• Paper-I Unit: I Periodic Table and Periodic Properties

1. PERIODIC TABLE :

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• The long form of periodic table contains periods and groups.
• Periods : The horizontal rows are called periods.

There are 7 periods or horizontal rows in the periodic table. i) The first period is made up of with only 2 elements namely, hydrogen and helium.

ii) The second period contains 8 elements, starts with lithium and end with noble gas neon.

iii) The third period also contain 8 elements begin with sodium and end with argon.

iv) The fourth period is having 18 elements, begins with alkali metal Potassium and end with krypton.

v) The fifth period like fourth period also contain 18 elements. It begins with rubidium and end with xenon.

vi) The sixth period is a long period having 32 elements. This period includes 8 normal elements, 10 transition elements and 14 rare earth elements.

vii) Seventh period also contain 32 elements.

• Groups: The vertical columns are known as groups.
• There are 18 groups are in the long form of the periodic table. According to IUPAC, the groups are numbered in Arabic numerals such as 1 to 18.

• Cause of periodicity :

Definition: The recurrence of similar properties of elements after certain intervals when they are arranged in the order of increasing atomic number is called periodicity.

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• Cause : The chemical properties of an element are related to the number as well as the arrangement of electrons around the nucleus. In fact the valence shell electrons determines the properties of atoms of various elements. Hence elements with similar E.C. of atoms should have same chemical properties and elements with different E.C. of atom should have different chemical properties.
• Thus the cause of periodicity is E.C. of the atoms of elements. To understand the cause of periodicity, let us consider the E.C. of alkali metals.

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• Division of elements in to s, p, d and f blocks :
• The elements arranged in the long form of periodic table, divided into four blocks known as – s, p, d and f blocks
• This classification depends up on the type of orbital in which the last electron enters.

1) s – Block Elements :

Definition : The elements whose atoms receive the last electron in the s- orbital of their outermost sub- orbital are called s block elements. Or The elements in which the last electron enters in the s- orbital of their outer most energy level are called s- block elements.

• This block consists with the elements of groups 1 and 2
• The elements of group 1 the general ground state E.C.ns¹ These elements are called alkali metals
• The elements of group 2 have the general E.C.ns² These are called alkaline earth metals

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• P- block Elements :

Definition : The elements in which the last electron enters in the p- sub shell of their outermost energy level are called p- block elements.

• This block consists with the groups 13, 14, 15, 16 , 17 and 18
• The general E.C. for the atoms of the elements of this group is - ns² np^1-6
• s and p block elements together are known as normal or representative elements

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• d- block Elements :
• Definition : The elements in which the last electron enters in (n-1)d i.e. last but one or anti penultimate sub shell or energy level are known as d-block elements.
• d- block elements are also called as Transition elements
• The elements of group IIIB, IVB, VB, VIIB, VIIB, VIIIB, IB and IIB belongs to this group
• The valence shell or general E.C. of d-block elements is- ns²(n-1)d^1-10
• d- block elements are classified into four transition series such as-

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• 1) First transition series (3d- series) : This series has 10 elements beginning with Sc (Z=21) and end at Zinc(Z=30).
• In the elements of this series 3d-orbitals are being progressively filled up with electrons
• The elements of this series lie in the 4^th period

2) Second transition series (4d-series) :

• This series also contains 10 elements beginning with Y(Z=39) and end at Cd(Z=48)
• In the elements of this series 4d-orbitals are being progressively filled up with the electrons
• The elements of this series lie in the 5^th period

3) Third transition series (5d Series) :

• This series also has 10 elements from La(Z=57) up to Hg(Z=80)
• In these elements 5d-orbitals are being progressively filled
• The elements of this series lie in the 6^th period

4) Fourth transition series (6d- series) :

• This series starts with Ac (Z=89) and end with Ha (Z=105)
• In these elements 6d-orbitals are being progressively filled
• They lie in the 7^th period of periodic table

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4) F-block elements :

Definition : The elements in which the last electron enters in (n-2)d i.e. last but two or anti penultimate sub shell are called f- block elements.

