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Where, n φ = azimuthal quantum number

So angular momentum of elliptical orbit = nr h + nφ h
2π 2π
rr φ2 rr φ11
Angular momentum = (nr + nφ ) h r φ2 r φ1

(5) Shape of elliptical orbit depends on, φ = change φ = change

Length of major axis n = nr + nφ r = change r = constant
Length of minor axis = nφ nφ

(6) n φ can take all integral values from l to ‘n’ values of n r depend on the value of n φ . For n = 3,
n φ can have values 1,2,3 and n r can have (n –1) to zero i.e. 2,1 and zero respectively.

Thus for n = 3, we have 3 paths

n nφ nr Nature of path K= 3

K= 2

3 1 3 elliptical K= 1

2 1 elliptical • Nuclear

3 0 circular

The possible orbits for n = 3 are shown in figure.

Thus Sommerfield showed that Bohr’s each major level was composed of several sub-levels. therefore it
provides the basis for existance of subshells in Bohr's shells (orbits).

(7) Limitation of Bohr sommerfield model :

(i) This model could not account for, why electrons does not absorb or emit energy when they are moving
in stationary orbits.

(ii) When electron jumps from inner orbit to outer orbit or vice –versa, then electron run entire distance but
absorption or emission of energy is discontinuous.

(iii) It could not explain the attainment of expression of nh for angular momentum. This model could not

explain Zeeman effect and Stark effect.

Dual nature of electron.

(1) In 1924, the french physicist, Louis de Broglie suggested that if light has both particle and wave like

nature, the similar duality must be true for matter. Thus an electron, behaves both as a material particle and as a
wave.
(2) This presented a new wave mechanical theory of matter. According to this theory, small particles like
electrons when in motion possess wave properties.

(3) According to de-broglie, the wavelength associated with a particle of mass m, moving with velocity v is

given by the relation

λ = h , where h = Planck’s constant.
mv

(4) This can be derived as follows according to Planck’s equation, E = hν = h.c  ν = c 
λ  λ 

energy of photon (on the basis of Einstein’s mass energy relationship), E = mc 2

equating both hc = mc 2 or λ = h which is same as de-Broglie relation. ( mc = p)
λ mc
(5) This was experimentally verified by Davisson and Germer by observing diffraction effects with an

electron beam. Let the electron is accelerated with a potential of V than the Kinetic energy is

1 mv 2 = eV ; m2 v 2 = 2eVm
2

mv = 2eVm = P ; λ = h
2eVm

(6) If Bohr’s theory is associated with de-Broglie’s equation then wave length of an electron can be
determined in bohr’s orbit and relate it with circumference and multiply with a whole number

2πr = nλ or λ = 2πr
n

From de-Broglie equation, λ = h . Thus h = 2πr or mvr = nh
mv mv n 2π

Note :  For a proton, electron and an α -particle moving with the same velocity have de-broglie

wavelength in the following order : Electron > Proton > α - particle.

(7) The de-Broglie equation is applicable to all material objects but it has significance only in case of
microscopic particles. Since, we come across macroscopic objects in our everyday life, de-broglie relationship has
no significance in everyday life.

Solution : (b) KE = 1 mv 2 = 4.55 × 10 −25 J
Example: 35 2

v2= 2× 4.55 × 10 −25 =1×106 ; v = 103 m / s
9.1 × 10 −31

De-Broglie wavelength λ = h = 6.626 × 10 −34 = 7.28 × 10 −7 m
mv 9.1×10 −31 ×10 3

The speed of the proton is one hundredth of the speed of light in vacuum. What is the de Broglie wavelength?
Assume that one mole of protons has a mass equal to one gram, h = 6.626×10−27 erg sec

(a) 3.31 × 10−3 Å (b) 1.33 × 10−3 Å (c) 3.13 × 10 −2 Å (d) 1.31 × 10−2 Å

Solution : (b) m = 1 10 23 g
6.023 ×

λ = h = 6.626 × 10 −27 × 6.023 × 10 23 = 1.33 × 10−11 cm
mv 1 × 3 × 108 cm sec −1

Heisenberg’s uncertainty principle.

(1) One of the important consequences of the dual nature of an electron is the uncertainty principle,

developed by Warner Heisenberg.

(2) According to uncertainty principle “It is impossible to specify at any given moment both the position and

momentum (velocity) of an electron”.

Mathematically it is represented as , ∆x .∆p ≥ h

Where ∆x = uncertainty is position of the particle, ∆p = uncertainty in the momentum of the particle

Now since ∆p = m ∆v

So equation becomes, ∆x. m∆v ≥ h or ∆x × ∆v ≥ h
4π 4πm

The sign ≥ means that the product of ∆x and ∆p (or of ∆x and ∆v ) can be greater than, or equal to but

never smaller than h . If ∆x is made small, ∆p increases and vice versa.

(3) In terms of uncertainty in energy, ∆E and uncertainty in time ∆t, this principle is written as, ∆E . ∆t ≥ h

Note : Heisenberg’s uncertainty principle cannot we apply to a stationary electron because its velocity is 0

and position can be measured accurately.

Example: 36 What is the maximum precision with which the momentum of an electron can be known if the uncertainty in

the position of electron is ± 0.001Å ? Will there be any problem in describing the momentum if it has a value

of h , where a0 is Bohr’s radius of first orbit, i.e., 0.529Å?
2πa 0

Solution : ∆x . ∆p = h

 ∆x = 0.001Å = 10−13 m

∴ ∆p = 6.625 × 10 −34 = 5.27 × 10 −22
4 × 3.14 × 10 −13

Example: 37 Calculate the uncertainty in velocity of an electron if the uncertainty in its position is of the order of a 1Å.

Solution : According to Heisenberg’s uncertainty principle

∆v . ∆x ≈ h
4πm

∆v ≈ h = 22 6.625 × 10−34 = 5.8 × 10 5 m sec −1
4πm.∆x 7 × 9.108 × 10−31
4 × × 10−10

Example: 38 A dust particle having mass equal to 10−11 g, diameter of 10−4 cm and velocity 10−4 cm sec −1 . The error in
measurement of velocity is 0.1%. Calculate uncertainty in its positions. Comment on the result .

Solution : ∆v = 0.1 × 10 −4 = 1×10−7 cm sec −1
100

 ∆v . ∆x = h
4πm

∴ ∆x = 6.625 × 10−27 = 5.27 × 10−10 cm
4 × 3.14 × 10−11 × 1 × 10−7

The uncertainty in position as compared to particle size.

= ∆x = 5.27 × 10 −10 = 5.27 × 10−6 cm
diameter 10 −4

The factor being small and almost being negligible for microscope particles.

Schrödinger wave equation.

(1) Schrodinger wave equation is given by Erwin Schrödinger in 1926 and based on dual nature of
electron.

(2) In it electron is described as a three dimensional wave in the electric field of a positively charged nucleus.
(3) The probability of finding an electron at any point around the nucleus can be determined by the help of
Schrodinger wave equation which is,

∂2Ψ + ∂2Ψ + ∂2Ψ + 8π 2m (E − V)Ψ = 0
∂x 2 ∂y 2 ∂z 2 h2

Where x, y and z are the 3 space co-ordinates, m = mass of electron, h = Planck’s constant,

E = Total energy, V = potential energy of electron, Ψ = amplitude of wave also called as wave function.
∂ = stands for an infinitesimal change.
(4) The Schrodinger wave equation can also be written as :

∇2Ψ + 8π 2m (E − V) Ψ = 0
h2

Where ∇ = laplacian operator.

(5) Physical Significance of Ψ and Ψ 2

(i) The wave function Ψ represents the amplitude of the electron wave. The amplitude Ψ is thus a
function of space co-ordinates and time i.e. Ψ = Ψ(x, y, z......times)

(ii) For a single particle, the square of the wave function (Ψ 2 ) at any point is proportional to the
probability of finding the particle at that point.

(iii) If Ψ 2 is maximum than probability of finding e − is maximum around nucleus. And the place where
probability of finding e − is maximum is called electron density, electron cloud or an atomic orbital. It
is different from the Bohr’s orbit.

(iv) The solution of this equation provides a set of number called quantum numbers which describe
specific or definite energy state of the electron in atom and information about the shapes and
orientations of the most probable distribution of electrons around the nucleus.

Quantum numbers and Shapes of orbitals.

Quantum numbers

(1) Each orbital in an atom is specified by a set of three quantum numbers (n, l, m) and each electron is
designated by a set of four quantum numbers (n, l, m and s).

(2) Principle quantum number (n)
(i) It was proposed by Bohr’s and denoted by ‘n’.
(ii) It determines the average distance between electron and nucleus, means it is denoted the size of atom.

r = n2 × 0.529 Å
Z

(iii) It determine the energy of the electron in an orbit where electron is present.

