yet been discovered
In which family / group would you place these elements and also give the electronic configuration in each case
Solution We see from , that element with Z = 117, would belong to the halogen family (Group 17) and the electronic configuration would be [Rn] 5f146d107s27p5
The element with Z = 120, will be placed in Group 2 (alkaline earth metals), and will have the electronic configuration [Uuo]8s2.
3.6.5 Metals, Non-metals and Metalloids In addition to displaying the classification of elements into s-, p-, d-, and f-blocks, shows another broad classification of elements based on their properties
The elements can be divided into Metals and Non-Metals
Metals comprise more than 78% of all known elements and appear on the left side of the Periodic Table
Metals are usually solids at room temperature [mercury is an exception; gallium and caesium also have very low melting points (303K and 302K, respectively)]
Metals usually have high melting and boiling points
They are good conductors of heat and electricity
They are malleable (can be flattened into thin sheets by hammering) and ductile (can be drawn into wires)
In contrast, non-metals are located at the top right hand side of the Periodic Table
In fact, in a horizontal row, the property of elements change from metallic on the left to non-metallic on the right
Non-metals are usually solids or gases at room temperature with low melting and boiling points (boron and carbon are exceptions)
They are poor conductors of heat and electricity
Most non-metallic solids are brittle and are neither malleable nor ductile
The elements become more metallic as we go down a group; the non-metallic character increases as one goes from left to right across the Periodic Table
The change from metallic to non-metallic character is not abrupt as shown by the thick zig-zag line in
The elements (e.g., silicon, germanium, arsenic, antimony and tellurium) bordering this line and running diagonally across the Periodic Table show properties that are characteristic of both metals and non-metals
These elements are called Semi-metals or Metalloids
Problem 3.4 Considering the atomic number and position in the periodic table, arrange the following elements in the increasing order of metallic character : Si, Be, Mg, Na, P
Solution Metallic character increases down a group and decreases along a period as we move from left to right
Hence the order of increasing metallic character is: P < Si < Be < Mg < Na.
3.7 PERIODIC TRENDS IN PROPERTIES OF ELEMENTS There are many observable patterns in the physical and chemical properties of elements as we descend in a group or move across a period in the Periodic Table
For example, within a period, chemical reactivity tends to be high in Group 1 metals, lower in elements towards the middle of the table, and increases to a maximum in the Group 17 non-metals
Likewise within a group of representative metals (say alkali metals) reactivity increases on moving down the group, whereas within a group of non-metals (say halogens), reactivity decreases down the group
But why do the properties of elements follow these trends? And how can we explain periodicity? To answer these questions, we must look into the theories of atomic structure and properties of the atom
In this section we shall discuss the periodic trends in certain physical and chemical properties and try to explain them in terms of number of electrons and energy levels
3.7.1 Trends in Physical Properties There are numerous physical properties of elements such as melting and boiling points, heats of fusion and vaporization, energy of atomization, etc
which show periodic variations
However, we shall discuss the periodic trends with respect to atomic and ionic radii, ionization enthalpy, electron gain enthalpy and electronegativity
(a) Atomic Radius You can very well imagine that finding the size of an atom is a lot more complicated than measuring the radius of a ball
Do you know why? Firstly, because the size of an atom (~ 1.2 Å i.e., 1.2 × 10–10 m in radius) is very small
Secondly, since the electron cloud surrounding the atom does not have a sharp boundary, the determination of the atomic size cannot be precise
In other words, there is no practical way by which the size of an individual atom can be measured
However, an estimate of the atomic size can be made by knowing the distance between the atoms in the combined state
One practical approach to estimate the size of an atom of a non-metallic element is to measure the distance between two atoms when they are bound together by a single bond in a covalent molecule and from this value, the “Covalent Radius” of the element can be calculated
For example, the bond distance in the chlorine molecule (Cl2) is 198 pm and half this distance (99 pm), is taken as the atomic radius of chlorine
For metals, we define the term “Metallic Radius” which is taken as half the internuclear distance separating the metal cores in the metallic crystal
For example, the distance between two adjacent copper atoms in solid copper is 256 pm; hence the metallic radius of copper is assigned a value of 128 pm
For simplicity, in this book, we use the term Atomic Radius to refer to both covalent or metallic radius depending on whether the element is a non-metal or a metal
Atomic radii can be measured by X-ray or other spectroscopic methods
The atomic radii of a few elements are listed in Table 3.6
Two trends are obvious
We can explain these trends in terms of nuclear charge and energy level
The atomic size generally decreases across a period as illustrated in (a) for the elements of the second period
It is because within the period the outer electrons are in the same valence shell and the effective nuclear charge increases as the atomic number increases resulting in the increased attraction of electrons to the nucleus
Within a family or vertical column of the periodic table, the atomic radius increases regularly with atomic number as illustrated in (b)
For alkali metals and halogens, as we descend the groups, the principal quantum number (n) increases and the valence electrons are farther from the nucleus
This happens because the inner energy levels are filled with electrons, which serve to shield the outer electrons from the pull of the nucleus
Consequently the size of the atom increases as reflected in the atomic radii
Note that the atomic radii of noble gases are not considered here
Being monoatomic, their (non-bonded radii) values are very large
In fact radii of noble gases should be compared not with the covalent radii but with the van der Waals radii of other elements
Table 3.6(a) Atomic Radii/pm Across the Periods
Table 3.6(b) Atomic Radii/pm Down a Family
(b) Ionic Radius
The removal of an electron from an atom results in the formation of a cation, whereas gain of an electron leads to an anion
The ionic radii can be estimated by measuring the distances between cations and anions in ionic crystals
In general, the ionic radii of elements exhibit the same trend as the atomic radii
A cation is smaller than its parent atom because it has fewer electrons while its nuclear charge remains the same
The size of an anion will be larger than that of the parent atom because the addition of one or more electrons would result in increased repulsion among the electrons and a decrease in effective nuclear charge
For example, the ionic radius of fluoride ion (F– ) is 136 pm whereas the atomic radius of fluorine is only 64 pm
On the other hand, the atomic radius of sodium is 186 pm compared to the ionic radius of 95 pm for Na+
When we find some atoms and ions which contain the same number of electrons, we call them isoelectronic species*
For example, O2–, F–, Na+ and Mg2+ have the same number of electrons (10)
Their radii would be different because of their different nuclear charges
The cation with the greater positive charge will have a smaller radius because of the greater attraction of the electrons to the nucleus
Anion with the greater negative charge will have the larger radius
In this case, the net repulsion of the electrons will outweigh the nuclear charge and the ion will expand in size.
Problem 3.5 Which of the following species will have the largest and the smallest size? Mg, Mg2+, Al, Al3+
Solution Atomic radii decrease across a period
Cations are smaller than their parent atoms
Among isoelectronic species, the one with the larger positive nuclear charge will have a smaller radius
Hence the largest species is Mg; the smallest one is Al3+.
(c) Ionization Enthalpy A quantitative measure of the tendency of an element to lose electron is given by its Ionization Enthalpy
It represents the energy required to remove an electron from an isolated gaseous atom (X) in its ground state
In other words, the first ionization enthalpy for an element X is the enthalpy change (∆i H) for the reaction depicted in
X(g) → X+(g) + e– (3.1) The ionization enthalpy is expressed in units of kJ mol–1
We can define the second ionization enthalpy as the energy required to remove the second most loosely bound electron; it is the energy required to carry out the reaction shown in
X+(g) → X2+(g) + e– (3.2) Energy is always required to remove electrons from an atom and hence ionization enthalpies are always positive
The second ionization enthalpy will be higher than the first ionization enthalpy because it is more difficult to remove an electron from a positively charged ion than from a neutral atom
In the same way the third ionization enthalpy will be higher than the second and so on
The term “ionization enthalpy”, if not qualified, is taken as the first ionization enthalpy.
* Two or more species with same number of atoms, same number of valence electrons and same structure, regardless of the nature of elements involved.
The first ionization enthalpies of elements having atomic numbers up to 60 are plotted in
The periodicity of the graph is quite striking
You will find maxima at the noble gases which have closed electron shells and very stable electron configurations
On the other hand, minima occur at the alkali metals and their low ionization enthalpies can be correlated with their high reactivity
In addition, you will notice two trends the first ionization enthalpy generally increases as we go across a period and decreases as we descend in a group
These trends are illustrated in Figs
3.6(a) and 3.6(b) respectively for the elements of the second period and the first group of the periodic table
You will appreciate that the ionization enthalpy and atomic radius are closely related properties
To understand these trends, we have to consider two factors : the attraction of electrons towards the nucleus, and the repulsion of electrons from each other
The effective nuclear charge experienced by a valence electron in an atom will be less than the actual charge on the nucleus because of “shielding” or “screening” of the valence electron from the nucleus by the intervening core electrons
For example, the 2s electron in lithium is shielded from the nucleus by the inner core of 1s electrons
As a result, the valence electron experiences a net positive charge which is less than the actual charge of +3
In general, shielding is effective when the orbitals in the inner shells are completely filled
This situation occurs in the case of alkali metals which have single outermost ns-electron preceded by a noble gas electronic configuration.
3.6 (a)
3.6 (b)
When we move from lithium to fluorine across the second period, successive electrons are added to orbitals in the same principal quantum level and the shielding of the nuclear charge by the inner core of electrons does not increase very much to compensate for the increased attraction of the electron to the nucleus
Thus, across a period, increasing nuclear charge outweighs the shielding
Consequently, the outermost electrons are held more and more tightly and the ionization enthalpy increases across a period
As we go down a group, the outermost electron being increasingly farther from the nucleus, there is an increased shielding of the nuclear charge by the electrons in the inner levels
In this case, increase in shielding outweighs the increasing nuclear charge and the removal of the outermost electron requires less energy down a group
From (a), you will also notice that the first ionization enthalpy of boron (Z = 5) is slightly less than that of beryllium (Z = 4) even though the former has a greater nuclear charge
When we consider the same principal quantum level, an s-electron is attracted to the nucleus more than a p-electron
In beryllium, the electron removed during the ionization is an s-electron whereas the electron removed during ionization of boron is a p-electron
The penetration of a 2s-electron to the nucleus is more than that of a 2p-electron; hence the 2p electron of boron is more shielded from the nucleus by the inner core of electrons than the 2s electrons of beryllium
Therefore, it is easier to remove the 2p-electron from boron compared to the removal of a 2s- electron from beryllium
Thus, boron has a smaller first ionization enthalpy than beryllium
Another “anomaly” is the smaller first ionization enthalpy of oxygen compared to nitrogen
This arises because in the nitrogen atom, three 2p-electrons reside in different atomic orbitals (Hund’s rule) whereas in the oxygen atom, two of the four 2p-electrons must occupy the same 2p-orbital resulting in an increased electron-electron repulsion
Consequently, it is easier to remove the fourth 2p-electron from oxygen than it is, to remove one of the three 2p-electrons from nitrogen.
Problem 3.6 The first ionization enthalpy (∆i H ) values of the third period elements, Na, Mg and Si are respectively 496, 737 and 786 kJ mol–1
Predict whether the first ∆i H value for Al will be more close to 575 or 760 kJ mol–1 ? Justify your answer
Solution It will be more close to 575 kJ mol–1
The value for Al should be lower than that of Mg because of effective shielding of 3p electrons from the nucleus by 3s-electrons.