• They are also called as inner transition elements
• They are placed at the bottom of periodic table
• They are located in IIIB group of periodic table
• The general E.C. of f-block elements is-
• F-block elements consists with two inner transition series as- ns²(n-1)d¹⁰(n-2)f^1-14

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i) Lanthanide series or (4f-series) :

• This series has 14 elements beginning with Ce(Z=58) and end with Lu(Z=71)
• In these elements the last electron enters in 4f-orbital
• They are also called as- rare earths or lanthanones or lanthanides
• ii) Actinide series or (5f-series) :
• 4f-series also has 14 elements with Th(Z=90) and end at Lw(Z=103)
• Last electron enters in 5f-orbital
• They are also known as actinones or actinides

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• General characteristics of s, p, d and f block elements: 1 ) General characteristics of s-block elements :
• s- block elements are metallic in nature and they are soft metals

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• They are highly electropositive and have low I.E. therefore they are good reducing agents

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• They are highly reactive hence do not occur free state in nature

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• They are good conductors of heat and electricity

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• The oxidation state of first group elements is +1 and that of second group is +2

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• They form ionic compounds except Li and Be

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• They give characteristic colour in the flame

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• They form oxides, hydroxides, hydrides and halides of their respective metals

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• 2) General characteristics of p-block elements :
• P-block consists with some metals, non-metals and metalloids
• Metallic characters increases from top to bottom and decreases along the periods
• Most of them are highly electronegative in nature
• They have high I.E. and form covalent compounds
• They show variable oxidation states
• They are good oxidizing and reducing agents
• Most of them form acidic oxides
• Some of the p-block elements and their salts have characteristic flame colouration
• Electron affinity value increase on moving from left to right along the period
• Most of them form hydrides and halides
• The elements of group 16 are called chalcogens, Elements of group 17 are halogens and elements of group 18 are known as noble gases

3) General characteristics of d-block elements :

• They are hard, malleable and ductile metals with high tensile strength

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• As they are metals have high melting and boiling points

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• They show variable oxidation states

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• They exhibit all three types of structures i.e. fcc, hcp and bcc.

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• They form covalent as well as ionic compounds

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• Their ionization energy is larger than s-block elements and lower than d- block elements

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• Most of them are colored metal ions

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• They form colored complexes

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• They are good conductors of heat and electricity

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• Majority of transition metals exhibit catalytic properties

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• Most of the transition metal are paramagnetic in nature

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• General Characteristics of f-block elements :
• They are heavy metals with high melting and boiling points

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• They form colored ions

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• They show variable oxidation states and +3 is common oxidation state

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• They have the tendency to form complexes

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• Actinoids are radioactive in nature

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• They exhibit paramagnetic behaviour

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B) Periodic properties:

1. Atomic and ionic size: Definition and explanation of-

i) Atomic radius/ Atomic size/ Atomic radii :

Definition: It is defined as the distance from centre of nucleus up to the last orbital in which electron is present. OR

“ The distance from the centre of nucleus to the point where the electron density is effectively zero.”

Explanation : i) An atom is composed of a compact nucleus surrounded by electron cloud

ii) Which does not have a sharply defined boundry because of its diffused nature

iii) The diffused nature of the electron cloud make it difficult for us to give an exact definition of atomic radius

iv) It is not possible to determine the exact radius of atom because

• it is not possible to isolate an atom in free state
• According to wave mechanics, there is no certainty with regard to the exact position occupied by electrons at any time.
• Theoratically an electron, at times, may be very close to the nucleus, while at other time it may be far away from the nucleus.
• v) The size of atom changes from bonded state to another
• vi) The distribution of electrons in an atom is affected by the presence of other atoms in its neighbourhood.

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b) Ionic radius :

Definition : “ It is the effective distance from the centre of nucleus of an ion upto which it has its influence on its electron cloud.”