E = − Z2 × 313.3 Kcal per mole
n2

(iv) The maximum number of an electron in an orbit represented by this quantum number as 2n2. No
energy shell in atoms of known elements possess more than 32 electrons.

(v) It gives the information of orbit K, L, M, N------------.
(vi) The value of energy increases with the increasing value of n.
(vii) It represents the major energy shell or orbit to which the electron belongs.
(viii) Angular momentum can also be calculated using principle quantum number

mvr = nh

(3) Azimuthal quantum number (l)

(i) Azimuthal quantum number is also known as angular quantum number. Proposed by Sommerfield and
denoted by ‘l’.

(ii) It determines the number of sub shells or sublevels to which the electron belongs.
(iii) It tells about the shape of subshells.

(iv) It also expresses the energies of subshells s < p < d < f (increasing energy).

(v) The value of l = (n − 1) always where ‘n’ is the number of principle shell.

(vi) Value of l =0 1 2 3………..(n-1)

Name of subshell =s p d f
Shape of subshell Complex
= Spherical Dumbbell Double
dumbbell

(vii) It represent the orbital angular momentum. Which is equal to h l(l + 1)

(viii) The maximum number of electrons in subshell = 2(2l + 1)

s − subshell → 2 electrons d − subshell → 10 electrons

p − subshell → 6 electrons f − subshell → 14 electrons.

(ix) For a given value of ‘n’ the total value of ‘l’ is always equal to the value of ‘n’.

(x) The energy of any electron is depend on the value of n & l because total energy = (n + l). The
electron enters in that sub orbit whose (n + l) value or the value of energy is less.

(4) Magnetic quantum number (m)

(i) It was proposed by Zeeman and denoted by ‘m’.

(ii) It gives the number of permitted orientation of subshells.

(iii) The value of m varies from –l to +l through zero.

(iv) It tells about the splitting of spectral lines in the magnetic field i.e. this quantum number proved the
Zeeman effect.

(v) For a given value of ‘n’ the total value of ’m’ is equal to n2.

(vi) For a given value of ‘l’ the total value of ‘m’ is equal to (2l + 1).

(vii) Degenerate orbitals : Orbitals having the same energy are known as degenerate orbitals. e.g. for p
subshell px py pz

(viii) The number of degenerate orbitals of s subshell =0.

(5) Spin quantum numbers (s)

(i) It was proposed by Goldshmidt & Ulen Back and denoted by the symbol of ‘s’.

(ii) The value of ' s' is + 1/2 and - 1/2, which is signifies the spin or rotation or direction of electron on it’s

axis during movement.

(iii) The spin may be clockwise or anticlockwise.

(iv) It represents the value of spin angular momentum is equal to h s(s + 1).

(v) Maximum spin of an atom = 1 / 2 × number of unpaired electron.

Magnetic field
NS

+1/2 –1/2

SN

(vi) This quantum number is not the result of solution of schrodinger equation as solved for H-atom.

Distribution of electrons among the quantum levels

n lm s Designation of Electrons Total no. of

orbitals present electrons

1 (K shell) 0 0 +1/2, –1/2 1s 22

2 (L shell) 0 0 +1 / 2, − 1 / 2 2s 2
2p
+1 + 1 / 2, − 1 / 2  8

1 0 + 1 / 2, − 1 / 2 6
–1 + 1 / 2, − 1 / 2

3 (M shell) 0 0 +1 / 2,−1 / 2 3s 2
3p 
+1 + 1 / 2,−1 / 2 
3d
1 0 + 1 / 2,−1 / 2 4s 6
4p 
–1 +1 / 2,−1 / 2 
4d 
+ 1 / 2,−1 / 2  18
+2 + 1 / 2,−1 / 2 4f 
+1 + 1 / 2,−1 / 2  32
2 0 + 1 / 2,−1 / 2 
–1 + 1 / 2,−1 / 2  Z
–2  Y
0 0 +1 / 2,−1 / 2  X
+1 + 1 / 2,−1 / 2 
1 0 + 1 / 2,−1 / 2 Nucleus
–1 + 1 / 2,−1 / 2 10
2
+2 + 1 / 2,−1 / 2
+1 + 1 / 2,−1 / 2 
+ 1 / 2,−1 / 2 
2 0 + 1 / 2,−1 / 2 6
–1 + 1 / 2,−1 / 2 
–2 

4(N shell) 

+3 + 1 / 2,−1 / 2 
+2 + 1 / 2,−1 / 2 
+ 1 / 2,−1 / 2 
3 +1 + 1 / 2,−1 / 2 
+0 + 1 / 2,−1 / 2 
–1 + 1 / 2,−1 / 2 10

14

–2 + 1 / 2,−1 / 2

–3

Shape of orbitals

(1) Shape of ‘s’ orbital
(i) For ‘s’ orbital l=0 & m=0 so ‘s’ orbital have only one unidirectional
orientation i.e. the probability of finding the electrons is same in all
directions.
(ii) The size and energy of ‘s’ orbital with increasing ‘n’ will be
1s < 2s < 3s < 4s.
(iii) It does not possess any directional property. s orbital has spherical shape.

(2) Shape of ‘p’ orbitals

(i) For ‘p’ orbital l=1, & m=+1,0,–1 means there are three ‘p’ orbitals, which is symbolised as px , py , pz .

(ii) Shape of ‘p’ orbital is dumb bell in which the two lobes on opposite side separated by the nodal plane.
(iii) p-orbital has directional properties.

ZY Nodal ZY Nodal Z
Nodal Plane Plane Y
Plane X
X Nodal Py orbital Nodal X
Plane Plane
Px orbital Pz orbital

(3) Shape of ‘d’ orbital
(i) For the ‘d’ orbital l =2 then the values of ‘m’ are –2,–1,0,+1,+2. It shows that the ‘d’ orbitals has five
orbitals as d xy , dyz , dzx , d x2 −y2 , dz2.

(ii) Each ‘d’ orbital identical in shape, size and energy.
(iii) The shape of d orbital is double dumb bell .
(iv) It has directional properties.

ZY ZY ZY Y Y
X X X Z X

X

dZX dXY dYZ dX2–Y2 dZ2

(4) Shape of ‘f’ orbital
(i) For the ‘f’ orbital l=3 then the values of ‘m’ are –3, –2, –1,0,+1,+2,+3. It shows that the ‘f’ orbitals
have seven orientation as fx(x 2 −y2 ), fy(x 2 −y2 ), fz(x 2 −y2 ), fxyz , fz3 , fyz3 and fxz 2 .
(ii) The ‘f’ orbital is complicated in shape.

Electronic configuration principles.

The distribution of electrons in different orbitals of atom is known as electronic configuration of the atoms.
Filling up of orbitals in the ground state of atom is governed by the following rules:
(1) Aufbau principle

(i) Auf bau is a German word, meaning ‘building up’.
(ii) According to this principle, “In the ground state, the atomic orbitals are filled in order of increasing

energies i.e. in the ground state the electrons first occupy the lowest energy orbitals available”.

(iii) In fact the energy of an orbital is determined by the quantum number n and l with the help of (n+l)
rule or Bohr Bury rule.

(iv) According to this rule

(a) Lower the value of n + l, lower is the energy of the orbital and such an orbital will be filled up first.
(b) When two orbitals have same value of (n+l) the orbital having lower value of “n” has lower energy

and such an orbital will be filled up first .
Thus, order of filling up of orbitals is as follows:

1s < 2s < 2p < 3s < 3p < 4s < 4 p < 5s < 4d < 5p < 6s < 6 f < 5d

(2) Pauli’s exclusion principle
(i) According to this principle, “No two electrons in an atom can have same set of all the four quantum
numbers n, l, m and s .

(ii) In an atom any two electrons may have three quantum numbers identical but fourth quantum number
must be different.

(iii) Since this principle excludes certain possible combinations of quantum numbers for any two electrons
in an atom, it was given the name exclusion principle. Its results are as follows :

(a) The maximum capacity of a main energy shell is equal to 2n2 electron.
(b) The maximum capacity of a subshell is equal to 2(2l+1) electron.
(c) Number of sub-shells in a main energy shell is equal to the value of n.

(d) Number of orbitals in a main energy shell is equal to n2.
(e) One orbital cannot have more than two electrons.
(iv) According to this principle an orbital can accomodate at the most two electrons with spins opposite to
each other. It means that an orbital can have 0, 1, or 2 electron.

(v) If an orbital has two electrons they must be of opposite spin.

Correct Incorrect

(3) Hund’s Rule of maximum multiplicity

(i) This rule provides the basis for filling up of degenerate orbitals of the same sub-shell.

(ii) According to this rule “Electron filling will not take place in orbitals of same energy until all the
available orbitals of a given subshell contain one electron each with parallel spin”.

(iii) This implies that electron pairing begins with fourth, sixth and eighth electron in p, d and f orbitals of
the same subshell respectively.