(d) Electron Gain Enthalpy When an electron is added to a neutral gaseous atom (X) to convert it into a negative ion, the enthalpy change accompanying the process is defined as the Electron Gain Enthalpy (∆egH)
Electron gain enthalpy provides a measure of the ease with which an atom adds an electron to form anion as represented by
X(g) + e– → X–(g) (3.3) Depending on the element, the process of adding an electron to the atom can be either endothermic or exothermic
For many elements energy is released when an electron is added to the atom and the electron gain enthalpy is negative
For example, group 17 elements (the halogens) have very high negative electron gain enthalpies because they can attain stable noble gas electronic configurations by picking up an electron
On the other hand, noble gases have large positive electron gain enthalpies because the electron has to enter the next higher principal quantum level leading to a very unstable electronic configuration
It may be noted that electron gain enthalpies have large negative values toward the upper right of the periodic table preceding the noble gases.
Table 3.7 Electron Gain Enthalpies* / (kJ mol–1) of Some Main Group Elements
The variation in electron gain enthalpies of elements is less systematic than for ionization enthalpies
As a general rule, electron gain enthalpy becomes more negative with increase in the atomic number across a period
The effective nuclear charge increases from left to right across a period and consequently it will be easier to add an electron to a smaller atom since the added electron on an average would be closer to the positively charged nucleus
We should also expect electron gain enthalpy to become less negative as we go down a group because the size of the atom increases and the added electron would be farther from the nucleus
This is generally the case (Table 3.7)
However, electron gain enthalpy of O or F is less negative than that of the succeeding element
This is because when an electron is added to O or F, the added electron goes to the smaller n = 2 quantum level and suffers significant repulsion from the other electrons present in this level
For the n = 3 quantum level (S or Cl), the added electron occupies a larger region of space and the electron-electron repulsion is much less.
Problem 3.7 Which of the following will have the most negative electron gain enthalpy and which the least negative? P, S, Cl, F
Explain your answer
Solution Electron gain enthalpy generally becomes more negative across a period as we move from left to right
Within a group, electron gain enthalpy becomes less negative down a group
However, adding an electron to the 2p-orbital leads to greater repulsion than adding an electron to the larger 3p-orbital
Hence the element with most negative electron gain enthalpy is chlorine; the one with the least negative electron gain enthalpy is phosphorus.
(e) Electronegativity A qualitative measure of the ability of an atom in a chemical compound to attract shared electrons to itself is called electronegativity
Unlike ionization enthalpy and electron gain enthalpy, it is not a measureable quantity
However, a number of numerical scales of electronegativity of elements viz., Pauling scale, Mulliken-Jaffe scale, Allred-Rochow scale have been developed
The one which is the most widely used is the Pauling scale
Linus Pauling, an American scientist, in 1922 assigned arbitrarily a value of 4.0 to fluorine, the element considered to have the greatest ability to attract electrons
Approximate values for the electronegativity of a few elements are given in Table 3.8(a)
* In many books, the negative of the enthalpy change for the process depicted in is defined as the ELECTRON AFFINITY (Ae ) of the atom under consideration
If energy is released when an electron is added to an atom, the electron affinity is taken as positive, contrary to thermodynamic convention
If energy has to be supplied to add an electron to an atom, then the electron affinity of the atom is assigned a negative sign
However, electron affinity is defined as absolute zero and, therefore at any other temperature (T) heat capacities of the reactants and the products have to be taken into account in ∆egH = –Ae – 5/2 RT.
The electronegativity of any given element is not constant; it varies depending on the element to which it is bound
Though it is not a measurable quantity, it does provide a means of predicting the nature of force that holds a pair of atoms together – a relationship that you will explore later
Electronegativity generally increases across a period from left to right (say from lithium to fluorine) and decrease down a group (say from fluorine to astatine) in the periodic table
How can these trends be explained? Can the electronegativity be related to atomic radii, which tend to decrease across each period from left to right, but increase down each group ? The attraction between the outer (or valence) electrons and the nucleus increases as the atomic radius decreases in a period
The electronegativity also increases
On the same account electronegativity values decrease with the increase in atomic radii down a group
The trend is similar to that of ionization enthalpy.
Knowing the relationship between electronegativity and atomic radius, can you now visualise the relationship between electronegativity and non-metallic properties? Non-metallic elements have strong tendency to gain electrons
Therefore, electronegativity is directly related to that non-metallic properties of elements
It can be further extended to say that the electronegativity is inversely related to the metallic properties of elements
Thus, the increase in electronegativities across a period is accompanied by an increase in non-metallic properties (or decrease in metallic properties) of elements
Similarly, the decrease in electronegativity down a group is accompanied by a decrease in non-metallic properties (or increase in metallic properties) of elements
All these periodic trends are summarised in figure 3.7.
Table 3.8(a) Electronegativity Values (on Pauling scale) Across the Periods
Table 3.8(b) Electronegativity Values (on Pauling scale) Down a Family 3.7.2 Periodic Trends in Chemical Properties Most of the trends in chemical properties of elements, such as diagonal relationships, inert pair effect, effects of lanthanoid contraction etc
will be dealt with along the discussion of each group in later units
In this section we shall study the periodicity of the valence state shown by elements and the anomalous properties of the second period elements (from lithium to fluorine)
(a) Periodicity of Valence or Oxidation States The valence is the most characteristic property of the elements and can be understood in terms of their electronic configurations
The valence of representative elements is usually (though not necessarily) equal to the number of electrons in the outermost orbitals and / or equal to eight minus the number of outermost electrons as shown below
Nowadays the term oxidation state is frequently used for valence
Consider the two oxygen containing compounds: OF2 and Na2O
The order of electronegativity of the three elements involved in these compounds is F > O > Na
Each of the atoms of fluorine, with outer electronic configuration 2s22p5, shares one electron with oxygen in the OF2 molecule
Being highest electronegative element, fluorine is given oxidation state –1
Since there are two fluorine atoms in this molecule, oxygen with outer electronic configuration 2s22p4 shares two electrons with fluorine atoms and thereby exhibits oxidation state +2
In Na2O, oxygen being more electronegative accepts two electrons, one from each of the two sodium atoms and, thus, shows oxidation state –2
On the other hand sodium with electronic configuration 3s1 loses one electron to oxygen and is given oxidation state +1
Thus, the oxidation state of an element in a particular compound can be defined as the charge acquired by its atom on the basis of electronegative consideration from other atoms in the molecule.
Problem 3.8 Using the Periodic Table, predict the formulas of compounds which might be formed by the following pairs of elements; (a) silicon and bromine (b) aluminium and sulphur
Solution (a) Silicon is group 14 element with a valence of 4; bromine belongs to the halogen family with a valence of 1
Hence the formula of the compound formed would be SiBr4
(b) Aluminium belongs to group 13 with a valence of 3; sulphur belongs to group 16 elements with a valence of 2
Hence, the formula of the compound formed would be Al2S3.
Some periodic trends observed in the valence of elements (hydrides and oxides) are shown in Table 3.9
Other such periodic trends which occur in the chemical behaviour of the elements are discussed elsewhere in this book
There are many elements which exhibit variable valence
This is particularly characteristic of transition elements and actinoids, which we shall study later.
Table 3.9 Periodic Trends in Valence of Elements as shown by the Formulas of Their Compounds
(b) Anomalous Properties of Second Period Elements The first element of each of the groups 1 (lithium) and 2 (beryllium) and groups 13-17 (boron to fluorine) differs in many respects from the other members of their respective group
For example, lithium unlike other alkali metals, and beryllium unlike other alkaline earth metals, form compounds with pronounced covalent character; the other members of these groups predominantly form ionic compounds
In fact the behaviour of lithium and beryllium is more similar with the second element of the following group i.e., magnesium and aluminium, respectively
This sort of similarity is commonly referred to as diagonal relationship in the periodic properties
What are the reasons for the different chemical behaviour of the first member of a group of elements in the s- and p-blocks compared to that of the subsequent members in the same group? The anomalous behaviour is attributed to their small size, large charge/radius ratio and high electronegativity of the elements
In addition, the first member of group has only four valence orbitals (2s and 2p) available for bonding, whereas the second member of the groups have nine valence orbitals (3s, 3p, 3d)
As a consequence of this, the maximum covalency of the first member of each group is 4 (e.g., boron can only form [ BF4]-, whereas the other members of the groups can expand their valence shell to accommodate more than four pairs of electrons e.g., aluminium [ AIF4]- forms)
Furthermore, the first member of p-block elements displays greater ability to form pπ – pπ multiple bonds to itself (e.g., C = C, C ≡ C, N = N, N ≡ Ν) and to other second period elements (e.g., C = O, C = N, C ≡ N, N = O) compared to subsequent members of the same group.
Problem 3.9 Are the oxidation state and covalency of Al in [AlCl(H2O)5]2+ same ? Solution No
The oxidation state of Al is +3 and the covalency is 6.
3.7.3 Periodic Trends and Chemical Reactivity We have observed the periodic trends in certain fundamental properties such as atomic and ionic radii, ionization enthalpy, electron gain enthalpy and valence
We know by now that the periodicity is related to electronic configuration
That is, all chemical and physical properties are a manifestation of the electronic configuration of elements
We shall now try to explore relationships between these fundamental properties of elements with their chemical reactivity
The atomic and ionic radii, as we know, generally decrease in a period from left to right
As a consequence, the ionization enthalpies generally increase (with some exceptions as outlined in section 3.7.1(a)) and electron gain enthalpies become more negative across a period
In other words, the ionization enthalpy of the extreme left element in a period is the least and the electron gain enthalpy of the element on the extreme right is the highest negative (note : noble gases having completely filled shells have rather positive electron gain enthalpy values)
This results into high chemical reactivity at the two extremes and the lowest in the centre
Thus, the maximum chemical reactivity at the extreme left (among alkali metals) is exhibited by the loss of an electron leading to the formation of a cation and at the extreme right (among halogens) shown by the gain of an electron forming an anion
This property can be related with the reducing and oxidizing behaviour of the elements which you will learn later
However, here it can be directly related to the metallic and non-metallic character of elements
Thus, the metallic character of an element, which is highest at the extremely left decreases and the non-metallic character increases while moving from left to right across the period
The chemical reactivity of an element can be best shown by its reactions with oxygen and halogens
Here, we shall consider the reaction of the elements with oxygen only
Elements on two extremes of a period easily combine with oxygen to form oxides
The normal oxide formed by the element on extreme left is the most basic (e.g., Na2O), whereas that formed by the element on extreme right is the most acidic (e.g., Cl2O7)
Oxides of elements in the centre are amphoteric (e.g., Al2O3, As2O3) or neutral (e.g., CO, NO, N2O)
Amphoteric oxides behave as acidic with bases and as basic with acids, whereas neutral oxides have no acidic or basic properties.
Problem 3.10 Show by a chemical reaction with water that Na2O is a basic oxide and Cl2O7 is an acidic oxide
Solution Na2O with water forms a strong base whereas Cl2O7 forms strong acid
Na2O + H2O → 2NaOH Cl2O7 + H2O → 2HClO4 Their basic or acidic nature can be qualitatively tested with litmus paper.
Among transition metals (3d series), the change in atomic radii is much smaller as compared to those of representative elements across the period
The change in atomic radii is still smaller among inner-transition metals (4f series)
The ionization enthalpies are intermediate between those of s- and p-blocks
As a consequence, they are less electropositive than group 1 and 2 metals
In a group, the increase in atomic and ionic radii with increase in atomic number generally results in a gradual decrease in ionization enthalpies and a regular decrease (with exception in some third period elements as shown in section 3.7.1(d)) in electron gain enthalpies in the case of main group elements
Thus, the metallic character increases down the group and non-metallic character decreases
This trend can be related with their reducing and oxidizing property which you will learn later
In the case of transition elements, however, a reverse trend is observed
This can be explained in terms of atomic size and ionization enthalpy.