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Explanation : i) A cation is always much smaller than the corresponding atom

ii) If further, more number if electrons are removed, smaller will be the size of resulting cation. For. Ex. rFe > rFe⁺² > rFe⁺³

^{1.26 0.76 0.64}

This is due to –

iii) A cation formed by the loss of electron may result in the complete disappearance of the shell. Thus the cation is much smaller than the atom.

For. Ex.

Na Na⁺

^{(2 , 8 , 1 )} ( 2, 8 )

iv) As a result the effective nuclear charge is increased and electrons are pulled towards nucleus.

hence, the cation becomes smaller.

v) On the other hand an anion is always larger than the corresponding atom.

For. Ex. Atomic radius of I atom = 1.23

Ionic radius of I^{- ion} = 2.16

vi) The ionic radius is measured with the help of X-ray diffraction method. It is measured in A⁰ .

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C) Covalent radius :

Definition : It is defined as one half of the internuclear distances (i.e. bond distance or bond length) between the centers of two nuclei of two similar atoms bonded together by a single covalent bond.

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Explanation : i) According to definition it is assumed that atoms are incompressible spheres touching to each other in normal covalent

bonds formed.

ii) However, atoms are neither fully incompressible nor do they touch each other in a covalent molecule.

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iii) Therefore, the covalent radii calculated on the basis

of above definition cannot be regarded as exact.

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iv) Covalent radius can be measured by X- ray diffraction or spectroscopic studies.

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v) It is measured in the unit A⁰ .

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• Thus, the covalent radius can be calculated by using the formula

r_{A = Bond length /2}

_{For.Ex. 1) If the bond length of hydrogen molecule is 0.74 A then what will be the covalent radius of hydrogen atom.}

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r_{H =} Bond length/2 = o.74/2 = 0.37

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_{2) Covalent radius can be used for the calculation bond length of hetero atomic molecule by using}

Bond length of A.B = r_A + r_B = d_A2 + d_{B2/ 2}

• Where dA2 is bond length of A2 molecule and dB2 is bond length of B2 molecule.

Ex. 2) Covalent radius of C is 0.77 and C-H bond length in CH4 is 1.14. What is the covalent radius of hydrogen.

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• Solution : Bond length of C-H = d_{c - H} = r_H + r_c

_{1.14 =} r_{H +} 0.77

r_{H = 1.14 - 0.77}

_{= 0.37}A⁰

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3) However, if atoms forming the covalent bond are hetero atoms i.e. one is more electronegative than other then the covalent radius is determined by the following equation.

A – B = r_{A +} r_{B -} 0.09 ( X_A - X_B)

where, X_A and X_{B are electronegativities of the atoms A and B.}

_{For Ex.}

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D) Van der waal’s radius :

Definition : It is defined as- “One half of the distance between the nuclei of two identical atoms belonging to two neighbouring molecules of an element in the solid state”.

Explanation:  

1. When two non-bonded isolated atoms of two

adjacent molecules of an element in solid state

approach each other without overlapping their

electron clouds to form a bond between them.

ii ) They cannot come closer than a minimum

distance without forming a bond.

iii) This minimum distance is called van der wall’s

distance and half of this distance is called van

der wall’s radius.

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iv) The name van der waal’s radius is used because the forces existing between the molecules are the van der wall’s forces of attractoin.

v) These forces are maximum in solid states and absent in gaseous condition while in liquid state is very small.

vi) Therefore, van der wall’s radius is determined only in solid state

vi) The van der wall’s radii is also known as non-bonded radii

vii) The van der wall’s radius is determined by X- ray diffraction studies

viii) van der wall’s radius is always greater than the covalent radius

xi) The noble gases do not form covalent bonds. Thus for noble in solid state have van der wall’s radii

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• Variation of atomic size :

a) Variation along the Periods: Atomic size/radius decreases on moving from left to right in a period.

b) Variation down the groups: Atomic size/radius increases from top to bottom within a group of periodic table.