(iv) The reason behind this rule is related to repulsion between identical charged electron present in the
same orbital.

(v) They can minimise the repulsive force between them serves by occupying different orbitals.

(vi) Moreover, according to this principle, the electron entering the different orbitals of subshell have
parallel spins. This keep them farther apart and lowers the energy through electron exchange or
resonance.

(vii) The term maximum multiplicity means that the total spin of unpaired e − is maximum in case of
correct filling of orbitals as per this rule.

Energy level diagram

The representation of relative energy levels of various atomic orbital is made in the terms of energy level
diagrams.

One electron system : In this system 1s 2 level and all orbital of same principal quantum number have same
energy, which is independent of (l). In this system l only determines the shape of the orbital.

Multiple electron system : The energy levels of such system not only depend upon the nuclear charge but
also upon the another electron present in them.

5 4s 4p 4d 4f 6p
4 3p 3d 5d
2p 4f
3sEnergy 6s
3 Energy 5p
4d
2s 5s
2 4p
3d
1s 4s
3p
Energy level diagram of one
electron system 3s
2p

2s
1s

Energy level diagram of multiple
electron system

Diagram of multi-electron atoms reveals the following points :

(i) As the distance of the shell increases from the nucleus, the energy level increases. For example energy
level of 2 > 1.

(ii) The different sub shells have different energy levels which possess definite energy. For a definite shell, the

subshell having higher value of l possesses higher energy level. For example in 4th shell.

Energy level order 4f > 4d > 4p > 4s

l= 3 l=2 l=1 l= 0

(iii) The relative energy of sub shells of different energy shell can be explained in the terms of the (n+l) rule.

(a) The sub-shell with lower values of (n + l) possess lower energy.

For 3d n = 3 l= 2 ∴ n + l = 5

For 4s n = 4 l=0 n+l=4

(b) If the value of (n + l) for two orbitals is same, one with lower values of ‘n’ possess lower energy level.

Extra stability of half filled and completely filled orbitals
Half-filled and completely filled sub-shell have extra stability due to the following reasons :

(i) Symmetry of orbitals
(a) It is a well kown fact that symmetry leads to stability.

(b) Thus, if the shift of an electron from one orbital to another orbital differing slightly in energy results in
the symmetrical electronic configuration. It becomes more stable.

(c) For example p3 , d 5 , f 7 configurations are more stable than their near ones.

(ii) Exchange energy

(a) The electron in various subshells can exchange their positions, since electron in the same subshell have
equal energies.

(b) The energy is released during the exchange process with in the same subshell.

(c) In case of half filled and completely filled orbitals, the exchange energy is maximum and is greater than
the loss of orbital energy due to the transfer of electron from a higher to a lower sublevel e.g. from 4s
to 3d orbitals in case of Cu and Cr .

(d) The greater the number of possible exchanges between the electrons of parallel spins present in the
degenerate orbitals, the higher would be the amount of energy released and more will be the stability.

(e) Let us count the number of exchange that are possible in d 4 and d 5 configuraton among electrons
with parallel spins.

d4 (1) (2) (3)

3 exchanges by 1st e– 2 exchanges by 2nd e– Only 1 exchange by 3rd e–

To number of possible exchanges = 3 + 2 + 1 =6

d5 (1) (2) (3)

4 exchanges by 1st e– 3 exchanges by 2nd e– 2 exchange by 3rd e–

(4)

1 exchange by 4th e–

To number of possible exchanges = 4 + 3 + 2 +1 = 10

Electronic configurations of Elements.

(1) On the basis of the elecronic configuration priciples the electronic configuration of various elements are
given in the following table :
Electronic Configuration (E.C.) of Elements Z=1 to 36

Element Atomic 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f
Number

H 11

He 2 2

Li 3 2 1

Be 4 2 2

B 5 221

C 6 222

N 7 223

O 8 224

F 9 225

Ne 10 2 2 6

Na 11 2 2 6 1

Mg 12 2

Al 13 21

Si 14 10 2 2

P 15 electrons 23

S 16 24

Cl 17 25

Ar 18 2 2 6 2 6

K 19 2 2 6 2 6 1

Ca 20 2

Sc 21 12

Ti 22 22

V 23 32

Cr 24 51

Mn 25 52

Fe 26 62

Co 27 18 72

Ni 28 electrons 82

Cu 29 10 1

Zn 30 10 2

Ga 31 10 2 1

Ge 32 10 2 2

As 33 10 2 3

Se 34 10 2 4

Br 35 10 2 5

Kr 36 2 2 6 2 6 10 2 6

(2) The above method of writing the electronic configurations is quite cumbersome. Hence, usually the
electronic configuration of the atom of any element is simply represented by the notation.

nl x NUMBER OF

ELECTRONS
PRESENT

NUMBER OF SYMBOL OF
PRINCIPAL SUBSHELL

SHELL

e.g. 1s2 means 2 electrons are present in the s- subshell of
the 1st main shell.

(3) (i) Elements with atomic number 24(Cr), 42(Mo) and 74(W) have ns1(n − 1)d 5 configuration and not
ns 2(n − 1)d 4 due to extra stability of these atoms.

(ii) Elements with atomic number 29(Cu), 47(Ag) and 79(Au) have ns1(n − 1)d10 configuration instead of
ns 2(n − 1)d 9 due to extra stability of these atoms.

Cr (24) [Ar] 3d5 Cu (29) [Ar] 3d10

4s1 4s1

(4) In the formation of ion, electrons of the outer most orbit are lost. Hence, whenever you are required to
write electronic configuration of the ion, first write electronic configuration of its atom and take electron from

outermost orbit. If we write electronic configuration of Fe 2+ (Z = 26, 24 e − ), it will not be similar to Cr (with 24 e − )

but quite different.

Fe[Ar] 4s 2 3d 6  outer most orbit is 4th shell hence, electrons from 4s have been removed to make Fe 2+ .

Fe 2+ [Ar] 4s 3d 6 

(5) Ion/atom will be paramagnetic if there are unpaired electrons. Magnetic moment (spin only) is

µ = n(n + 2) BM (Bohr Magneton). (1BM = 9.27 × 10−24 J / T) where n is the number of unpaired electrons.

(6) Ion with unpaired electron in d or f orbital will be coloured. Thus, Cu+ with electronic configuration

[Ar]3d10 is colourless and Cu2+ with electronic configuration [Ar]3d 9 (one unpaired electron in 3d) is coloured

(blue).
(7) Position of the element in periodic table on the basis of electronic configuration can be determined as,
(i) If last electron enters into s-subshell, p-subshell, penultimate d-subshell and anti penultimate f-subshell
then the element belongs to s, p, d and f – block respectively.
(ii) Principle quantum number (n) of outermost shell gives the number of period of the element.

(iii) If the last shell contains 1 or 2 electrons (i.e. for s-block elements having the configuration ns1−2 ), the
group number is 1 in the first case and 2 in the second case.

(iv) If the last shell contains 3 or more than 3 electrons (i.e. for p-block elements having the configuration

ns 2 np1−6 ), the group number is the total number of electrons in the last shell plus 10.

(v) If the electrons are present in the (n –1)d orbital in addition to those in the ns orbital (i.e. for d-block

elements having the configuration (n –1) d1−10ns1−2 ), the group number is equal to the total number
of electrons present in the (n –1)d orbital and ns orbital.

Chemical bonding

Atoms of different elements excepting noble gases donot have complete octet so they combine with other
atoms to form chemical bond. The force which holds the atoms or ions together within the molecule is called a
chemical bond and the process of their combination is called Chemical Bonding.

Chemical bonding depends on the valency of atoms. Valency was termed as the number of chemical bonds
formed by an atom in a molecule or number of electrons present in outermost shell i.e., valence electrons. Valence
electrons actually involved in bond formation are called bonding electrons. The remaining valence electrons still
available for bond formation are referred to as non-bonding electrons.

• • • • • • • • + • •–
• • • • •• • •

• p+n • • • • p+ n • • • • p +n • • • p+ n • • •
•• •• •• • ••

•• • • •• •• •• • •

Na (2, 8, 1) Cl (2, 8, 7) Bond formation takes place

Cause and Modes of chemical combination.

Chemical combination takes place due to following reasons.

(1) Chemical bonding takes place to acquire a state of minimum energy and maximum stability.

(2) By formation of chemical bond, atoms convert into molecule to acquire stable configuration of the nearest
noble gas.

Modes : Chemical bonding can occur in the following manner.

Transfer of electrons from one Ionic bond
atom to another

Mutual sharing of electrons between Covalent bond
the atoms

Mutual sharing of electrons provided Co-ordination bond
entirely by one of the atoms
Electrovalent bond.