SUMMARY In this Unit, you have studied the development of the Periodic Law and the Periodic Table
Mendeleev’s Periodic Table was based on atomic masses
Modern Periodic Table arranges the elements in the order of their atomic numbers in seven horizontal rows (periods) and eighteen vertical columns (groups or families)
Atomic numbers in a period are consecutive, whereas in a group they increase in a pattern
Elements of the same group have similar valence shell electronic configuration and, therefore, exhibit similar chemical properties
However, the elements of the same period have incrementally increasing number of electrons from left to right, and, therefore, have different valencies
Four types of elements can be recognized in the periodic table on the basis of their electronic configurations
These are s-block, p-block, d-block and f-block elements
Hydrogen with one electron in the 1s orbital occupies a unique position in the periodic table
Metals comprise more than seventy eight per cent of the known elements
Non-metals, which are located at the top of the periodic table, are less than twenty in number
Elements which lie at the border line between metals and non-metals (e.g., Si, Ge, As) are called metalloids or semi-metals
Metallic character increases with increasing atomic number in a group whereas decreases from left to right in a period
The physical and chemical properties of elements vary periodically with their atomic numbers
Periodic trends are observed in atomic sizes, ionization enthalpies, electron gain enthalpies, electronegativity and valence
The atomic radii decrease while going from left to right in a period and increase with atomic number in a group
Ionization enthalpies generally increase across a period and decrease down a group
Electronegativity also shows a similar trend
Electron gain enthalpies, in general, become more negative across a period and less negative down a group
There is some periodicity in valence, for example, among representative elements, the valence is either equal to the number of electrons in the outermost orbitals or eight minus this number
Chemical reactivity is highest at the two extremes of a period and is lowest in the centre
The reactivity on the left extreme of a period is because of the ease of electron loss (or low ionization enthalpy)
Highly reactive elements do not occur in nature in free state; they usually occur in the combined form
Oxides formed of the elements on the left are basic and of the elements on the right are acidic in nature
Oxides of elements in the centre are amphoteric or neutral.
Exercises 3.1 What is the basic theme of organisation in the periodic table? 3.2 Which important property did Mendeleev use to classify the elements in his periodic table and did he stick to that? 3.3 What is the basic difference in approach between the Mendeleev’s Periodic Law and the Modern Periodic Law? 3.4 On the basis of quantum numbers, justify that the sixth period of the periodic table should have 32 elements
3.5 In terms of period and group where would you locate the element with Z =114? 3.6 Write the atomic number of the element present in the third period and seventeenth group of the periodic table
3.7 Which element do you think would have been named by Lawrence Berkeley Laboratory Seaborg’s group? 3.8 Why do elements in the same group have similar physical and chemical properties? 3.9 What does atomic radius and ionic radius really mean to you? 3.10 How do atomic radius vary in a period and in a group? How do you explain the variation? 3.11 What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions
F– Ar Mg2+ (iv) Rb+ 3.12 Consider the following species : N3–, O2–, F–, Na+, Mg2+ and Al3+ (a) What is common in them? (b) Arrange them in the order of increasing ionic radii
3.13 Explain why cation are smaller and anions larger in radii than their parent atoms? 3.14 What is the significance of the terms — ‘isolated gaseous atom’ and ‘ground state’ while defining the ionization enthalpy and electron gain enthalpy? Hint : Requirements for comparison purposes
3.15 Energy of an electron in the ground state of the hydrogen atom is –2.18×10–18J
Calculate the ionization enthalpy of atomic hydrogen in terms of J mol–1
Hint: Apply the idea of mole concept to derive the answer
3.16 Among the second period elements the actual ionization enthalpies are in the order Li < B < Be < C < O < N < F < Ne
Explain why Be has higher ∆i H than B O has lower ∆i H than N and F? 3.17 How would you explain the fact that the first ionization enthalpy of sodium is lower than that of magnesium but its second ionization enthalpy is higher than that of magnesium? 3.18 What are the various factors due to which the ionization enthalpy of the main group elements tends to decrease down a group? 3.19 The first ionization enthalpy values (in kJ mol–1) of group 13 elements are : B Al Ga In Tl 801 577 579 558 589 How would you explain this deviation from the general trend ? 3.20 Which of the following pairs of elements would have a more negative electron gain enthalpy? O or F F or Cl 3.21 Would you expect the second electron gain enthalpy of O as positive, more negative or less negative than the first? Justify your answer
3.22 What is the basic difference between the terms electron gain enthalpy and electronegativity? 3.23 How would you react to the statement that the electronegativity of N on Pauling scale is 3.0 in all the nitrogen compounds? 3.24 Describe the theory associated with the radius of an atom as it (a) gains an electron (b) loses an electron 3.25 Would you expect the first ionization enthalpies for two isotopes of the same element to be the same or different? Justify your answer
3.26 What are the major differences between metals and non-metals? 3.27 Use the periodic table to answer the following questions
(a) Identify an element with five electrons in the outer subshell
(b) Identify an element that would tend to lose two electrons
(c) Identify an element that would tend to gain two electrons
(d) Identify the group having metal, non-metal, liquid as well as gas at the room temperature
3.28 The increasing order of reactivity among group 1 elements is Li < Na < K < Rb <Cs whereas that among group 17 elements is F > CI > Br > I
Explain
3.29 Write the general outer electronic configuration of s-, p-, d- and f- block elements
3.30 Assign the position of the element having outer electronic configuration ns2np4 for n=3 (n-1)d2ns2 for n=4, and (n-2) f 7 (n-1)d1ns2 for n=6, in the periodic table
3.31 The first (∆iH1) and the second (∆iH2) ionization enthalpies (in kJ mol–1) and the (∆egH) electron gain enthalpy (in kJ mol–1) of a few elements are given below:
Which of the above elements is likely to be : (a) the least reactive element
(b) the most reactive metal
(c) the most reactive non-metal
(d) the least reactive non-metal
(e) the metal which can form a stable binary halide of the formula MX2(X=halogen)
(f) the metal which can form a predominantly stable covalent halide of the formula MX (X=halogen)?
3.32 Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements
(a) Lithium and oxygen (b) Magnesium and nitrogen (c) Aluminium and iodine (d) Silicon and oxygen (e) Phosphorus and fluorine (f) Element 71 and fluorine
3.33 In the modern periodic table, the period indicates the value of : (a) atomic number (b) atomic mass (c) principal quantum number (d) azimuthal quantum number.
3.34 Which of the following statements related to the modern periodic table is incorrect? (a) The p-block has 6 columns, because a maximum of 6 electrons can occupy all the orbitals in a p-shell
(b) The d-block has 8 columns, because a maximum of 8 electrons can occupy all the orbitals in a d-subshell
(c) Each block contains a number of columns equal to the number of electrons that can occupy that subshell
(d) The block indicates value of azimuthal quantum number (l) for the last subshell that received electrons in building up the electronic configuration.
3.35 Anything that influences the valence electrons will affect the chemistry of the element
Which one of the following factors does not affect the valence shell? (a) Valence principal quantum number (n) (b) Nuclear charge (Z) (c) Nuclear mass (d) Number of core electrons.
3.36 The size of isoelectronic species — F–, Ne and Na+ is affected by (a) nuclear charge (Z) (b) valence principal quantum number (n) (c) electron-electron interaction in the outer orbitals (d) none of the factors because their size is the same.
3.37 Which one of the following statements is incorrect in relation to ionization enthalpy? (a) Ionization enthalpy increases for each successive electron
(b) The greatest increase in ionization enthalpy is experienced on removal of electron from core noble gas configuration
(c) End of valence electrons is marked by a big jump in ionization enthalpy
(d) Removal of electron from orbitals bearing lower n value is easier than from orbital having higher n value
3.38 Considering the elements B, Al, Mg, and K, the correct order of their metallic character is : (a) B > Al > Mg > K (b) Al > Mg > B > K (c) Mg > Al > K > B (d) K > Mg > Al > B 3.39 Considering the elements B, C, N, F, and Si, the correct order of their non-metallic character is : (a) B > C > Si > N > F (b) Si > C > B > N > F (c) F > N > C > B > Si (d) F > N > C > Si > B 3.40 Considering the elements F, Cl, O and N, the correct order of their chemical reactivity in terms of oxidizing property is : (a) F > Cl > O > N (b) F > O > Cl > N (c) Cl > F > O > N (d) O > F > N > Cl
Table of Contents
Unit 3
Classification of Elements and Periodicity in Properties
3.1 WHY DO WE NEED TO CLASSIFY ELEMENTS ?
3.2 GENESIS OF PERIODIC CLASSIFICATION
3.3 MODERN PERIODIC LAW AND THE PRESENT FORM OF THE PERIODIC TABLE
3.4 NOMENCLATURE OF ELEMENTS WITH ATOMIC NUMBERS > 100
3.5 ELECTRONIC CONFIGURATIONS OF ELEMENTS AND THE PERIODIC TABLE
3.6 ELECTRONIC CONFIGURATIONS AND TYPES OF ELEMENTS: s-, p-, d-, f- BLOCKS
3.6.1 The s-Block Elements
3.6.2 The p-Block Elements
3.6.3 The d-Block Elements (Transition Elements)
3.6.4 The f-Block Elements (Inner-Transition Elements)
3.6.5 Metals, Non-metals and Metalloids
3.7 PERIODIC TRENDS IN PROPERTIES OF ELEMENTS
3.7.1 Trends in Physical Properties
3.7.2 Periodic Trends in Chemical Properties
3.7.3 Periodic Trends and Chemical Reactivity
SUMMARY
Exercises
Landmarks
Cover
Unit 3 Classification of Elements and Periodicity in Properties
Chapter Eight
Gravitation
8.1 Introduction
8.1 Introduction 8.2 Kepler’s laws 8.3 Universal law of gravitation 8.4 The gravitational constant 8.5 Acceleration due to gravity of the earth 8.6 Acceleration due to gravity below and above the surface of earth 8.7 Gravitational potential energy 8.8 Escape speed 8.9 Earth satellites 8.10 Energy of an orbiting satellite 8.11 Geostationary and polar satellites 8.12 Weightlessness Summary Points to ponder Exercises Additional exercises
8.1 Introduction Early in our lives, we become aware of the tendency of all material objects to be attracted towards the earth
Anything thrown up falls down towards the earth, going uphill is lot more tiring than going downhill, raindrops from the clouds above fall towards the earth and there are many other such phenomena
Historically it was the Italian Physicist Galileo (1564-1642) who recognised the fact that all bodies, irrespective of their masses, are accelerated towards the earth with a constant acceleration
It is said that he made a public demonstration of this fact
To find the truth, he certainly did experiments with bodies rolling down inclined planes and arrived at a value of the acceleration due to gravity which is close to the more accurate value obtained later
A seemingly unrelated phenomenon, observation of stars, planets and their motion has been the subject of attention in many countries since the earliest of times
Observations since early times recognised stars which appeared in the sky with positions unchanged year after year
The more interesting objects are the planets which seem to have regular motions against the background of stars
The earliest recorded model for planetary motions proposed by Ptolemy about 2000 years ago was a ‘geocentric’ model in which all celestial objects, stars, the sun and the planets, all revolved around the earth
The only motion that was thought to be possible for celestial objects was motion in a circle
Complicated schemes of motion were put forward by Ptolemy in order to describe the observed motion of the planets
The planets were described as moving in circles with the centre of the circles themselves moving in larger circles
Similar theories were also advanced by Indian astronomers some 400 years later
However a more elegant model in which the Sun was the centre around which the planets revolved – the ‘heliocentric’ model – was already mentioned by Aryabhatta (5th century A.D.) in his treatise
A thousand years later, a Polish monk named Nicolas Copernicus (1473-1543) proposed a definitive model in which the planets moved in circles around a fixed central sun
His theory was discredited by the church, but notable amongst its supporters was Galileo who had to face prosecution from the state for his beliefs
It was around the same time as Galileo, a nobleman called Tycho Brahe (1546-1601) hailing from Denmark, spent his entire lifetime recording observations of the planets with the naked eye
His compiled data were analysed later by his assistant Johannes Kepler (1571-1640)
He could extract from the data three elegant laws that now go by the name of Kepler’s laws
These laws were known to Newton and enabled him to make a great scientific leap in proposing his universal law of gravitation
8.2 Kepler’s laws The three laws of Kepler can be stated as follows: 1
Law of orbits : All planets move in elliptical orbits with the Sun situated at one of the foci of the ellipse
This law was a deviation from the Copernican model which allowed only circular orbits
The ellipse, of which the circle is a special case, is a closed curve which can be drawn very simply as follows.