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b) Ionization energy/ Ionization potential :

Definition: Ionization energy of an element is defined as- “ The amount of energy required to remove the most loosely bound electron from isolated neutral gaseous atom in its ground state to produce a cation”.

Exlpanation : Lets consider the general reaction-

M(g) + Energy M⁺_(g) + e^-

Isolated gaseous

atom

• The energy required to bring out the above change is called ionization energy.

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• The smaller the I.E. it is easier for the neutral atom to change into a cation

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• I.E. is expressed in the unit KJ/mole, / eV/atom/ Kcal/mole

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• I.E. is measured by using spectroscopic methods

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• These quantities are related as -

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1 eV/atom = 96.4705 KJ/mole = 23.06 Kcal/mole

1 Kcal/mole = 4.185 KJ/mole

• I.E. are shown by a +ve sign which is placed before them, plus sign represents the absorption of energy

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• Successive/ (Higher ) ionization energy:
• The amount of energy required to remove the first electron is called its first ionization energy (IE1)

M_(g) + Energy M⁺_(g) + e^- (IE1)

• The amount of energy required to required to remove the second electron is called second ionization energy (IE2).

M⁺ + Energy M²⁺ + e^- (IE₂)

• The amount of energy required to remove third, fourth electrons from dipositive and tripositive ions are called third and fourth ionization energy (IE3 and IE4).

M²⁺ + Energy M³⁺ + e^- (IE₃)

• Similarly ionization potentials of higher and higher grades are also known. These are obtained by removing the electrons one by one.
• Thus I1 < I2 < I3 < I4…. And so on.

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• Factors affecting ionization energy :
• Following are the factors which influence the magnitude of ionization energy

a) Atomic size :

i) Greater the size of an atom, the smaller is ionization energy. This is because as the size of atom is increases, the outer shell electron far away from the nucleus.

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ii) Thus the size of atom increases, the force of attraction on the electron decreases.

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iii) Hence, less is the energy needed to remove the electron. Therefore IE decreases with increase in atomic size/ atomic radius.

b) Effective Nuclear Charge :

i) The force of attraction between the nucleus and the outermost electron increases with increase in nuclear charge.

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ii) Thus, greater the nuclear charge, the greater is the energy needed to pull out an electron from the atom.

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iii) Hence, IE increases with increase in nuclear charge.

C) Screening/ shielding effect :

i) The electrons present in valence shell of am atom are attracted by the nucleus due to nuclear charge

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ii) The force of attraction also depends on the distance between the nucleus and valence shell electron and also on the inner shell electrons.

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iii) These inner shell electrons exert a force of repulsion on valence shell electrons.

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iv) Thus inner shell electrons acts as a screen / shield between nucleus and valence shell electrons.

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v) Hence, these outer electrons feel lesser nuclear charge is denoted with Z_eff.

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vi) Thus, if screening effect increases, Zeff decreases, force of attraction on valence shell electron decreases.

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vii) Thus, IE decrease with with an increase in number of inner electrons i.e. screening effect.

d) Half filled and completely filled orbitals :

i) According to Hund’s rule, half-filled (ns¹, np³ , nd⁵) and full-filled(ns²,np⁶,nd¹⁰) orbital’s are comparatively more stable.

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ii) Hence, more energy is needed to remove an electron from such orbitals.

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iii) This maens that the IE of an atom having half-filled or completely -filled orbitals in its electronic configuration is relatively higher than that expected normally from its position in the periodic table.

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For.Ex. Be₄ = 1s² 2s² has extra stability due to completely filled 2s sub-shell

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• e) Penetration effect of electrons/types of orbitals :

i) We well know that, the s- orbital electrons are closer to the nucleus than the p ,d or f electrons.

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ii) Thus, the s orbital electrons experience more attraction towards nucleus than the p, d or f orbital electrons.

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iii) Therefore, the energy required for pulling out an s orbital electron is maximum and it decreases in pulling out p, d and f orbital electrons.