When a bond is formed by complete transfer of electrons from one atom to another so as to complete their
outermost orbits by acquiring 8 electrons (i.e., octet) or 2 electrons (i.e., duplet) in case of hydrogen, helium etc.
and hence acquire the stable nearest noble gas configuration, the bond formed is called ionic bond,
electrovalent bond or polar bond. Compounds containing ionic bond are called ionic, electrovalent or polar
compounds.

• ••   +  •• −
   
Example : Na + • Cl • → Na • Cl • or Na +Cl −
• • •
   • • 
••

Some other examples are: MgCl2, CaCl2, MgO, Na2S, CaH2, AlF3, NaH, KH, K2O , KI, RbCl, NaBr, CaH2 etc.

(1) Conditions for formation of electrovalent bond

(i) Number of valency electrons : The atom which changes into cation (+ ive ion) should possess 1, 2 or

3 valency electrons. The other atom which changes into anion (– ive ion) should possess 5, 6 or 7

electrons in the valency shell.

(ii) Electronegativity difference : A high difference of electronegativity (about 2) of the two atoms is

necessary for the formation of an electrovalent bond. Electrovalent bond is not possible between

similar atoms.

(iii) Small decrease in energy : There must be overall decrease in energy i.e., energy must be released.

For this an atom should have low value of Ionisation potential and the other atom should have high

value of electron affinity.

(iv) Lattice energy : Higher the lattice energy, greater will be the ease of forming an ionic compound. The

amount of energy released when free ions combine together to form one mole of a crystal is called lattice

energy (U).

Magnitude of lattice energy ∝ Charge of ion
size of ion

A+ (g) + B− (g) → AB(s) + U

Determination of lattice energy (Born Haber cycle)
When a chemical bond is formed between two atoms (or ions), the potential energy of the system constituting
the two atoms or ions decreases. If there is no fall in potential energy of the system, no bonding is possible, the
energy changes involved in the formation of ionic compounds from their constituent elements can be studied with
the help of a thermochemical cycle called Born Haber cycle.

Example : The formation of 1 mole of NaCl from sodium and chlorine involves following steps :

Step I : Conversion of metallic sodium into gaseous sodium atoms: Na(s)+ S → Na(g) , where S= sublimation
1 mole

energy i.e., the energy required for the conversion of one mole of metallic sodium into gaseous sodium atoms.
Step II : Dissociation of chlorine molecules into chlorine atoms : Cl2(g) + D → 2Cl(g) , where D = Dissociation

energy of Cl2 so the energy required for the formation of one mole of gaseous chlorine atoms = D / 2 .

Step III: Conversion of gaseous sodium atoms into sodium

ions : Na(g)+ IE → Na + (g) + e − , where IE = Na(s) 1 Cl (g)
1 mole 2
+S + 2 ∆H f
Ionisation energy of sodium.
Na(g) 1/2D NaCl (Crystal)
Step IV: Conversion of gaseous chlorine atoms into
chloride ions : Cl(g)+ e − → Cl − (g) + EA , where EA = Electron +IE – e– Cl (g) –U

1 mole – EA +e–

affinity of chlorine. Na+(g) + Cl − (g)

(Born Haber Cycle)

Step V : Combination of gaseous sodium and chloride ions
to form solid sodium chloride crystal.

Na + (g) + Cl − (g) → NaCl(s)+ U , where U = lattice energy of NaCl
1 mole

The overall change may be represented as : Na(s) + 1 Cl 2 (g) → NaCl(s), ∆H f , where ∆H f is the heat of
formation for 1 mole of NaCl(s) . 2

According to Hess's law of constant heat summation, heat of formation of one mole of NaCl should be same
whether it takes place directly in one step or through a number of steps. Thus,

∆H f = S+ 1 D + IE + EA + U
2

(2) Types of ions

The following types of ions are encountered :
(i) Ions with inert gas configuration : The atoms of the representative elements of group I, II and III by

complete loss of their valency electrons and the elements of group V, VI, and VII by gaining 3,2 and 1
electrons respectively form ions either with ns 2 configuration or ns 2 p6 configuration.

(a) Ions with 1s 2 (He) configuration : H − , Li+ , Be 2+ etc. The formation of Li + and Be 2+ is difficult due to

their small size and high ionisation potential.
(b) Ions with ns 2 p6 configuration : More than three electrons are hardly lost or gained in the ion formation

Cations : Na + , Ca 2+ , Al 3+ etc.

Anions : Cl − , O 2− , N 3− , etc.

(ii) Ions with pseudo inert gas configuration : The Zn2+ ; ion is formed when zinc atom loses its outer 4s
electrons. The outer shell configuration of Zn2+ ions is 3s 2 3p6 3d10 . The ns 2np6nd10 outer shell

configuration is often called pseudo noble gas configuration which is considered as stable one.

Examples: Zn2+ , Cd 2+ , Hg 2+ , Cu+ Ag + , Au+ , Ga 3+ etc

(iii) Exceptional configurations : Many d- and f block elements produce ions with configurations different
than the above two. Ions like Fe 3+ , Mn2+ , etc., attain a stable configuration half filled d- orbitals

Fe 3+ 3s 2 3p 6 3d 5 ; Mn2+ 3s 2 3p 6 3d 5

Examples of other configurations are many.

Ti 2+ (3s 2 3p 6 3d 2 ) ; V 2+ (3s 2 3p 6 3d 3 )

Cr 2+ (3s 2 3p 6 3d 4 ) ; Fe 2+ (3s 2 3p 6 3d 6 )

However, such ions are comparatively less stable

(iv) Ions with ns 2 configuration : Heavier members of groups III, IV and V lose p-electrons only to form ions
with ns 2 configuration. Tl + , Sn2+ , Pb 2+ , Bi3+ are the examples of this type. These are stable ions.

(v) Polyatomic ions : The ions which are composed of more than one atom are called polyatomic ions.
These ions move as such in chemical reactions. Some common polyatomic ions are

NH + (Ammonium); NO3− (Nitrate)
4

PO43− (phosphate); SO42− (Sulphate)

CO32− (Carbonate) ; SO32− (Sulphite), etc.

(vi) Polyhalide ions : Halogens or interhalogens combine with halide ions to form polyhalide ions.

I − , ICl − , ICl − etc. Fluorine due to highest electronegativity and absence of d-oribitals does not form
3 4 2

polyhalide ions.

The atoms within the polyatomic ions are held to each other by covalent bonds.

The electro valencies of an ion (any type) is equal to the number of charges present on it.

(3) Method of writing formula of an ionic compound

In order to write the formula of an ionic compound which is made up of two ions (simple or polyatomic)
having electrovalencies x and y respectively, the following points are followed :

(i) Write the symbols of the ions side by side in such a way that positive ion is at the left and negative ion at
the right as AB.

(ii) Write their electrovalencies in figures on the top of each symbol as A x By

(iii) Divide their valencies by H.C.F

(iv) Now apply criss cross rule as x y , i.e., formula Ay Bx
A B

Examples :

Name of Exchange of Formula Name of Exchange of Formula
compound valencies CaCl2 compound valencies Al 2 O3

Calcium chloride 21 Aluminium oxide 32
Ca Cl Al O

Potassium 13 K3 PO4 Magnesium 2 3 Mg3 N2
phosphate K PO4 CaO nitride Mg N (NH 4 )2 SO4

Calcium oxide 22 1 1 Ammonium 1 2
O sulphate NH4 SO4
CaO or Ca

(4) Difference between atoms and ions

The following are the points of difference between atoms and ions.

Atoms Ions

1. Atoms are perfectly neutral in nature, i.e., number of Ions are charged particles, cations are positively charged,

protons equal to number of electrons. Na (protons 11, i.e., number of protons more than the number of electrons.

electrons 11), Cl (Protons – 17, electrons –17) Anions are negatively charged, i.e., number of protons less

than the number of electrons.

Na+ (protons 11, electrons 10), Cl– (protons 17, electrons
18)

2. Except noble gases, atoms have less than 8 electrons Ions have generally 8 electrons in the outermost orbit, i.e.,

in the outermost orbit ns2np6 configuration.

Na 2,8,1; Ca 2,8,8,2 Na+ 2,8; Cl– 2,8,8

Cl 2,8,7; S 2,8,6 Ca2+ 2,8,8

3. Chemical activity is due to loss or gain or sharing of The chemical activity is due to the charge on the ion.

electrons as to acquire noble gas configuration Oppositely charged ions are held together by electrostatic

forces

(5) Characteristics of ionic compounds

(i) Physical state : Electrovalent compounds are generally crystalline is nature. The constituent ions are
arranged in a regular way in their lattice. These are hard due to strong forces of attraction between
oppositely charged ions which keep them in their fixed positions.