* Refer to information given in the Box on Page 182
Select two points F1 and F2
Take a length of a string and fix its ends at F1 and F2 by pins
With the tip of a pencil stretch the string taut and then draw a curve by moving the pencil keeping the string taut throughout
) The closed curve you get is called an ellipse
Clearly for any point T on the ellipse, the sum of the distances from F1 and F2 is a constant
F1, F2 are called the focii
Join the points F1 and F2 and extend the line to intersect the ellipse at points P and A as shown in (b)
The midpoint of the line PA is the centre of the ellipse O and the length PO = AO is called the semi-major axis of the ellipse
For a circle, the two focii merge into one and the semi-major axis becomes the radius of the circle
2
Law of areas : The line that joins any planet to the sun sweeps equal areas in equal intervals of time
This law comes from the observations that planets appear to move slower when they are farther from the sun than when they are nearer.
Table 8.1 Data from measurement of planetary motions given below confirm Kepler’s Law of Periods (a ≡ Semi-major axis in units of 1010 m
T ≡ Time period of revolution of the planet in years(y)
Q ≡ The quotient ( T2/a3 ) in units of 10 -34 y2 m-3.)
The law of areas can be understood as a consequence of conservation of angular momentum whch is valid for any central force
A central force is such that the force on the planet is along the vector joining the Sun and the planet
Let the Sun be at the origin and let the position and momentum of the planet be denoted by r and p respectively
Then the area swept out by the planet of mass m in time interval ∆t is ∆A given by ∆A = ½ (r × v∆t) (8.1) Hence ∆A /∆t =½ (r × p)/m, (since v = p/m) = L / (2 m) (8.2) where v is the velocity, L is the angular momentum equal to ( r × p)
For a central force, which is directed along r, L is a constant as the planet goes around
Hence, ∆A /∆t is a constant according to the last equation
This is the law of areas
Gravitation is a central force and hence the law of areas follows.
Johannes Kepler (1571–1630) was a scientist of German origin
He formulated the three laws of planetary motion based on the painstaking observations of Tycho Brahe and coworkers
Kepler himself was an assistant to Brahe and it took him sixteen long years to arrive at the three planetary laws
He is also known as the founder of geometrical optics, being the first to describe what happens to light after it enters a telescope.
* Refer to information given in the Box on Page 182
Example 8.1 Let the speed of the planet at the perihelion P in (a) be vP and the Sun-planet distance SP be rP
Relate {rP, vP} to the corresponding quantities at the aphelion {rA, vA}
Will the planet take equal times to traverse BAC and CPB ?
Answer The magnitude of the angular momentum at P is Lp = mp rp vp, since inspection tells us that rp and vp are mutually perpendicular
Similarly, LA = mp rA vA
From angular momentum conservation mp rp vp = mp rA vA or Since rA > rp, vp > vA
The area SBAC bounded by the ellipse and the radius vectors SB and SC is larger than SBPC in
From Kepler’s second law, equal areas are swept in equal times
Hence the planet will take a longer time to traverse BAC than CPB.
8.3 Universal law of gravitation Legend has it that observing an apple falling from a tree, Newton was inspired to arrive at an universal law of gravitation that led to an explanation of terrestrial gravitation as well as of Kepler’s laws
Newton’s reasoning was that the moon revolving in an orbit of radius Rm was subject to a centripetal acceleration due to earth’s gravity of magnitude (8.3)
where V is the speed of the moon related to the time period T by the relation
The time period T is about 27.3 days and Rm was already known then to be about 3.84 × 10­8m
If we substitute these numbers in Eq
(8.3), we get a value of am much smaller than the value of acceleration due to gravity g on the surface of the earth, arising also due to earth’s gravitational attraction
Central Forces
We know the time rate of change of the angular momentum of a single particle about the origin is
The angular momentum of the particle is conserved, if the torquedue to the force F on it vanishes
This happens either when F is zero or when F is along r
We are interested in forces which satisfy the latter condition
Central forces satisfy this condition
A ‘central’ force is always directed towards or away from a fixed point, i.e., along the position vector of the point of application of the force with respect to the fixed point
(See Figure below.) Further, the magnitude of a central force F depends on r, the distance of the point of application of the force from the fixed point; F = F(r)
In the motion under a central force the angular momentum is always conserved
Two important results follow from this: (1) The motion of a particle under the central force is always confined to a plane
(2) The position vector of the particle with respect to the centre of the force (i.e
the fixed point) has a constant areal velocity
In other words the position vector sweeps out equal areas in equal times as the particle moves under the influence of the central force
Try to prove both these results
You may need to know that the areal velocity is given by : dA/dt = ½ r v sin α
An immediate application of the above discussion can be made to the motion of a planet under the gravitational force of the sun
For convenience the sun may be taken to be so heavy that it is at rest
The gravitational force of the sun on the planet is directed towards the sun
This force also satisfies the requirement F = F(r), since F = G m1m2/r2 where m1and m2 are respectively the masses of the planet and the sun and G is the universal constant of gravitation
The two results (1) and (2) described above, therefore, apply to the motion of the planet
In fact, the result (2) is the well-known second law of Kepler.
Tr is the trejectory of the particle under the central force
At a position P, the force is directed along OP, O is the centre of the force taken as the origin
In time ∆t, the particle moves from P to P′, arc PP′ = ∆s = v ∆t
The tangent PQ at P to the trajectory gives the direction of the velocity at P
The area swept in ∆t is the area of sector POP′ ≈ (r sin α ) PP′/2 = (r v sin a) ∆t/2.)
This clearly shows that the force due to earth’s gravity decreases with distance
If one assumes that the gravitational force due to the earth decreases in proportion to the inverse square of the distance from the centre of the earth, we will have and we get (8.4) in agreement with a value of g ≅ 9.8 m s-2 and the value of am from Eq
(8.3)
These observations led Newton to propose the following Universal Law of Gravitation : Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them
The quotation is essentially from Newton’s famous treatise called ‘Mathematical Principles of Natural Philosophy’ (Principia for short)
Stated Mathematically, Newton’s gravitation law reads : The force F on a point mass m2 due to another point mass m1 has the magnitude (8.5)
Equation (8.5) can be expressed in vector form as
where G is the universal gravitational constant, is the unit vector from m1 to m2 and r = r2 – r1 as shown in .
The gravitational force is attractive, i.e., the force F is along – r
The force on point mass m1 due to m2 is of course – F by Newton’s third law
Thus, the gravitational force F12 on the body 1 due to 2 and F21 on the body 2 due to 1 are related as F12 = – F21.
Before we can apply Eq
(8.5) to objects under consideration, we have to be careful since the law refers to point masses whereas we deal with extended objects which have finite size
If we have a collection of point masses, the force on any one of them is the vector sum of the gravitational forces exerted by the other point masses as shown in Fig 8.4.
Example 8.2 Three equal masses of m kg each are fixed at the vertices of an equilateral triangle ABC
(a) What is the force acting on a mass 2m placed at the centroid G of the triangle? (b) What is the force if the mass at the vertex A is doubled ? Take AG = BG = CG = 1 m (see )
Answer (a) The angle between GC and the positive x-axis is 30° and so is the angle between GB and the negative x-axis
The individual forces in vector notation are
From the principle of superposition and the law of vector addition, the resultant gravitational force FR on (2m) is FR = FGA + FGB + FGC
Alternatively, one expects on the basis of symmetry that the resultant force ought to be zero
(b) Now if the mass at vertex A is doubled then
For the gravitational force between an extended object (like the earth) and a point mass, Eq
(8.5) is not directly applicable
Each point mass in the extended object will exert a force on the given point mass and these force will not all be in the same direction
We have to add up these forces vectorially for all the point masses in the extended object to get the total force
This is easily done using calculus
For two special cases, a simple law results when you do that : (1) The force of attraction between a hollow spherical shell of uniform density and a point mass situated outside is just as if the entire mass of the shell is concentrated at the centre of the shell
Qualitatively this can be understood as follows: Gravitational forces caused by the various regions of the shell have components along the line joining the point mass to the centre as well as along a direction prependicular to this line
The components prependicular to this line cancel out when summing over all regions of the shell leaving only a resultant force along the line joining the point to the centre
The magnitude of this force works out to be as stated above.
Newton’s Principia
Kepler had formulated his third law by 1619
The announcement of the underlying universal law of gravitation came about seventy years later with the publication in 1687 of Newton’s masterpiece Philosophiae Naturalis Principia Mathematica, often simply called thePrincipia.
Around 1685, Edmund Halley (after whom the famous Halley’s comet is named), came to visit Newton at Cambridge and asked him about the nature of the trajectory of a body moving under the influence of an inverse square law
Without hesitation Newton replied that it had to be an ellipse, and further that he had worked it out long ago around 1665 when he was forced to retire to his farm house from Cambridge on account of a plague outbreak
Unfortunately, Newton had lost his papers
Halley prevailed upon Newton to produce his work in book form and agreed to bear the cost of publication
Newton accomplished this feat in eighteen months of superhuman effort
The Principia is a singular scientific masterpiece and in the words of Lagrange it is “the greatest production of the human mind.” The Indian born astrophysicist and Nobel laureate S
Chandrasekhar spent ten years writing a treatise on the Principia
His book, Newton’s Principia for the Common Reader brings into sharp focus the beauty, clarity and breath taking economy of Newton’s methods.
(2) The force of attraction due to a hollow spherical shell of uniform density, on a point mass situated inside it is zero
Qualitatively, we can again understand this result
Various regions of the spherical shell attract the point mass inside it in various directions
These forces cancel each other completely.
8.4 The Gravitational Constant The value of the gravitational constant G entering the Universal law of gravitation can be determined experimentally and this was first done by English scientist Henry Cavendish in 1798
The apparatus used by him is schematically shown in figure.8.6
If L is the length of the bar AB , then the torque arising out of F is F multiplied by L
At equilibrium, this is equal to the restoring torque and hence (8.7)
Observation of θ thus enables one to calculate G from this equation
Since Cavendish’s experiment, the measurement of G has been refined and the currently accepted value is G = 6.67×10-11 N m2/kg2 (8.8)
8.5 Acceleration due to gravity of the earth The earth can be imagined to be a sphere made of a large number of concentric spherical shells with the smallest one at the centre and the largest one at its surface
A point outside the earth is obviously outside all the shells
Thus, all the shells exert a gravitational force at the point outside just as if their masses are concentrated at their common centre according to the result stated in section 8.3
The total mass of all the shells combined is just the mass of the earth
Hence, at a point outside the earth, the gravitational force is just as if its entire mass of the earth is concentrated at its centre
For a point inside the earth, the situation is different
This is illustrated in .