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iv) Thus, the probability of finding/penetrating electrons near the nucleus follows the following order.

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s > p > d > f

• Variation of ionization energy :
• Down the group : As we move proceed from top to bottom in a group, the IE of the elements decreases due to –

i) increase in nuclear charge

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ii) There is a gradual decrease in atomic size and

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iii) Increase in screening effect due to number of inner electrons

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• Along the period :In general, as we move from left to right in a period the IE/IP of the elements increases due to –

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i) Successive increase in nuclear charge

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ii) Decrease in atomic size

• Applications of IE to chemical behavior of an element :

1) Nature of elements : Elements having lower IE are metallic in character and of higher IE are non-metallic in nature.

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2) Reactivity : Elements with lower IE are more reactive where as higher

IE are less reactive.

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3) Reducing Power : Lower the value of IP of an element, greater is its

reducing power.

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4) Basic character of the element : Lower the value of IP of an element,

the grater will be basic character.

C) Electron Affinity/ Electron Gain Enthalpy (EA / egH)

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Definition : “ The amount of energy released in adding an extra electron from outside to an isolated gaseous atom in its in its ground state to convert it into a gaseous anion is known as electron affinity.”

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Explanation : Thus electron affinity of an atom M(g) can be defined by the following process :

M(g) + e- M^-_(g) + Energy released = - EA1

isolated gaseous atom gaseous anion

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• Just as IE measures the tendency of an atom to change into a cation where as EA measures the tendency of an atom to change into an anion. In short IE and EA are opposite processes.

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• The EA defined above is called first electron affinity, it corresponds to the addition of one electron only. Hence it is represented as - EA1.

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• Where negative sign represents the release of energy , hence it is an exothermic process.

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• EA is also called as electron affinity energy. It is measured in electron volts (eV/KJ Mol^-1 ) or Kcal or KJ/mole.

• Successive Electron Affinity :
• If only one electron added to gaseous atom, then energy change is known as - first electron affinity (EA1).

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• If an same atom accepts the electrons one after other , then the energy

change involved are known as – successive EA.

For Ex.

• X_(g) + e^_ X^{- = EA1}
• X^- + e- X^{2- = EA2}
• X^2- + e^- X^{3- = EA3}

• The first EA/ electron gain enthalpy may be positive or negative but the values of second, third and the higher gain enthalpies have always positive values

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• This is because if an electron is added to the uninegative ion, it experience a repulsive force

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• As a result, the energy has to be supplied to overcome the repulsive force. Thus in order to add second electron, the energy is required rather than release.

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• Therefore the value of successive EA/electron gain enpthalpies are positive
• For example,

O_(g) + e^- O^-_{(g) =} EA₁ = - 141 KJ/mole

O^-_(g) + e^- O^2-_(g) = EA₂ = + 780 KJ/mole

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• Factors affecting EA :

EA depends on the following factors

1) Atomic size : If the size of atom is small, the distance between the nucleus

and the incoming electron will also be small

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• Hence the incoming electron will experience a greater force of attraction by the nucleus and held very firmly

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• Thus large amount of energy will be released in this process and EA value/electron gain enthalpy high

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• While if larger the size of atom, the force of attraction on the added electron will decrease, so EA value become less negative.

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2) Nuclear charge :

• Higher the effective effective nuclear charge, greater is the tendency of an atom to attract the additional electron towards itself.

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• Greater the force of attraction exerted by the nucleus on the extra electron being added to the outer shell of atom, then higher the amount of energy released.
• The EA values are more negative with increase in nuclear charge.

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• This is because the force of attraction between the nucleus and added electron increase with increase in nuclear charge.

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• Thus the atoms with higher effective nuclear charge have higher electron affinity values and vice versa.