(ii) Melting and boiling points : Ionic compounds possess high melting and boiling points. This is because
ions are tightly held together by strong electrostatic forces of attraction and hence a huge amount of

energy is required to break the crystal lattice. For example order of melting and boiling points in
halides of sodium and oxides of IInd group elements is as,

NaF > NaCl > NaBr > NaI, MgO > CaO > BaO

(iii) Hard and brittle : Electrovalent compounds are har in nature. The hardness is due to strong forces of
attraction between oppositely charged ion which keep them in their alloted positions. The brittleness
of the crystals is due to movement of a layer of a crystal on the other layer by application of external
force when like ions come infront of each other. The forces of repulsion come into play. The breaking
of crystal occurs on account of these forces or repulsion.

(iv) Electrical conductivity : Electrovalent solids donot conduct electricity. This is because the ions remain
intact occupying fixed positions in the crystal lattice. When ionic compounds are melted or dissolved
in a polar solvent, the ions become free to move. They are attracted towards the respective electrode
and act as current carriers. Thus, electrovalent compounds in the molten state or in solution conduct
electricity.

(v) Solubility : Electrovalent compounds are fairly soluble in polar solvents and insoluble in non-polar
solvents. The polar solvents have high values of dielectric constants. Water is one of the best polar
solvents as it has a high value of dielectric constant. The dielectric constant of a solvent is
defined as its capacity to weaken the force of attraction between the electrical charges immersed in that
solvent. In solvent like water, the electrostate force of attraction between the ions decreases. As a result
there ions get separated and finally solvated.

The values of dielectric constants of some of the compounds are given as :

Compound Water Methyl AIc Ethyl AIc. Acetone Ether
Dielectric constant
81 35 27 21 4.1

Capacity to dissolve electrovalent compounds decreases

Lattice energy and solvation energy also explains the solubility of electrovalent compounds. These
compounds dissolve in such a solvent of which the value of solvation energy is higher than the lattice
energy of the compound. The value of solvation energy depends on the relative size of the ions. Smaller the ion
more of solvation, hence higher the solvation energy.

Note :  Some ionic compounds e.g., BaSO4 , PbSO4 , AgCl, AgBr, AgI, Ag 2CrO4 etc. are sparingly soluble

in water because in all such cases higher values of lattice energy predominates over solvation energy.

(vi) Space isomerism :The electrovalent bonds are non-rigid and non-directional. Thus these compound
do not show space isomerism e.g. geometrical or optical isomerism.

(vii) Ionic reactions : Electrovalent compounds furnish ions in solution. The chemical reaction of these
compounds are ionic reactions, which are fast. Ionic bonds are more common in inorganic
compounds.

K + Cl − + A+g NO− 3 → A+g C−l ↓ + K+ −
(Precipitate)
NO3

(viii) Isomorphism : Electrovalent compounds show isomorphism. Compound having same electronic

structures are isomorphous to each other.

(ix) Cooling curve : Cooling curve of an ionic compound is not smooth, it has two break points
corresponding to time of solidification.

A  liquid

M.Pt- B C
Temp

D

Time
Solidification time

(x) Electrovalency and Variable electrovalency : The capacity of an element to form electro-valent or ionic
bond is called its electro-valency or the number of electrons lost or gained by the atom to form ionic
compound is known as its electro-valency.
Certain metallic element lose different number of electrons under different conditions, thereby
showing variable electrovalency. The following are the reasons:

(a) Unstability of core : The residue configuration left after the loss of valency electrons is called kernel or
core. In the case of the atoms of transition elements, ions formed after the loss of valency electrons do
not possess a stable core as the configuration of outermost shell is not ns 2np6 but ns 2np6 d1 to 10 . The
outer shell lose one or more electrons giving rise to metal ions of higher valencies.

Example : Fe 2+ = 3s 2 3p6 3d 6 ,4s 0 (not stable)

Fe 3+ = 3s 2 3p6 3d 5 ,4s 0 (stable)

(b) Inert pair effect : Some of heavier representative elements of third, fourth and fifth groups having
configuration of outermost shell ns 2 np1, ns 2 np 2 and ns 2 np 3 show valencies with a difference of
2, i.e., (1 : 3) (2 : 4) (3 : 5) respectively. In the case of lower valencies, only the electrons present in p–
subshell are lost and ns2 electrons remain intact. The reluctance of s-electron pair to take part in bond
formation is known as the inert pair effect.

Covalent bond.

Covalent bond was first proposed by Lewis in 1916. The bond formed between the two atoms by mutual
sharing of electrons so as to complete their octets or duplets (in case of elements having only one shell) is called
covalent bond or covalent linkage. A covalent bond between two similar atoms is non-polar covalent bond
while it is polar between two different atom having different electronegativities. Covalent bond may be single,
double or a triple bond.

Example : Formation of chlorine molecule : chlorine atom has seven electrons in the valency shell. In the
formation of chlorine molecule, each chlorine atom contributes one electron and the pair of electrons is shared
between two atoms. both the atoms acquire stable configuration of argon.

•• ** * •• ∗∗
*
• Cl • ∗ Cl → • Cl • Cl ∗ or Cl − Cl
• • * ∗
•• **
•• ∗∗
( 2, 8, 7) ( 2, 8, 7)
(2,8,8) (2,8,8)

Formation of HCl molecule : Both hydrogen and chlorine contribute one electron each and then the pair of
electrons is equally shared. Hydrogen acquires the configuration of helium and chlorine acquires the configuration
of argon.

** ∗∗ or H − Cl
H• Cl * H Cl
∗ * → • ∗
* ∗
**
(1) (2, 8, 7) ∗∗
(2) (2, 8,8)

Formation of water molecule : Oxygen atom has 6 valency electrons. It can achieve configuration of neon by
sharing two electrons, one with each hydrogen atom.

** H ∗∗ or H − O − H
O H
H•+ ∗O∗+ • H → • ∗
* • (2)
**
(1) (2, 8,7) (1) ∗∗

(2) (2, 8,8)

Formation of O2 molecule : Each oxygen atom contributes two electrons and two pairs of electrons are the
shared equally. Both the atoms acquire configuration of neon.

** •• ∗ ∗ •• or O = O
O * ••O O O
* + → ∗ •
• •
** ••
(2, 6) ∗ ∗ ••

(2, 6) (2, 8) (2, 8)

Formation of N2 molecule : Nitrogen atom has five valency electrons. Both nitrogen atoms achieve
configuration of neon by sharing 3 pairs of electrons, i.e., each atom contributes 3 electrons.

N N* *** ••• • → N* **∗ N••• • or N ≡ N
• •
* *

(2, 5) (2, 5) (2, 8) (2, 8)

Some other examples are : H2S, NH3, HCN, PCl3, PH3, C2 H 2 , H2, C2H4, SnCl4 , FeCl 3 , BH 3 , graphite,
BeCl 2 etc.

(1) Conditions for formation of covalent bonds

(i) Number of valency electrons : The combining atoms should be short by 1, 2 or 3 electrons in the
valency shell in comparison to stable noble gas configuration.

(ii) Electronegativity difference : Electronegativity difference between the two atoms should be zero or
very small.

(iii) Small decrease in energy : The approach of the atoms towards one another should be accompanied
by decrease of energy.

(2) Characteristics of covalent compounds

(i) Physical state : These exist as gases or liquids under the normal conditions of temperature and
pressure. This is because very weak forces of attraction exist between discrete molecules. Some
covalent compounds exist as soft solids.

(ii) Melting and boiling points : Diamond, Carborandum (SiC), Silica (SiO2), AlN etc. have giant three
dimensional network structures; therefore have exceptionally high melting points otherwise these
compounds have relatively low melting and boiling points. This is due to weak forces of attraction
between the molecules.

(iii) Electrical conductivity : In general covalent substances are bad conductor of electricity. Polar covalent
compounds like HCl in solution conduct electricity. Graphite can conduct electricity in solid state since
electrons can pass from one layer to the other.

(iv) Solubility : These compounds are generally insoluble in polar solvent like water but soluble in non-
polar solvents like benzene etc. some covalent compounds like alcohol, dissolve in water due to
hydrogen bonding.

(v) Isomerism : The covalent bond is rigid and directional. These compounds, thus show isomerism
(structural and space).

(vi) Molecular reactions : Covalent substances show molecular reactions. The reaction rates are usually
low because it involves two steps (i) breaking of covalent bonds of the reactants and (ii) establishing of
new bonds while the ionic reactions involved only regrouping of ions.

(vii) Covalency and Variable covalency : The number of electrons contributed by an atom of the element
for sharing with other atoms is called covalency of the element. The variable covalency of an element
is equal to the total number of unpaired electrons in s, p and d-orbitals of its valency shell.

Covalency = 8 – [Number of the group to which element belongs]

Examples : Nitrogen 7 N = 2s Covalency of N = 3
2p
The element such as P, S, Cl, Br, I have vacant d-orbitals in their valency shell. These elements show variable

covalency by increasing the number of unpaired electrons under excited conditions. The electrons from paired

orbitals get excited to vacant d-orbitals of the same shell.

Promotion energy : The energy required for excitation of electrons.