We assume that the entire earth is of uniform density and hence its mass is where ME is the mass of the earth RE is its radius and ρ is the density
On the other hand the mass of the sphere Mr of radius r is and hence (8.10)
If the mass m is situated on the surface of earth, then r = RE and the gravitational force on it is, from Eq
(8.10) (8.11)
The acceleration experienced by the mass m, which is usually denoted by the symbol g is related to F by Newton’s 2nd law by relation F = mg
Thus (8.12)
Acceleration g is readily measurable
RE is a known quantity
The measurement of G by Cavendish’s experiment (or otherwise), combined with knowledge of g and RE enables one to estimate ME from Eq
(8.12)
This is the reason why there is a popular statement regarding Cavendish : “Cavendish weighed the earth”
8.6 Acceleration due to gravity below and above the surface of earth Consider a point mass m at a height h above the surface of the earth as shown in (a)
The radius of the earth is denoted by RE
Since this point is outside the earth, its distance from the centre of the earth is (RE + h )
If F (h) denoted the magnitude of the force on the point mass m , we get from Eq
(8.5) :
(8.13)
This is clearly less than the value of g on the surface of earth : For we can expand the RHS of Eq
(8.14) : For , using binomial expression, . (8.15)
Equation (8.15) thus tells us that for small heights h above the value of g decreases by a factor Now, consider a point mass m at a depth d below the surface of the earth ), so that its distance from the centre of the earth is as shown in the figure
The earth can be thought of as being composed of a smaller sphere of radius (RE – d ) and a spherical shell of thickness d
The force on m due to the outer shell of thickness d is zero because the result quoted in the previous section
As far as the smaller sphere of radius ( RE – d ) is concerned, the point mass is outside it and hence according to the result quoted earlier, the force due to this smaller sphere is just as if the entire mass of the smaller sphere is concentrated at the centre
If Ms is the mass of the smaller sphere, then, Ms/ME = ( RE – d)3 / RE3 ( 8.16) Since mass of a sphere is proportional to be cube of its radius.
(b) g at a depth d
In this case only the smaller sphere of radius (RE–d) contributes to g
Thus the force on the point mass is F (d) = G Ms m / (RE – d ) 2 (8.17) Substituting for Ms from above , we get F (d) = G ME m ( RE – d ) / RE 3 (8.18) and hence the acceleration due to gravity at a depth d, g(d) = is (8.19)
Thus, as we go down below earth’s surface, the acceleration due gravity decreases by a factor The remarkable thing about acceleration due to earth’s gravity is that it is maximum on its surface decreasing whether you go up or down.
8.7 Gravitational potential energy We had discussed earlier the notion of potential energy as being the energy stored in the body at its given position
If the position of the particle changes on account of forces acting on it, then the change in its potential energy is just the amount of work done on the body by the force
As we had discussed earlier, forces for which the work done is independent of the path are the conservative forces
The force of gravity is a conservative force and we can calculate the potential energy of a body arising out of this force, called the gravitational potential energy
Consider points close to the surface of earth, at distances from the surface much smaller than the radius of the earth
In such cases, the force of gravity is practically a constant equal to mg, directed towards the centre of the earth
If we consider a point at a height h1 from the surface of the earth and another point vertically above it at a height h2 from the surface, the work done in lifting the particle of mass m from the first to the second position is denoted by W12 W12 = Force × displacement = mg (h2 – h1) (8.20) If we associate a potential energy W(h) at a point at a height h above the surface such that W(h) = mgh + Wo (8.21) (where Wo = constant) ; then it is clear that W12 = W(h2) – W(h1) (8.22) The work done in moving the particle is just the difference of potential energy between its final and initial positions.Observe that the constant Wo cancels out in Eq
(8.22)
Setting h = 0 in the last equation, we get W ( h = 0 ) = Wo
h = 0 means points on the surface of the earth
Thus, Wo is the potential energy on the surface of the earth
If we consider points at arbitrary distance from the surface of the earth, the result just derived is not valid since the assumption that the gravitational force mg is a constant is no longer valid
However, from our discussion we know that a point outside the earth, the force of gravitation on a particle directed towards the centre of the earth is (8.23)
where ME = mass of earth, m = mass of the particle and r its distance from the centre of the earth
If we now calculate the work done in lifting a particle from r = r1 to r = r2 (r2 > r1) along a vertical path, we get instead of Eq
(8.20) (8.24)
In place of Eq
(8.21), we can thus associate a potential energy W(r) at a distance r, such that (8.25)
valid for r > R , so that once again W12 = W(r2) – W(r1)
Setting r = infinity in the last equation, we get W ( r = infinity ) = W1
Thus, W1 is the potential energy at infinity
One should note that only the difference of potential energy between two points has a definite meaning from Eqs
(8.22) and (8.24)
One conventionally sets W1 equal to zero, so that the potential energy at a point is just the amount of work done in displacing the particle from infinity to that point
We have calculated the potential energy at a point of a particle due to gravitational forces on it due to the earth and it is proportional to the mass of the particle
The gravitational potential due to the gravitational force of the earth is defined as the potential energy of a particle of unit mass at that point
From the earlier discussion, we learn that the gravitational potential energy associated with two particles of masses m1 and m2 separated by distance by a distance r is given by (if we choose V = 0 as r → ∞ ) It should be noted that an isolated system of particles will have the total potential energy that equals the sum of energies (given by the above equation) for all possible pairs of its constituent particles
This is an example of the application of the superposition principle.
Example 8.3 Find the potential energy of a system of four particles placed at the vertices of a square of side l
Also obtain the potential at the centre of the square.
Answer Consider four masses each of mass m at the corners of a square of side l; See
We have four mass pairs at distance l and two diagonal pairs at distance Hence,
8.8 Escape Speed If a stone is thrown by hand, we see it falls back to the earth
Of course using machines we can shoot an object with much greater speeds and with greater and greater initial speed, the object scales higher and higher heights
A natural query that arises in our mind is the following: ‘can we throw an object with such high initial speeds that it does not fall back to the earth?’ The principle of conservation of energy helps us to answer this question
Suppose the object did reach infinity and that its speed there was Vf
The energy of an object is the sum of potential and kinetic energy
As before W1 denotes that gravitational potential energy of the object at infinity
The total energy of the projectile at infinity then is (8.26)
If the object was thrown initially with a speed Vi from a point at a distance (h+RE) from the centre of the earth (RE = radius of the earth), its energy initially was (8.27)
By the principle of energy conservation Eqs
(8.26) and (8.27) must be equal
Hence (8.28)
The R.H.S
is a positive quantity with a minimum value zero hence so must be the L.H.S
Thus, an object can reach infinity as long as Vi is such that
(8.29)
The minimum value of Vi corresponds to the case when the L.H.S
of Eq
(8.29) equals zero
Thus, the minimum speed required for an object to reach infinity (i.e
escape from the earth) corresponds to (8.30)
If the object is thrown from the surface of the earth, h = 0, and we get (8.31)
Using the relation , we get (8.32)
Using the value of g and RE, numerically (Vi)min≈11.2 km/s
This is called the escape speed, sometimes loosely called the escape velocity
Equation (8.32) applies equally well to an object thrown from the surface of the moon with g replaced by the acceleration due to Moon’s gravity on its surface and rE replaced by the radius of the moon
Both are smaller than their values on earth and the escape speed for the moon turns out to be 2.3 km/s, about five times smaller
This is the reason that moon has no atmosphere
Gas molecules if formed on the surface of the moon having velocities larger than this will escape the gravitational pull of the moon.
Example 8.4 Two uniform solid spheres of equal radii R, but mass M and 4 M have a centre to centre separation 6 R, as shown in 0
The two spheres are held fixed
A projectile of mass m is projected from the surface of the sphere of mass M directly towards the centre of the second sphere
Obtain an expression for the minimum speed v of the projectile so that it reaches the surface of the second sphere.
Answer The projectile is acted upon by two mutually opposing gravitational forces of the two spheres
The neutral point N (see 0) is defined as the position where the two forces cancel each other exactly
If ON = r, we have (6R – r)2 = 4r2 6R – r = ±2r r = 2R or – 6R
The neutral point r = – 6R does not concern us in this example
Thus ON = r = 2R
It is sufficient to project the particle with a speed which would enable it to reach N
Thereafter, the greater gravitational pull of 4M would suffice
The mechanical energy at the surface of M is
At the neutral point N, the speed approaches zero
The mechanical energy at N is purely potential
From the principle of conservation of mechanical energy or A point to note is that the speed of the projectile is zero at N, but is nonzero when it strikes the heavier sphere 4 M
The calculation of this speed is left as an exercise to the students.
8.9 Earth Satellites Earth satellites are objects which revolve around the earth
Their motion is very similar to the motion of planets around the Sun and hence Kepler’s laws of planetary motion are equally applicable to them
In particular, their orbits around the earth are circular or elliptic
Moon is the only natural satellite of the earth with a near circular orbit with a time period of approximately 27.3 days which is also roughly equal to the rotational period of the moon about its own axis
Since, 1957, advances in technology have enabled many countries including India to launch artificial earth satellites for practical use in fields like telecommunication, geophysics and meteorology
We will consider a satellite in a circular orbit of a distance (RE + h) from the centre of the earth, where RE = radius of the earth
If m is the mass of the satellite and V its speed, the centripetal force required for this orbit is F(centripetal) = (8.33)
directed towards the centre
This centripetal force is provided by the gravitational force, which is F(gravitation) = (8.34)
where ME is the mass of the earth
Equating R.H.S of Eqs
(8.33) and (8.34) and cancelling out m, we get (8.35)
Thus V decreases as h increases
From ,the speed V for h = 0 is (8.36)
where we have used the relation g =
In every orbit, the satellite traverses a distance 2π(RE + h) with speed V
Its time period T therefore is (8.37)
on substitution of value of V from Eq
(8.35)
Squaring both sides of Eq
(8.37), we get T 2 = k ( RE + h)3 (where k = 4 π2 / GME) (8.38) which is Kepler’s law of periods, as applied to motion of satellites around the earth
For a satellite very close to the surface of earth h can be neglected in comparison to RE in Eq
(8.38)
Hence, for such satellites, T is To, where (8.39)
If we substitute the numerical values g ≅ 9.8 m s-2 and RE = 6400 km., we get
Which is approximately 85 minutes.
Example 8.5 The planet Mars has two moons, phobos and delmos
phobos has a period 7 hours, 39 minutes and an orbital radius of 9.4 ×103 km
Calculate the mass of mars
Assume that earth and mars move in circular orbits around the sun, with the martian orbit being 1.52 times the orbital radius of the earth
What is the length of the martian year in days ?
Answer We employ Eq
(8.38) with the sun’s mass replaced by the martian mass Mm = 6.48 × 1023 kg
Once again Kepler’s third law comes to our aid,
where RMS is the mars -sun distance and RES is the earth-sun distance
∴ TM = (1.52)3/2 × 365 = 684 days We note that the orbits of all planets except Mercury, Mars and Pluto* are very close to being circular
For example, the ratio of the semi-minor to semi-major axis for our Earth is, b/a = 0.99986.
Example 8.6 Weighing the Earth : You are given the following data: g = 9.81 ms–2, RE = 6.37×106 m, the distance to the moon R = 3.84×108 m and the time period of the moon’s revolution is 27.3 days
Obtain the mass of the Earth ME in two different ways.
Answer From Eq
(8.12) we have
= 5.97× 1024 kg
The moon is a satellite of the Earth
From the derivation of Kepler’s third law [see Eq
(8.38)] Both methods yield almost the same answer, the difference between them being less than 1%.
Example 8.7 Express the constant k of Eq
(8.38) in days and kilometres
Given k = 10–13 s2 m–3
The moon is at a distance of 3.84 × 105 km from the earth
Obtain its time-period of revolution in days.