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3) Electronic configuration :

The effect of E.C. on the magnitude of EA can be explained with the help of following examples.

i) EA values of IIA group elements :

• In IIA group elements the s- subshells are completely filled. Hence the addition of any extra electron to this s-subshell is not possible.
• Therefore, the elements of IIA group have zero electron affinity.

ii) EA values of N and P :

The valence shell E.C. of N and P are :

N 2s² 2p³ ; P 3s²3p³

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• 2p and 3p orbitals in N and P are half filled hence are extra stable. Thus the addition of extra electron to these orbitals is not possible.
• Therefore, N and P have very low EA values.

iii) EA values of halogens :

• The valence–shell E.C. of halogen atoms is (ns²np⁵ ) has a sort of one electron to stabilise its noble gas configuration (ns²np⁶ ) which is very stable.

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• Thus halogen atoms have a strong tendency to accept an extra electron and acquire stable E.C. as like noble gas.

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• Hence, the halogen atoms have very high values of EA.

iv) EA of noble gases :

• The outer shell E.C. of noble gases is ( ns²np⁶ ) which is extra-ordinarily stable

and have no tendency to accept electron from outside.

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• Hence, the EA values of inert gases is practically zero.

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• Variation of Electron Affinity :

a) Along the periods :

• On moving from left to right in a period, the size of atoms increases and the effective nuclear charge also increases.

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• Both these factors favour an increase in the force of attraction exerted by the nucleus on the electron.

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• Thus, the atom has greater tendency to attract an electron from outside towards itself.

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• Hence, the EA increases along the periods.

b) Down the groups :

• On moving down the groups both the size of atom and the effective nuclear charge increases.

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• The increase in atomic size tends to decrease the EA values while the increase in nuclear charge tends to increase the EA values.

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• Thus, the net result is that the EA goes eon decreasing as we move from top to bottom down the groups.

• Applications of EA to chemical behavior of an element :

1) Tendency to form anions :

• The magnitude of EA of an element gives us an idea the tendency of an element to accept an electron and to form an anion.

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• Greater the value of EA of an element, greater is the tendency to accept the electrons and to form anions.

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• Thus the elements with high EA values for.e.g. halogens have a strong tendency to accept an electron and to form anion easily.

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• While the elements with low EA values for. e.g. alkali and alkaline earth metals are not able to accept electrons hence they do not form an anion.

2) Reducing and oxidizing power of elements :

• The oxidizing power of the elements decreases down the group and increases from left to right along the period.

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• Thus the elements lying at the extreme left of the periodic table (for e.g. alkali and alkaline earth metals) which have low value of EA are poor oxidizing agents.

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• While the elements lying at extreme right of the periodic table (i.e. halogens) which have high value of EA are strong oxidizing agents.

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• M(g) - e- M⁺(g)

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Reducing agent

( lower Valency stast = 0) ( higher v. s.=+1)

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M(g) + e^- M^-(g)

Oxidizing agent (LVS = -1)

(HVS = 0)

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3) Metallic and non-metallic characters of elements :

• Metallic character of an element is defined as- its tendency to lose one or more electrons and form a cation.

M - e^- M⁺

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• Non-metallic character of an element is defined as- its tendency to accept one or more electrons and form an anion.

M + e^- M^-

• Thus, greater the value of EA of an element, greater is is its tendency to accept the electron and to give anion.
• This means that greater the vlaue of EA of an element, greater is its non-metallic chatecter and vice versa.

d) Elecronegativity :

Definition : The tendency/ability/power of a bonded atom in a molecule to attract the shared pair of electrons towards itself is termed as its electronegativity.

Explanation :

• The formation of covalent bond involves the sharing of electrons between the combining atoms. For e.g.

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• When covalent bond is formed between two similar atoms or the atoms having same electronegativity, say A and A.

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• The compound has 100% covalent character.

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• In such type of compounds the shared electron pair distribute equally between both the atoms which is shown in the following figure.

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• On the other hand, consider the formation of a covalent bond between two dissimilar atoms of a molecule like HCl.

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• In this molecule the electron pair is not shared equally by H and Cl.
• In fact the electron pair lies near to Cl atom than hydrogen.