Promotion rule : Excitation of electrons in the same shell

Phosphorus : Ground state
Phosphorus Covalency 3

3s 3p
: Excited state

3s 3p Covalency-5
PCl3 is more stable due to inert pair effect.
3d

Sulphur : Ground state

Sulphur : 3s 3p 3d Covalency-2 (as in SF2)
Excited state 3d Covalency-4 (as in SF4)
1st excited state
3s 3p

2nd excited state 3s 3p 3d Covalency-6 (as in SF6)

So variable valency of S is 2, 4 and 6.

Iodine can have maximum 7 unpaired electrons in its orbitals. It's variable valencies are 1, 3, 5 and 7.

Four elements, H, N, O and F do not possess d-orbitals in their valency shell. Thus, such an excitation is not
possible and variable valency is not shown by these elements. This is reason that NCl3 exists while NCl5 does not.

(3) The Lewis theory : The Lewis theory gave the first explanation of a covalent bond in terms of electrons
that was generally accepted. The tendency of atoms to achieve eight electrons in their outermost shell is
known as lewis octet rule. Octet rule is the basis of electronic theory of valency. It is suggested that valency
electrons themselves are responsible for chemical combination. The valency electrons in atoms are shown in
terms of Lewis dot formulae. To write Lewis formulae for an element, we write down its symbol surrounded by a

number of dots or crosses equal to the number of valency electrons. Lewis dot formulae are also used to represent
atoms covalently bonded in a molecule. Paired and unpaired valency electrons are also indicated.

Lewis symbols for the representative elements are given in the following table :

1 2 13 14 15 16 17
IA IIA IIIA IVA
Group VA VIA VIIA
•X• • •
Lewis symbol X • • X• •X• • •• • ••
• X• • X• • X
• •• •
•• ••

CO is not an exception to octet rule : C− ≡ O+ : or : C = O :
..

(4) Failure of octet rule :

There are several stable molecules known in which the octet rule is violated i.e., atoms in these molecules have
number of electrons in the valency shell either short of octet or more than octet.

In BF3 molecules, boron atom forms three single covalent bonds with three fluorine atoms, i.e., it attains six
electrons in the outer shell.

B F* • • F• • • • F
|
•• B−F
|
* * + 3 • • • F F• •• •∗ • ••• F
• • • * * •
• B
•• ••

PCl5 molecule : Phosphorus atom have five electrons in valency shell. It forms five single covalent bonds with
five chlorine atoms utilising all the valency electrons and thereby attains 10 electrons in the outer shell.

• •C• l • Cl Cl • •C• l••
• • P •

•∗ •∗

P* •• C• •l ∗ ••
• Cl
** * * + 5 • Cl • • • P •
• • • ∗ •• • Cl Cl
Cl
• ••

Cl •∗ •∗

• •• • • Cl••
• • •

••

(i) Sugden’s concept of singlet linkage explains the stability of such molecules. In PCl5 , three chlorine atoms
phosphorus achieves 8 electrons in the outermost shell.

• •C• l • Cl
• • Cl

•∗ Cl P

C• •l ∗ ••• Cl
Cl Cl
• • P •
• ∗ •• •

••

•∗ ∗

• Cl • • •C•• l••
• •• • •

This structure indicates that the nature of two chlorine atoms is different than the other three as singlet
linkage is weaker than normal covalent bond. The above observation is confirmed by the fact that on
heating, PCl5 dissociates into PCl3 and Cl2 .

PCl5 ⇌ PCl3 + Cl2

Similarly, in SF6 four singlet linkages are present while in IF7 , six singlet linkages are present.

• • • • •• F
F• • F• • F
• • F
• • S F

∗ ∗ F
F
• •• F• • •
• F S
• ∗ •
• ••
••

F• •∗ •∗
• •
•• • F •

•• ••

(ii) Sidgwick’s concept of maximum covalency
• This rule states that the covalency of an element may exceed four and octet can be exceeded.
• The maximum covalency of an element actually depends on the period of periodic table to which it
belongs.
• This rule explains the formation of PCl5 and SF6.

• This also explains why nitrogen does not form NF5 or NCl5 because nitrogen belongs to second
period and the maximum covalency of nitrogen is three.

(iii) Odd electron bond : In 1916 Luder postulated that there are number of stable molecules in which double
bonds are formed by sharing of an odd number of electrons, i.e., one, three, five, etc., between the two
bonded atoms. the bonds of this type are called odd electron bonds.

The normal valence bond structure of oxygen molecule, •• ** * , fails to account for the paramagnetic
• O O *
• =

nature of oxygen. Thus, structure involving three electrons bond has been suggested by Pauling. The

following structure : • O • • • → O•• . Explains the paramagnetic nature and high dissociation energy of
• •••

oxygen molecule.

N  –
 
Some other examples are : • N O •  • O O • 
• • • •
•• ••
• O O •  
Nitric oxide • •
(NO) ••
•• −
Superoxide ion (O 2 )
Nitrogen dioxide (NO2)

The number of singlet bonds = Total number of bonds – Number of electrons required to complete the octet.

Properties of Odd Electron bond

(i) The odd electron bonds are generally established either between two like atoms or between different
atoms which have not more than 0.5 difference in their electronegativities.

(ii) Odd electron bonds are approximately half as strong as a normal covalent bond.

(iii) Molecules containing odd electrons are extremely reactive and have the tendency to dimerise.

(iv) Bond length of one electron bond is greater than that of a normal covalent bond. Whereas the bond
length of a three electron bond is intermediate between those of a double and a triple bond.

(v) One electron bond is a resonance hybrid of the two structures i.e., A • B ←→ A • B

Similarly, a three electron bond is a resonance hybrid of the two structures i.e., A• • B ←→ A • • B
• •

(5) Construction of structures for molecules and poly atomic ions : The following method is
applicable to species in which the octet rule is not violated.

(i) Determine the total number of valence electrons in all the atoms present, including the net charge on
the species (n1).

(ii) Determine n2 = [2 × (number of H atoms) + 8 × (number of other atoms)].
(iii) Determine the number of bonding electrons, n3, which equals n2 – n1. No. of bonds equals n3/2.
(iv) Determine the number of non-bonding electrons, n4, which equals n1 – n3. No. of lone pairs equals

n4/2.
(v) Knowing the central atom (you’ll need to know some chemistry here, math will not help!), arrange and

distribute other atoms and n3/2 bonds. Then complete octets using n4/2 lone pairs.
(vi) Determine the ‘formal charge’ on each atom.

(vii) Formal Charge = [valence electrons in atom) – (no. of bonds) – (no. of unshared electrons)]

(viii) Other aspects like resonance etc. can now be incorporated.

Illustrative examples :

(i) CO32−; n1 = 4 + (6 × 3) + 2 = 24 [2 added for net charge]
n2 = (2 × 0) + (8 × 4) = 32 (no. H atom, 4 other atoms (1’C’ and 3 ‘O’)
n3 = 32 – 24 = 8, hence 8/2 = 4 bonds
n4 = 24 – 8 = 16, hence 8 lone pairs.

Since carbon is the central atom, 3 oxygen atoms are to be arranged around it, thus,
O

|

O − C − O , but total bonds are equal to 4.

..

O .O :

| . | ..

Hence, we get O − C = O . Now, arrange lone pairs to complete octet : O − C = O :
..

(ii) CO2; n1 = 4 + (6 × 2 ) = 16

n2 = (2 × 0) + (8 × 3) = 24
n3 = 24 – 16 = 8, hence 4 bonds
n4 = 16 – 8 = 8, hence 4 lone-pairs
Since C is the central atom, the two oxygen atoms are around to be arranged it thus the structure would
be; O – C – O, but total no. of bonds = 4

.. ..

Thus, O = C = O. After arrangement of lone pairs to complete octets, we get, : O = C = O : and thus

.. ..

final structure is : O = C = O :

Co-ordinate covalent or Dative bond.

This is a special type of covalent bond where the shared pair of electrons are contributed by one species only
but shared by both. The atom which contributes the electrons is called the donor while the other which only shares
the electron pair is known as acceptor. This bond is usually represented by an arrow ( → ) pointing from donor to
the acceptor atom.