Answer Given k = 10–13 s2 m–3 = = 1.33 ×10–14 d2 km–3 Using Eq
(8.38) and the given value of k, the time period of the moon is T2 = (1.33 × 10-14)(3.84 × 105)3 T = 27.3 d Note that Eq
(8.38) also holds for elliptical orbits if we replace (RE+h) by the semi-major axis of the ellipse
The earth will then be at one of the foci of this ellipse
8.10 Energy of an orbiting Satellite Using Eq
(8.35), the kinetic energy of the satellite in a circular orbit with speed v is
(8.40)
Considering gravitational potential energy at infinity to be zero, the potential energy at distance (RE+h) from the centre of the earth is (8.41)
The K.E is positive whereas the P.E is negative
However, in magnitude the K.E
is half the P.E, so that the total E is (8.42)
The total energy of an circularly orbiting satellite is thus negative, with the potential energy being negative but twice is magnitude of the positive kinetic energy
When the orbit of a satellite becomes elliptic, both the K.E
and P.E
vary from point to point
The total energy which remains constant is negative as in the circular orbit case
This is what we expect, since as we have discussed before if the total energy is positive or zero, the object escapes to infinity
Satellites are always at finite distance from the earth and hence their energies cannot be positive or zero
Example 8.8 A 400 kg satellite is in a circular orbit of radius 2RE about the Earth
How much energy is required to transfer it to a circular orbit of radius 4RE ? What are the changes in the kinetic and potential energies ?
Answer Initially, While finally The change in the total energy is ∆E = Ef – Ei The kinetic energy is reduced and it mimics ∆E, namely, ∆K = Kf – Ki = – 3.13 × 109 J
The change in potential energy is twice the change in the total energy, namely ∆V = Vf – Vi = – 6.25 × 109 J
8.11 Geostationary and Polar Satellites An interesting phenomenon arises if in we arrange the value of (RE+ h) such that T in Eq
(8.37) becomes equal to 24 hours
If the circular orbit is in the equatorial plane of the earth, such a satellite, having the same period as the period of rotation of the earth about its own axis would appear stationery viewed from a point on earth
The (RE + h) for this purpose works out to be large as compared to RE : (8.43)
and for T = 24 hours, h works out to be 35800 km
which is much larger than RE
Satellites in a circular orbits around the earth in the equatorial plane with T = 24 hours are called Geostationery Satellites
Clearly, since the earth rotates with the same period, the satellite would appear fixed from any point on earth
It takes very powerful rockets to throw up a satellite to such large heights above the earth but this has been done in view of the several benefits of many practical applications.
India’s Leap into Space India started its space programme in 1962 when Indian National Committee for Space Research was set up by the Government of India which was superseded by the Indian Space Research Organisation (ISRO) in 1969
ISRO identified the role and importance of space technology in nation’s development and bringing space to the service of the common man
India launched its first low orbit satellite Aryabhata in 1975, for which the launch vehicle was provided by the erstwhile Soviet Union
ISRO started employing its indigenous launching vehicle in 1979 by sending Rohini series of satellites into space from its main launch site at Satish Dhawan Space Center, Sriharikota, Andhra Pradesh
The tremendous progress in India’s space programme has made ISRO one of the six largest space agencies in the world
ISRO develops and delivers application specific satellite products and tools for broadcasts, communication, weather forecasts, disaster management tools, Geographic Information System, cartography, navigation, telemedicine, dedicated distance education satellite etc
In order to achieve complete self-reliance in these applications, cost effective and reliable Polar Satellite Launch Vehicle (PSLV) was developed in early 1990s
PSLV has thus become a favoured carrier for satellites of various countries, promoting unprecedented international collaboration
In 2001, the Geosynchronous Satellite Launch Vehicle (GSLV) was developed for launching heavier and more demanding Geosynchronous communication satellites
Various research centers and autonomous institutions for remote sensing, astronomy and astrophysics, atmospheric sciences and space research are functioning under the aegis of the Department of Space, Government of India
Success of lunar (Chandrayaan) and inter planetary (Mangalyaan) missions along with other scientific projects has been landmark achievements of ISRO
Future endeavors of ISRO include human space flight projects, the development of heavy lift launchers, reusable launch vehicles, semi-cryogenic engines, single and two stage to orbit (SSTO and TSTO) vehicles, development and use of composite materials for space application etc
In 1984 Rakesh Sharma became the first Indian to go into outer space aboard in a USSR spaceship
(www.isro.gov.in)
Thus radio waves broadcast from an antenna can be received at points far away where the direct wave fail to reach on account of the curvature of the earth
Waves used in television broadcast or other forms of communication have much higher frequencies and thus cannot be received beyond the line of sight
A Geostationery satellite, appearing fixed above the broadcasting station can however receive these signals and broadcast them back to a wide area on earth
The INSAT group of satellites sent up by India are one such group of Geostationary satellites widely used for telecommunications in India
Another class of satellites are called the Polar satellites
These are low altitude (h ≈ 500 to 800 km) satellites, but they go around the poles of the earth in a north-south direction whereas the earth rotates around its axis in an east-west direction
Since its time period is around 100 minutes it crosses any altitude many times a day
However, since its height h above the earth is about 500-800 km, a camera fixed on it can view only small strips of the earth in one orbit
Adjacent strips are viewed in the next orbit, so that in effect the whole earth can be viewed strip by strip during the entire day
These satellites can view polar and equatorial regions at close distances with good resolution
Information gathered from such satellites is extremely useful for remote sensing, meterology as well as for environmental studies of the earth.
8.12 Weightlessness Weight of an object is the force with which the earth attracts it
We are conscious of our own weight when we stand on a surface, since the surface exerts a force opposite to our weight to keep us at rest
The same principle holds good when we measure the weight of an object by a spring balance hung from a fixed point e.g
the ceiling
The object would fall down unless it is subject to a force opposite to gravity
This is exactly what the spring exerts on the object
This is because the spring is pulled down a little by the gravitational pull of the object and in turn the spring exerts a force on the object vertically upwards
Now, imagine that the top end of the balance is no longer held fixed to the top ceiling of the room
Both ends of the spring as well as the object move with identical acceleration g
The spring is not stretched and does not exert any upward force on the object which is moving down with acceleration g due to gravity
The reading recorded in the spring balance is zero since the spring is not stretched at all
If the object were a human being, he or she will not feel his weight since there is no upward force on him
Thus, when an object is in free fall, it is weightless and this phenomenon is usually called the phenomenon of weightlessness
In a satellite around the earth, every part and parcel of the satellite has an acceleration towards the centre of the earth which is exactly the value of earth’s acceleration due to gravity at that position
Thus in the satellite everything inside it is in a state of free fall
This is just as if we were falling towards the earth from a height
Thus, in a manned satellite, people inside experience no gravity
Gravity for us defines the vertical direction and thus for them there are no horizontal or vertical directions, all directions are the same
Pictures of astronauts floating in a satellite show this fact
Summary 1. Newton’s law of universal gravitation states that the gravitational force of attraction between any two particles of masses m1 and m2 separated by a distance r has the magnitude where G is the universal gravitational constant, which has the value 6.672 ×10–11 N m2 kg–2
If we have to find the resultant gravitational force acting on the particle m due to a number of masses M1, M2, ….Mn etc
we use the principle of superposition
Let F1, F2, ….Fn be the individual forces due to M1, M2, ….Mn, each given by the law of gravitation
From the principle of superposition each force acts independently and uninfluenced by the other bodies
The resultant force FR is then found by vector addition FR = F1 + F2 + ……+ Fn = where the symbol ‘Σ’ stands for summation
Kepler’s laws of planetary motion state that (a) All planets move in elliptical orbits with the Sun at one of the focal points (b) The radius vector drawn from the Sun to a planet sweeps out equal areas in equal time intervals
This follows from the fact that the force of gravitation on the planet is central and hence angular momentum is conserved
(c) The square of the orbital period of a planet is proportional to the cube of the semi-major axis of the elliptical orbit of the planet The period T and radius R of the circular orbit of a planet about the Sun are related by where Ms is the mass of the Sun
Most planets have nearly circular orbits about the Sun
For elliptical orbits, the above equation is valid if R is replaced by the semi-major axis, a
4. The acceleration due to gravity
(a) at a height h above the earth’s surface for h << RE (b) at depth d below the earth’s surface is 5. The gravitational force is a conservative force, and therefore a potential energy function can be defined
The gravitational potential energy associated with two particles separated by a distance r is given by where V is taken to be zero at r → ∞
The total potential energy for a system of particles is the sum of energies for all pairs of particles, with each pair represented by a term of the form given by above equation
This prescription follows from the principle of superposition
6. If an isolated system consists of a particle of mass m moving with a speed v in the vicinity of a massive body of mass M, the total mechanical energy of the particle is given by That is, the total mechanical energy is the sum of the kinetic and potential energies
The total energy is a constant of motion
If m moves in a circular orbit of radius a about M, where M >> m, the total energy of the system is with the choice of the arbitrary constant in the potential energy given in the point 5., above
The total energy is negative for any bound system, that is, one in which the orbit is closed, such as an elliptical orbit
The kinetic and potential energies are The escape speed from the surface of the earth is = and has a value of 11.2 km s–1
If a particle is outside a uniform spherical shell or solid sphere with a spherically symmetric internal mass distribution, the sphere attracts the particle as though the mass of the sphere or shell were concentrated at the centre of the sphere
10. If a particle is inside a uniform spherical shell, the gravitational force on the particle is zero
If a particle is inside a homogeneous solid sphere, the force on the particle acts toward the centre of the sphere
This force is exerted by the spherical mass interior to the particle
. A geostationary (geosynchronous communication) satellite moves in a circular orbit in the equatorial plane at a approximate distance of 4.22 × 104 km from the earth’s centre
Points to Ponder 1. In considering motion of an object under the gravitational influence of another object the following quantities are conserved: (a) Angular momentum (b) Total mechanical energy Linear momentum is not conserved 2. Angular momentum conservation leads to Kepler’s second law
However, it is not special to the inverse square law of gravitation
It holds for any central force
3. In Kepler’s third law (see Eq
(8.1) and T2 = KS R3
The constant KS is the same for all planets in circular orbits
This applies to satellites orbiting the Earth [(Eq
(8.38)]
4. An astronaut experiences weightlessness in a space satellite
This is not because the gravitational force is small at that location in space
It is because both the astronaut and the satellite are in “free fall” towards the Earth
5. The gravitational potential energy associated with two particles separated by a distance r is given by The constant can be given any value
The simplest choice is to take it to be zero
With this choice This choice implies that V → 0 as r → ∞
Choosing location of zero of the gravitational energy is the same as choosing the arbitrary constant in the potential energy
Note that the gravitational force is not altered by the choice of this constant
6. The total mechanical energy of an object is the sum of its kinetic energy (which is always positive) and the potential energy
Relative to infinity (i.e
if we presume that the potential energy of the object at infinity is zero), the gravitational potential energy of an object is negative
The total energy of a satellite is negative
7. The commonly encountered expression m g h for the potential energy is actually an approximation to the difference in the gravitational potential energy discussed in the point 6, above
8. Although the gravitational force between two particles is central, the force between two finite rigid bodies is not necessarily along the line joining their centre of mass
For a spherically symmetric body however the force on a particle external to the body is as if the mass is concentrated at the centre and this force is therefore central
The gravitational force on a particle inside a spherical shell is zero
However, (unlike a metallic shell which shields electrical forces) the shell does not shield other bodies outside it from exerting gravitational forces on a particle inside
Gravitational shielding is not possible.