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• The reason for this unequal sharing of electron pair is that the Cl atom has greater tendency to attract the electron pair towards itself.

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• This tendency is termed as electronegativity, which is shown in the following figure.

• Factors affecting the electronegativity :

The important factors which affects the magnitude of electronegativity of elements are as follows :

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1) Size of atom :

• Smaller atom has greater tendency to attract the shared electron pair towards itself

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• Thus the smaller atoms have greater electronegativity values than the larger atoms.

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2) Charge on ion :

• A cation attracts the electron pair more rapidly towards itself than the atom.

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• This is due to the smaller size of the cation as compared to its parent atom (M⁺ > M).

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• Thus a cation, M⁺ has higher electronegativity than its parent atom,M.

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• Higher the oxidation state of an atom, greater is its electronegativity.

For e.g. M²⁺ > M⁺ > M

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4) Number of inner shells :

• The atom with large number of inner shells between the nucleus and outer shell electron has less value of electronegativity than the atom with less number of inner shells.

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• For e.g. The electronegativity value of halogens decrease from F (Z=9) to At(Z= 85)

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• Since the number of inner shells increase with increase in atomic number.

5) Type of hybridization :

• The magnitude of electronegativity of an atom also depends on the type of hybridizatoin.

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• This is because the magnitude of electronegativity increase as the s-character increase in hybrid orbitals.
• For e.g.
• Compound- CH4 CH2=CH2 CH=CH
• Hybridization - sp³ sp² sp
• Order of elect- 25% 33% 50%

ronegetivity Increasing

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• Variation of electronegativity :

a) Along the period : On going from left to right in a period the electronegativity values increases because.

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i) On moving from left to right in a period, there is decrease in size of atoms. Smaller atoms have greater tendency to attract the electrons towards itself.

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i.e. smaller atoms have high value of electronegativity.

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ii) On moving from left to right there is increase in IE and EA of the elements. Thus, the electronegativity increases.

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b) Down the group : When we go down the group the electronegativity value decreases due to following facts :

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i) As we move down a group, there is an increase in size of atoms. Thus as size of atom increases, then their electronegativity decreases.

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ii) Down the group, the IE and EA decreases, with the decrease of IE and EA the electronegetivity value also decrease.

• Pauling approach of electronegativity :
• Pauling scale is based on an empirical relation between the energy of a bond called bond energy and electronegativity of the bonded atoms.

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• Let us consider a A-B bond between two dissimilar atoms, A and

B of a molecule

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• Let the bond of A-A, B-B, and A-B are represented as-E_A-A ,E_B-B, and E_A-B respectively.

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• It has been seen that the energy of A-B bond is almost greater than geometric mean of the energies of A-A and B-B.

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• i.e. E_A-B > E_A-A × E_B-B

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• The difference between E_A-A and under root E_A-A × E_B-B is called ionic-resonance energy of A-B bond is denoted by _{A-B .}Thus it is given by :

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_A-B = E_A-B - under root E_A.A × E_B.B

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• The square root of ionic-resonance energy is a measure of partial ionic character of an A-B covalent bond.

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• Pauling further suggested that the square root of A-B[i.e. (A-B)^1/2 ] is a measure of ionic character in A-B covalent bond.

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• With the increase in magnitude of ( A-B)^1/2, then the amount of ionic character in A-B covalent bond also increases, i.e.
• (A-B)^1/2 A-B)^{1/2 is directly proportional to Amount of ionic character in A-B bond}

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• And

X_A – X_B ∞ Amount of ionic character in A-B bond.

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• Consequently, X_A - X_B = K under root _A-B

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Now put the values of A-B, then we get

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X_A - X_B = K [ E_{A - A} – under root E_{A -A} × E_B-B]^1/2

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• The value of constant,K is equal to 0.208 which comes from the conversion of experimental values of E_A-B measured in Kcals/mole into eV.
• Thus :

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X_A-X_B = 0.208 [E_A-B - under root E_A-A × E_B-B ]^1/2

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• Mulliken’s approach :