For example, in BF3 molecule, boron is short of two electrons. So to complete its octet, it shares the lone pair
of nitrogen in ammonia forming a dative bond as shown in figure

∗∗ ∗∗

H ∗ F ∗ H ∗ F ∗ HF
∗ ∗ ∗ ∗
||
•∗ •∗ ∗∗ •∗ •∗ ∗∗
* H − N→ B− F
H*• N * + B • F ∗ → H • N ∗ B • F ∗ → ||
∗ ∗ * ∗ ∗ ∗ HF

•∗ •∗ ∗∗ •∗ •∗ ∗∗
H
∗ F ∗ H ∗ F ∗
∗ ∗ ∗ ∗
∗∗
∗∗

Formation of a co-ordinate
bond between NH3 and BF3

Examples : CO, N2O, H2O2, N2O3, N2O4, N2O5, HNO3, NO3− , SO2, SO3, H2SO4, SO42− , SO22− ,

H 3 PO4 , H 4 P2O7 , H 3 PO3 , Al2Cl6 (Anhydrous), O3 , SO2Cl2 , SOCl2 , HIO3 , HClO4 , HClO3 , CH 3 NC, N 2 H + ,
5

CH 3 NO2 , NH + , [Cu(NH 3 )4 ]2+ etc.
4

(1) Characteristics of co-ordinate covalent bond

(i) Melting and boiling points : Their melting and boiling points are higher than purely covalent
compounds and lower than purely ionic compounds.

(ii) Solubility : These are sparingly soluble in polar solvent like water but readily soluble in non-polar
solvents.

(iii) Conductivity : Like covalent compounds, these are also bad conductors of electricity. Their solutions
or fused masses do not allow the passage to electricity.

(iv) Directional character of bond : The bond is rigid and directional. Thus, coordinate compounds show
isomerism.

Table: Electron dot formulae and Bond formulae or Dash formulae of some compounds

No. Molecular formula Electron dot formula Dash formula or Bond formula
1. Sodium chloride NaCl
Na+ • C• •l • – Na+Cl −
× •
•• Cl −Mg ++Cl −
Cl −Ca++Cl −
2. Magnesium MgCl2 • C• •l •– Mg++•×C• •l • –
chloride × • •• • Mg ++O− −
••

3. Calcium chloride CaCl2 •×C• •l • –Ca++•×C• •l • –
•• • •• •

4. Magnesium oxide MgO Mg++ O×• ••– –
• ••
×

5. Sodium sulphide Na2S Na+ S•×••• – – Na+ Na+S− − Na+
• •×
H −Ca++ H −
6. Calcium hydride CaH 2 H•×– Ca++×• H–
F − Al 3+ F −
7. Aluminium AlF3 •• ••– •3•+–•×•••••• – F−
flouride ×
F Al F• × • H − Cl
F• ••
• H −O− H
••
H−S−H
8. Hydrogen HCl H×• C• •l ••
chloride H2O H
H2S ••
9. Water NH 3 |
H • O• •• H
10. Hydrogen × H−N
sulphide • •×
|
11. Ammonia H ×• S• •×• H
H
•• H−C≡ N

H H
H ×•HN×• ×•••
|
12. Hydrogen cyanide HCN H C N× ××× ••• •
• • H − C− H

13. Methane CH 4 H |
H •× •CH•×××• H
H
14. Ethane C2 H 6 HH HH

H • H•C• ×××× C•H• ×××• H ||
×
H − C− C− H
15. Ethene C2 H 4 HH
C× • C× • ||
××××
H× • H× • HH
HH
16. Ethyne C2 H 2 H C• ××× C•× H
17. Phosphene PH3 ||
× ×××
C=C

||

HH

H −C ≡ C−H

H • •P••×H H − P− H
×
H• × |

18. Phosphorous H
trichloride
PCl 3 × C×× ××l××•×C×•P•××l•×•××C×× ××l × Cl − P − Cl
× ×
|
19. Sodium hydroxide NaOH Na+ • O• • •× H –
* Cl
••
Na + [O − H]−
20. Potassium KCN K C N+ × ××× ••• –
cyanide CaCO3 * • K + [C ≡ N]−

21. Calcium
carbonate Ca O OC O++ • • • ••*• 2–   2−
• • • O O
*• •× ×• • Ca ++  − C− 
• •×••×
• ||

O
C = O
22. Carbon mono CO C O• ••×××× ×
oxide ×

23. Nitrous oxide N2O N N O× ×× × • • •• N ≡N→O
24. Hydrogen H 2O2 ×× × • •
N 2O3 × ×× H − O − O − H or H − O → O
peroxide
25. Dinitrogen H3O+ H • O• ••• O• •×• H or H • OH•• •×•••O• •••• |
N 2O4 × •• × H
trioxide ••
26. Hydronium ion O = N− N = O
• ••× × × • • ↓
27. Nitrogen dioxide •× ×× × • O
O N N O• • •
H − O → H+

× ×• •• ×• |

O• H
O=N−N =O

↓↓
H •× HO×• •••• H+ OO

• • ••××× × × × • • • O = N− O − N = O
• • × ×× • × • • • ↓↓
O ON NO O••• • •• ••• •• OO

28. Nitrogen N 2O5 × × ×× • • × ×• • × × ×× H−O−N =O
pentaoxide O N O N O× ↓
×• • •×× × • •× × O
× × × •×
O O× × × × × −O− N = O
×× × ↓
× O

29. Nitric acid HNO3 H O N O×*×× •× × × H−O−N =O
• •×
• × ×× −O− N = O
× × ××•
O×× × × O←S=O

30. Nitrate ion NO3− – O N O×*× ×• × ×× O← S =O
× × •× × ↓
•× O
×• •×
× OO
O× × × ↑↑
× H −O− S −O−O− S −O− H
↓↓
31. Nitrous acid HNO2 H • O× × N• • •• × ×O× × OO
32. Nitrite ion NO2− × • × ×
33. Sulphur dioxide SO2 ×× × H − O − Cl
34. Sulphur trioxide SO3
× × • • •• ×× × ×× H − O − Cl → O
O N O–*× × ×•× ×
OO
O S O× × ×• • •× ×× O Cl − O − Cl O
• •× × OO
×× •×
×

×× ×• × ××
× •• •× ×
O S O× × ••×

××
×
× ×

35. Peroxysulphuric H 2S2O8
acid
(Marshal acid) • • •• • • ••
O• •
•O• O• × × • O• •• •O• × × O• • •
H* S• × × • S• × × • H
• • *

O O• • • × ×• • •
• • ••
• • • × ×• • •
• • ••

36. Hypochlorous HOCl H * × O× ×× • C• •l •
acid HClO2 •
Cl 2 O7 ×× ••
37. Chlorous acid
H * • O• • • × C× ×l × O• • •
38. Perchloric × •
anhydride •• ×× ••

• • •• • • ••
O O• • • • •
O COl O COl O•••× × •• × × ×× • ••
• • × • • × × • ••
× × ×• ×•
• ×• ••

••• • ••• •

39. Sulphuric acid H 2SO4 • • •• O

O• ↑
H −O− S −O− H

• •• × ×• • • H ↓
H • O OS O• ×× • O
* • × × • • * O
• •
• • ↑
• •
−O − S− O−
40. Sulphate ion SO42− O• • • •• O↓

• H −O − S−O − H
– • • •• × × • • • •– ↓
O S O* * O
• • ×× • •
• × ×• −O − S− O−
O• • • • ↓
41. Sulphurus acid H 2SO3 O
H • • •••••×•××•××•×•• O• •• H
* O
O OS• ••* H − O − P↑ − O − H

42. Sulphite ion SO32− O OS O–• • •••••×•××•××•×•• • •• – |
* • ••*
O
43. Phosphoric acid H3 PO4 H*×O×××××××•×××OH•PO•×*×•××××•××O××××*× H
|
44. Pyrophosphoric H 4 P2O7 ×O× ××××•×××*OH•PO•×××•×××•×××O××××*×
acid H
O××× × ××
O*××××• O*••PH×•×•××× H OO
H ×
↑↑
××
× H −O− P−O− P−O−H

45. Persulphuric acid H 2SO5 × ×× ||
(caro’s acid) ×
O× × × OO
H ×* O OS O O××• • • •× × ××× × ×*× H
×× • • × × × ||
× ×
× × HH
× ××
O
46. Thiosulphurous H 2 S2O3 • • ••
acid S× × • ↑
H ×* O S× × • •• O× × H H −O− S −O−O− H
• ×
• • × ××* ↓
× × • × O
O× × × ×
S

H − O − S− O − H
O↓

47. Phosphorous acid H3 PO3 H H

H *× × × • •× O×× ××*× H |
× × •
O P× H −O− P−O−H
••× O↓
× ×××

×

48. Aluminium Al 2 Cl 6 C• •l C• •l C• •l Cl Al Cl Al Cl
chloride (Anhydrous) Cl Cl Cl
• •• • • •
• • • •

Al Al Cl
Cl Cl •• ••
• • •• ••
• •• • ••

49. Ozone O3 O• • O

O O• •• OO
•• ••
• •• Cl

50. Sulphuryl SO2 Cl 2 × O×× ××**•*•*C*C*S•***•l*l••****O×××××× |
chloride SOCl2 ×
HIO3 O← S →O
51. Sulphonyl O****** • •S• • C× ×l ×
chloride • C•×l × × |
× ××
52. Iodic acid × ×× × Cl
× O ← S − Cl

H O OI O×* × ×××××••×•••×••×××× ×××× |
× Cl

53. Perchloric acid HClO4 O× ×× H−O− I →O

× O
O× × ×× O× × ×
O
H * ×× • C• •l • × ×
× × • × ↑
O•
•× H − O − Cl → O
×× × O↓
× ×
S
54. Hyposulphurous H 2 S2O4 H O SS*××××××•••••••••×•×•• O× ×××
acid × ↑
×× O× ××* H
H − O − S− O − O − H
O× × ×× O↓
S
××
H − O − O − S↑ − O − O − H
55. Pyrosulphurus H 2S2O5 S××× ×××××•••••••••×××••• × ××× × O↓
acid H O O S O O H*×× × × ×
×* H − O − Cl → O
O×××× ×× ↓
O
××

56. Chloric acid HClO3 H * O××××•×××C••O× ×••l××•• O× ×
× × ××
×

Polarity of covalent bond.