Exercises 8.1 Answer the following : (a) You can shield a charge from electrical forces by putting it inside a hollow conductor
Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means ? (b) An astronaut inside a small space ship orbiting around the earth cannot detect gravity
If the space station orbiting around the earth has a large size, can he hope to detect gravity ? (c) If you compare the gravitational force on the earth due to the sun to that due to the moon, you would find that the Sun’s pull is greater than the moon’s pull
(you can check this yourself using the data available in the succeeding exercises)
However, the tidal effect of the moon’s pull is greater than the tidal effect of sun
Why ? 8.2 Choose the correct alternative : (a) Acceleration due to gravity increases/decreases with increasing altitude
(b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density)
(c) Acceleration due to gravity is independent of mass of the earth/mass of the body
(d) The formula –G Mm(1/r2 – 1/r1) is more/less accurate than the formulamg(r2 – r1) for the difference of potential energy between two points r2 and r1 distance away from the centre of the earth
8.3 Suppose there existed a planet that went around the sun twice as fast as the earth
What would be its orbital size as compared to that of the earth ? 8.4 Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius of the orbit is 4.22 × 108 m
Show that the mass of Jupiter is about one-thousandth that of the sun
8.5 Let us assume that our galaxy consists of 2.5 × 1011 stars each of one solar mass
How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 105 ly
8.6 Choose the correct alternative: (a) If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/potential energy
(b) The energy required to launch an orbiting satellite out of earth’s gravitational influence is more/less than the energy required to project a stationary object at the same height (as the satellite) out of earth’s influence
8.7 Does the escape speed of a body from the earth depend on (a) the mass of the body, (b) the location from where it is projected, (c) the direction of projection, (d) the height of the location from where the body is launched? 8 A comet orbits the sun in a highly elliptical orbit
Does the comet have a constant (a) linear speed, (b) angular speed, (c) angular momentum, (d) kinetic energy, (e) potential energy, (f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun
8.9 Which of the following symptoms is likely to afflict an astronaut in space (a) swollen feet, (b) swollen face, (c) headache, (d) orientational problem
8.10 In the following two exercises, choose the correct answer from among the given ones: The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12) a, b,c, (iv) 0.
APPENDIX 8.1 : LIST OF INDIAN SATELLITES
India has so far also launched 239 foreign satellites of 28 countries from Satish Dhawan Space Center, Sriharikota, Andhra Pradesh: May 26, 1999 (02); Oct
22, 2001 (02); Jan
10, 2007 (02); Apr
23, 2007 (01); Jan
21, 2008 (01); Apr
28,2008 (08); Sep
23,2009 (06); July 12, 2010 (03); Jan
12,2011 (01); Apr
20, 2011 (01) Sep
09, 2012 (02); Feb
25, 2013 (06); June 30, 2014 (05); July 10, 2015 (05); Sep
28, 2015 (06); Dec
16, 2015 (06); June 22, 2016 (17); Sep
26, 2016 (05); Feb
15, 2017 (101) and thus setting a world record; June 23, 2017 (29)
Jan 12, 2018 (28); Sep
16, 2018 (02)
Details can be seen at www.isro.gov.in
a Launched from Kapustin Yar Missile and Space Complex, Soviet Union (now Russia) b Launched from Satish Dhawan Space Centre, Sriharikota, Andhra Pradesh c Launched from Centre Spatial Guyanais, Kourou, French Guiana d Launched from Air Force Eastern Test Range, Florida e Launched from Baikonur Cosmodrome, Kazakhstan
Table of Contents
Chapter Eight
Gravitation
8.1 Introduction
8.2 Kepler’s laws
8.4 The Gravitational Constant
8.5 Acceleration due to gravity of the earth
8.6 Acceleration due to gravity below and above the surface of earth
8.7 Gravitational potential energy
8.8 Escape Speed
8.9 Earth Satellites
8.10 Energy of an orbiting Satellite
8.11 Geostationary and Polar Satellites
8.12 Weightlessness
Summary
Exercises
Landmarks
Cover
Chapter EightGRAVITATION
From the last chapter, we recall that all living organisms are made of cells
In unicellular organisms, a single cell performs all basic functions
For example, in Amoeba, a single cell carries out movement, intake of food, gaseous exchange and excretion
But in multi-cellular organisms there are millions of cells
Most of these cells are specialised to carry out specific functions
Each specialised function is taken up by a different group of cells
Since these cells carry out only a particular function, they do it very efficiently
In human beings, muscle cells contract and relax to cause movement, nerve cells carry messages, blood flows to transport oxygen, food, hormones and waste material and so on
In plants, vascular tissues conduct food and water from one part of the plant to other parts
So, multi-cellular organisms show division of labour
Cells specialising in one function are often grouped together in the body
This means that a particular function is carried out by a cluster of cells at a definite place in the body
This cluster of cells, called a tissue, is arranged and designed so as to give the highest possible efficiency of function
Blood, phloem and muscle are all examples of tissues
Chapter 6
Tissues A group of cells that are similar in structure and/or work together to achieve a particular function forms a tissue
6.1 Are Plants and Animals Made of Same Types of Tissues? Let us compare their structure and functions
Do plants and animals have the same structure? Do they both perform similar functions? There are noticeable differences between the two
Plants are stationary or fixed – they don’t move
Since they have to be upright, they have a large quantity of supportive tissue
The supportive tissue generally has dead cells
Animals on the other hand move around in search of food, mates and shelter
They consume more energy as compared to plants
Most of the tissues they contain are living
Another difference between animals and plants is in the pattern of growth
The growth in plants is limited to certain regions, while this is not so in animals
There are some tissues in plants that divide throughout their life
These tissues are localised in certain regions
Based on the dividing capacity of the tissues, various plant tissues can be classified as growing or meristematic tissue and permanent tissue
Cell growth in animals is more uniform
So, there is no such demarcation of dividing and non-dividing regions in animals
The structural organisation of organs and organ systems is far more specialised and localised in complex animals than even in very complex plants
This fundamental difference reflects the different modes of life pursued by these two major groups of organisms, particularly in their different feeding methods
Also, they are differently adapted for a sedentary existence on one hand (plants) and active locomotion on the other (animals), contributing to this difference in organ system design
It is with reference to these complex animal and plant bodies that we will now talk about the concept of tissues in some detail.
Questions 1. What is a tissue? 2. What is the utility of tissues in multi-cellular organisms?
6.2 Plant Tissues
6.2.1 Meristematic tissue
Jar 1 Jar 2 : Growth of roots in onion bulbs
Activity 6.1 • Take two glass jars and fill them with water
• Now, take two onion bulbs and place one on each jar, as shown in
• Observe the growth of roots in both the bulbs for a few days
• Measure the length of roots on day 1, 2 and 3
• On day 4, cut the root tips of the onion bulb in jar 2 by about 1 cm
After this, observe the growth of roots in both the jars and measure their lengths each day for five more days and record the observations in tables, like the table below: Length Day 1 Day 2 Day 3 Day 4 Day 5 Jar 1 Jar 2
• From the above observations, answer the following questions: 1. Which of the two onions has longer roots? Why? 2. Do the roots continue growing even after we have removed their tips? 3. Why would the tips stop growing in jar 2 after we cut them?
The growth of plants occurs only in certain specific regions
This is because the dividing tissue, also known as meristematic tissue, is located only at these points
Depending on the region where they are present, meristematic tissues are classified as apical, lateral and intercalary
New cells produced by meristem are initially like those of meristem itself, but as they grow and mature, their characteristics slowly change and they become differentiated as components of other tissues.
Apical meristem is present at the growing tips of stems and roots and increases the length of the stem and the root
The girth of the stem or root increases due to lateral meristem (cambium)
Intercalary meristem seen in some plants is located near the node
Cells of meristematic tissue are very active, they have dense cytoplasm, thin cellulose walls and prominent nuclei
They lack vacuoles
Can we think why they would lack vacuoles? (You might want to refer to the functions of vacuoles in the chapter on cells.)
6.2.2 Permanent tissue What happens to the cells formed by meristematic tissue? They take up a specific role and lose the ability to divide
As a result, they form a permanent tissue
This process of taking up a permanent shape, size, and a function is called differentiation
Differentiation leads to the development of various types of permanent tissues.
Activity 6.2 • Take a plant stem and with the help of your teacher cut into very thin slices or sections
• Now, stain the slices with safranin
Place one neatly cut section on a slide, and put a drop of glycerine
• Cover with a cover-slip and observe under a microscope
Observe the various types of cells and their arrangement
Compare it with
• Now, answer the following on the basis of your observation: 1. Are all cells similar in structure? 2. How many types of cells can be seen? Can we think of reasons why there would be so many types of cells? • We can also try to cut sections of plant roots
We can even try cutting sections of root and stem of different plants.
6.2.2 Simple permanent tissue A few layers of cells beneath the epidermis are generally simple permanent tissue
Parenchyma is the most common simple permanent tissue
It consists of relatively unspecialised cells with thin cell walls
They are living cells
They are usually loosely arranged, thus large spaces between cells (intercellular spaces) are found in this tissue
This tissue generally stores food
In some situations, it contains chlorophyll and performs photosynthesis, and then it is called chlorenchyma
In aquatic plants, large air cavities are present in parenchyma to help them float
Such a parenchyma type is called aerenchyma
The flexibility in plants is due to another permanent tissue, collenchyma
It allows bending of various parts of a plant like tendrils and stems of climbers without breaking
It also provides mechanical support
We can find this tissue in leaf stalks below the epidermis
The cells of this tissue are living, elongated and irregularly thickened at the corners
There is very little intercellular space .
Activity 6.3 • Take a freshly plucked leaf of Rhoeo
• Stretch and break it by applying pressure
• While breaking it, keep it stretched gently so that some peel or skin projects out from the cut
• Remove this peel and put it in a petri dish filled with water
• Add a few drops of safranin
• Wait for a couple of minutes and then transfer it onto a slide
Gently place a cover slip over it
• Observe under microscope.
What you observe is the outermost layer of cells, called epidermis
The epidermis is usually made of a single layer of cells
In some plants living in very dry habitats, the epidermis may be thicker since protection against water loss is critical
The entire surface of a plant has an outer covering epidermis
It protects all the parts of the plant
Epidermal cells on the aerial parts of the plant often secrete a waxy, water-resistant layer on their outer surface
This aids in protection against loss of water, mechanical injury and invasion by parasitic fungi
Since it has a protective role to play, cells of epidermal tissue form a continuous layer without intercellular spaces
Most epidermal cells are relatively flat
Often their outer and side walls are thicker than the inner wall.
(a) (b) : Guard cells and epidermal cells: (a) lateral view, (b) surface view
We can observe small pores here and there in the epidermis of the leaf
These pores are called stomata
Stomata are enclosed by two kidney-shaped cells called guard cells
They are necessary for exchanging gases with the atmosphere
Transpiration (loss of water in the form ofwater vapour) also takes place through stomata
Recall which gas is required for photosynthesis
Find out the role of transpiration in plants
Epidermal cells of the roots, whose function is water absorption, commonly bear long hair-like parts that greatly increase the total absorptive surface area
In some plants like desert plants, epidermis has a thick waxy coating of cutin (chemical substance with waterproof quality) on its outer surface
Can we think of a reason for this? Is the outer layer of a branch of a tree different from the outer layer of a young stem? As plants grow older, the outer protective tissue undergoes certain changes
A strip of secondary meristem located in the cortex forms layers of cells which constitute the cork
Cells of cork are dead and compactly arranged without intercellular spaces
They also have a substance called suberin in their walls that makes them impervious to gases and water.
6.2.2 Complex permanent tissue The different types of tissues we have discussed until now are all made of one type of cells, which look like each other
Such tissues are called simple permanent tissue
Yet another type of permanent tissue is complex tissue
Complex tissues are made of more than one type of cells
All these cells coordinate to perform a common function
Xylem and phloem are examples of such complex tissues
They are both conducting tissues and constitute a vascular bundle
Vascular tissue is a distinctive feature of the complex plants, one that has made possible their survival in the terrestrial environment
In showing a section of stem, can you see different types of cells in the vascular bundle? Xylem consists of tracheids, vessels, xylem parenchyma and xylem fibres
Tracheids and vessels have thick walls, and many are dead cells when mature
Tracheids and vessels are tubular structures
This allows them to transport water and minerals vertically
The parenchyma stores food
Xylem fibres are mainly supportive in function
Phloem is made up of five types of cells: sieve cells, sieve tubes, companion cells, phloem fibres and the phloem parenchyma
Sieve tubes are tubular cells with perforated walls
Phloem transports food from leaves to other parts of the plant
Except phloem fibres, other phloem cells are living cells.
Questions
1. Name types of simple tissues
2. Where is apical meristem found? 3. Which tissue makes up the husk of coconut? 4. What are the constituents of phloem?
6.3 Animal Tissues
When we breathe we can actually feel the movement of our chest
How do these body parts move? For this we have specialised cells called muscle cells
The contraction and relaxation of these cells result in movement.
During breathing we inhale oxygen
Where does this oxygen go? It is absorbed in the lungs and then is transported to all the body cells through blood
Why would cells need oxygen? The functions of mitochondria we studied earlier provide a clue to this question
Blood flows and carries various substances from one part of the body to the other
For example, it carries oxygen and food to all cells
It also collects wastes from all parts of the body and carries them to the liver and kidney for disposal
Blood and muscles are both examples of tissues found in our body
On the basis of the functions they perform we can think of different types of animal tissues, such as epithelial tissue, connective tissue, muscular tissue and nervous tissue
Blood is a type of connective tissue, and muscle forms muscular tissue.
6.3.1 Epithelial tissue The covering or protective tissues in the animal body are epithelial tissues
Epithelium covers most organs and cavities within the body
It also forms a barrier to keep different body systems separate
The skin, the lining of the mouth, the lining of blood vessels, lung alveoli and kidney tubules are all made of epithelial tissue
Epithelial tissue cells are tightly packed and form a continuous sheet
They have only a small amount of cementing material between them and almost no intercellular spaces
Obviously, anything entering or leaving the body must cross at least one layer of epithelium
As a result, the permeability of the cells of various epithelia play an important role in regulating the exchange of materials between the body and the external environment and also between different parts of the body
Regardless of the type, all epithelium is usually separated from the underlying tissue by an extracellular fibrous basement membrane.
Different epithelia show differing structures that correlate with their unique functions
For example, in cells lining blood vessels or lung alveoli, where transportation of substances occurs through a selectively permeable surface, there is a simple flat kind of epithelium
This is called the simple squamous epithelium (squama means scale of skin)
Simple squamous epithelial cells are extremely thin and flat and form a delicate lining
The oesophagus and the lining of the mouth are also covered with squamous epithelium
The skin, which protects the body, is also made of squamous epithelium
Skin epithelial cells are arranged in many layers to prevent wear and tear
Since they are arranged in a pattern of layers, the epithelium is called stratified squamous epithelium
Where absorption and secretion occur, as in the inner lining of the intestine, tall epithelial cells are present
This columnar (meaning ‘pillar-like’) epithelium facilitates movement across the epithelial barrier
In the respiratory tract, the columnar epithelial tissue also has cilia, which are hair-like projections on the outer surfaces of epithelial cells
These cilia can move, and their movement pushes the mucus forward to clear it
This type of epithelium is thus ciliated columnar epithelium
Cuboidal epithelium (with cube-shaped cells) forms the lining of kidney tubules and ducts of salivary glands, where it provides mechanical support
Epithelial cells often acquire additional specialisation as gland cells, which can secrete substances at the epithelial surface
Sometimes a portion of the epithelial tissue folds inward, and a multicellular gland is formed
This is glandular epithelium.
6.3.2 Connective tissue Blood is a type of connective tissue
Why would it be called ‘connective’ tissue? A clue is provided in the introduction of this chapter! Now, let us look at this type of tissue in some more detail
The cells of connective tissue are loosely spaced and embedded in an intercellular matrix
The matrix may be jelly like, fluid, dense or rigid
The nature of matrix differs in concordance with the function of the particular connective tissue.
Activity 6.4 Take a drop of blood on a slide and observe different cells present in it under a microscope.
Blood has a fluid (liquid) matrix called plasma, in which red blood corpuscles (RBCs), white blood corpuscles (WBCs) and platelets are suspended
The plasma contains proteins, salts and hormones
Blood flows and transports gases, digested food, hormones and waste materials to different parts of the body
Bone is another example of a connective tissue
It forms the framework that supports the body
It also anchors the muscles and supports the main organs of the body
It is a strong and nonflexible tissue (what would be the advantage of these properties for bone functions?)
Bone cells are embedded in a hard matrix that is composed of calcium and phosphorus compounds
Two bones can be connected to each other by another type of connective tissue called the ligament
This tissue is very elastic
It has considerable strength
Ligaments contain very little matrix and connect bones with bones
Tendons connect muscles to bones and are another type of connective tissue
Tendons are fibrous tissue with great strength but limited flexibility
Another type of connective tissue, cartilage, has widely spaced cells
The solid matrix is composed of proteins and sugars
Cartilage smoothens bone surfaces at joints and is also present in the nose, ear, trachea and larynx
We can fold the cartilage of the ears, but we cannot bend the bones in our arms
Think of how the two tissues are different! Areolar connective tissue is found between the skin and muscles, around blood vessels and nerves and in the bone marrow
It fills the space inside the organs, supports internal organs and helps in repair of tissues
Where are fats stored in our body? Fat-storing adipose tissue is found below the skin and between internal organs
The cells of this tissue are filled with fat globules
Storage of fats also lets it act as an insulator.
Where are fats stored in our body? Fatstoring adipose tissue is found below the skin and between internal organs
The cells of this tissue are filled with fat globules
Storage of fats also lets it act as an insulator.
6.3.3 Muscular tissue Muscular tissue consists of elongated cells, also called muscle fibres
This tissue is responsible for movement in our body
Muscles contain special proteins called contractile proteins, which contract and relax to cause movement
We can move some muscles by conscious will
Muscles present in our limbs move when we want them to, and stop when we so decide
Such muscles are called voluntary muscles
These muscles are also called skeletal muscles as they are mostly attached to bones and help in body movement
Under the microscope, these muscles show alternate light and dark bands or striations when stained appropriately
As a result, they are also called striated muscles
The cells of this tissue are long, cylindrical, unbranched and multinucleate (having many nuclei)
The movement of food in the alimentary canal or the contraction and relaxation of blood vessels are involuntary movements
We cannot really start them or stop them simply by wanting to do so! Smooth muscles or involuntary muscles control such movements
They are also found in the iris of the eye, in ureters and in the bronchi of the lungs
The cells are long with pointed ends (spindle-shaped) and uninucleate (having a single nucleus)
They are also called unstriated muscles – why would they be called that? Muscular tissue consists of elongated cells, also called muscle fibres
This tissue is responsible for movement in our body. Muscles contain special proteins called contractile proteins, which contract and relax to cause movement
We can move some muscles by conscious will
Muscles present in our limbs move when we want them to, and stop when we so decide
Such muscles are called voluntary muscles
These muscles are also called skeletal muscles as they are mostly attached to bones and help in body movement
Under the microscope, these muscles show alternate light and dark bands or striations when stained appropriately
As a result, they are also called striated muscles
The cells of this tissue are long, cylindrical, unbranched and multinucleate (having many nuclei). The movement of food in the alimentary canal or the contraction and relaxation of blood vessels are involuntary movements
We cannot really start them or stop them simply by wanting to do so! Smooth muscles or involuntary muscles control such movements
They are also found in the iris of the eye, in ureters and in the bronchi of the lungs
The cells are long with pointed ends (spindle-shaped) and uninucleate (having a single nucleus)
They are also called unstriated muscles – why would they be called that? The muscles of the heart show rhythmic contraction and relaxation throughout life
These involuntary muscles are called cardiac muscles
Heart muscle cells are cylindrical, branched and uninucleate
Activity 6.5 Compare the structures of different types of muscular tissues
Note down their shape, number of nuclei and position of nuclei within the cell in the Table 6.1.
6.3.4 Nervous tissue All cells possess the ability to respond to stimuli
However, cells of the nervous tissue are highly specialised for being stimulated and then transmitting the stimulus very rapidly from one place to another within the body
The brain, spinal cord and nerves are all composed of the nervous tissue
The cells of this tissue are called nerve cells or neurons
A neuron consists of a cell body with a nucleus and cytoplasm, from which long thin hair-like parts arise
Usually each neuron has a single long part (process), called the axon, and many short, branched parts (processes) called dendrites
An individual nerve cell may be up to a metre long
Many nerve fibres bound together by connective tissue make up a nerve.
The signal that passes along the nerve fibre is called a nerve impulse
Nerve impulses allow us to move our muscles when we want to
The functional combination of nerve and muscle tissue is fundamental to most animals
This combination enables animals to move rapidly in response to stimuli.
Questions 1. Name the tissue responsible for movement in our body
2. What does a neuron look like? 3. Give three features of cardiac muscles
4. What are the functions of areolar tissue?
What you have learnt • Tissue is a group of cells similar in structure and function
• Plant tissues are of two main types – meristematic and permanent
• Meristematic tissue is the dividing tissue present in the growing regions of the plant
• Permanent tissues are derived from meristematic tissue once they lose the ability to divide
They are classified as simple and complex tissues
• Parenchyma, collenchyma and sclerenchyma are three types of simple tissues
Xylem and phloem are types of complex tissues
• Animal tissues can be epithelial, connective, muscular and nervous tissue
• Depending on shape and function, epithelial tissue is classified as squamous, cuboidal, columnar, ciliated and glandular
• The different types of connective tissues in our body include areolar tissue, adipose tissue, bone, tendon, ligament, cartilage and blood
• Striated, unstriated and cardiac are three types of muscle tissues
• Nervous tissue is made of neurons that receive and conduct impulses.
Exercises 1. Define the term “tissue”
2. How many types of elements together make up the xylem tissue? Name them
3. How are simple tissues different from complex tissues in plants? 4. Differentiate between parenchyma, collenchyma and sclerenchyma on the basis of their cell wall
5. What are the functions of the stomata? 6. Diagrammatically show the difference between the three types of muscle fibres
7. What is the specific function of the cardiac muscle? 8. Differentiate between striated, unstriated and cardiac muscles on the basis of their structure and site/location in the body
9. Draw a labelled diagram of a neuron
10. Name the following
(a) Tissue that forms the inner lining of our mouth
(b) Tissue that connects muscle to bone in humans
(c) Tissue that transports food in plants
(d) Tissue that stores fat in our body
(e) Connective tissue with a fluid matrix
(f) Tissue present in the brain
11. Identify the type of tissue in the following: skin, bark of tree, bone, lining of kidney tubule, vascular bundle
12. Name the regions in which parenchyma tissue is present
13. What is the role of epidermis in plants?
14. How does the cork act as a protective tissue? 15. Complete the following chart:
Table of Contents
Chapter 6
Tissues
Questions
6.2 Plant Tissues
6.2.1 Meristematic tissue
6.2.2 Permanent tissue
6.2.2 Simple permanent tissue
6.2.2 Complex permanent tissue
Questions
6.3 Animal Tissues
6.3.1 Epithelial tissue
6.3.2 Connective tissue
6.3.3 Muscular tissue
6.3.4 Nervous tissue
Questions
What you have learnt
Exercises
Landmarks
Cover
Chapter 6Tissues