A covalent bond in which electrons are shared equally between bonded atoms, is called non polar covalent
bond while a covalent bond, in which electrons are shared unequally and the bonded atoms acquire a partial
positive and negative charge, is called a polar covalent bond. The atom having higher electronegativity draws the
bonded electron pair more towards itself resulting in partial charge separation. This is the reason that HCl molecule
in vapour state contains polar covalent bond

Polar covalent bond is indicated by notation : H+δ – C−δl

(1) Bond polarity in terms of ionic character : The polar covalent bond, has partial ionic character.
Which usually increases with increasing difference in the electronegativity (EN) between bonded atom

H–F H – Cl H – Br H–I

EN 2.1 4.0 2.1 3.0 2.1 2.8 2.1 2.5

Difference in EN 1.9 0.9 0.7 0.4

Ionic character decreases as the difference in electronegativity decreases

(2) Percentage ionic character : Hennay and Smith gave the following equation for calculating the
percentage of ionic character in A–B bond on the basis of the values of electronegativity of the atoms A and B.

Percentage of ionic character = [16 (χ A − χ B) + 3.5 (χ A − χ B)2] .
Whereas (xA − xB) is the electronegativity difference. This equation gives approximate calculation of
percentage of ionic character, e.g., 50% ionic character corresponds to (xA ∼ xB) equals to 1.7.

Dipole moment.

“The product of magnitude of negative or positive charge (q) and the distance (d) between the centres of
positive and negative charges is called dipole moment”.

It is usually denoted by µ. Mathematically, it can be expressed as follows :

µ = Electric charge × bond length
As q is in the order of 10–10 esu and d is in the order of 10–8 cm, µ is in the order of 10–18 esu cm. Dipole
moment is measured in “Debye” (D) unit. 1D = 10−18 esu cm = 3.33 × 10−30 coulomb metre.
Generally, as electronegativity difference increases in diatomic molecules, the value of dipole moment
increases. Greater the value of dipole moment of a molecule, greater the polarity of the bond between the atoms.
Dipole moment is indicated by an arrow having a symbol ( ) pointing towards the negative end. Dipole

moment has both magnitude and direction and therefore it is a vector quantity.
Symmetrical polyatomic molecules are not polar so they do not have any value of dipole moment.

FH

O CO B C
FF HH

H

µ = 0 due to symmetry
Some other examples are – CCl4,CS2 , PbCl4 , SF6 , SO3 , C6 H6 , naphthalene and all homonuclear molecules (H2,

O2, Cl2 etc)

Note :  Benzene, Naphthalene have zero dipole moment due to planar structure.

 Amongst isomeric dihalobenzenes, the dipole moment decreases in the order : o > m > p.

A molecule of the type MX4, MX3 has zero dipole moment, because the σ-bonding orbitals used by
M(Z < 21) must be sp3, sp2 hybridization respectively (e.g. CH4, CCl4, SiF4 , SnCl4, BF3 , AlCl3 etc.)

sp3 sp2
Unsymmetrical polyatomic molecules always have net value of dipole moment, thus such molecules are
polar in nature. H2O, CH3Cl, NH3, etc are polar molecules as they have some positive values of dipole moments.

Cl

O S C N
HH OO HH HH
Water µ = 1.84D
Sulphur dioxide H H
Methyl chloride Ammonia
µ = 1.60D µ = 1.46D
µ = 1.86D

µ ≠ 0 due to unsymmetry

Some other examples are – CH3Cl, CH2Cl2, CHCl3, SnCl2, ICl, C6H5CH3 , H2O2, O3, Freon etc.

Applications of dipole moment

(i) In determining the symmetry (or shape) of the molecules : Dipole moment is an important factor in
determining the shape of molecules containing three or more atoms. For instance, if any molecule
possesses two or more polar bonds, it will not be symmetrical if it possesses some molecular dipole
moment as in case of water (µ = 1.84D) and ammonia (µ = 1.49D). But if a molecule contains a

number of similar atoms linked to the central atom and the overall dipole moment of the molecule is
found to be zero, this will imply that the molecule is symmetrical, e.g., in case of BF3 , CH4 , CCl4 etc.,

(ii) In determining percentage ionic character : Every ionic compound having some percentage of
covalent character according to Fajan’s rule. The percentage of ionic character in a compound having
some covalent character can be calculated by the following equation.

The percent ionic character = Observed dipole moment × 100
Calculated dipole moment assuming 100% ionic bond

(iii) In determining the polarity of bonds as bond moment : As µ = q × d , obviously, greater is the

magnitude of dipole moment, higher will be the polarity of the bond. The contribution of individual
bond in the dipole moment of a polyatomic molecule is termed as bond moment. The measured
dipole moment of water molecule is 1.84 D. This dipole moment is the vectorial sum of the individual
bond moments of two O-H bonds having bond angle 104.5o.

Thus, µobs = 2µO−H cos 52.25 or 1.84 = 2µO – H × 0.6129 ; µO – H = 1. 50 D

Note :  ∆ EN ∝ dipole moment, so HF > HCl > HBr > HI , Where, ∆EN = Electronegativity difference

 ∆ EN ∝ bond polarity, so HF > H2O > NH3 > H2S.

If the electronegativity of surrounding atom decreases, then dipole moment increases. NCl3 < NBr3 < NI3

(iv) To distinguish cis and trans forms : The trans isomer usually possesses either zero dipole moment or

very low value in comparision to cis–form

H − C − Cl H − C − Cl

|| ||

H − C − Cl Cl − C − H

Cis – 1, 2 – dichloro ethene µ = 1.9 D Trans – 1, 2 –dichloro ethene, µ = 0

Example: Calculate the % of ionic character of a bond having length = 0.92 Å and 1.91 D as its observed dipole moment.

(a) 43.25 (b) 86.5 (c) 8.65 (d) 43.5

Solution: (a) Calculated µ considering 100% ionic bond [When we consider a compound ionic, then each ionic sphere

should have one electron charge on it of 4.80 × 10 −10 esu (in CGS unit) or 1.60 × 10 −19 C (in SI unit)]
= 4.8 × 10–10 × 0.92 × 10–8 esu cm = 4.416 D

% Ionic character = 1.91 × 100 = 43.25.
4.416

Important Tips

The dipole moment of CO molecule is greater than expected. This is due to the presence of a dative (co-ordinate) bond.
Critical temperature of water is higher than that of O2 because H2O molecule has dipole moment.
Liquid is not deflected by a non uniform electrostatic field in hexane because of µ = 0

Change of ionic character to covalent character and Fajan’s rule.

Although in an ionic compound like M+X– the bond is considered to be 100% ionic, but it has some covalent
character. The partial covalent character of an ionic bond has been explained on the basis of polarization.

Polarization : When a cation of small size approaches an anion, the electron cloud of the bigger anion is
attracted towards the cation and hence gets distorted. This distortion effect is called polarization of the anion. The
power of the cation to polarize nearby anion is called its polarizing power. The tendency of an anion to get distorted
or polarized by the cation is called polarizability. Due to polarization, some sort of sharing electrons occurs between
two ions and the bond shows some covalent character.

Fajan’s rule : The magnitude of polarization or increased covalent character depends upon a number of
factors. These factors were suggested by Fajan and are known as Fajan’s rules.

Factors favouring the covalent character

(i) Small size of cation : Smaller size of cation greater is its polarizing power i.e. greater will be the
covalent nature of the bond. On moving down a group, the polarizing power of the cation goes on
decreasing. While it increases on moving left to right in a period. Thus polarizing power of cation

follows the order Li + > Na + > K + > Rb + > Cs + . This explains why LiCl is more covalent than KCl .

(ii) Large size of anion : Larger the size of anion greater is its polarizing power i.e. greater will be the
covalent nature of the bond. The polarizability of the anions by a given cation decreases in moving left
to right in a period. While it increases on moving down a group. Thus polarzibility of the anion follows

the order I − > Br − > Cl − > F − . This explains why iodides are most covalent in nature.

(iii) Large charge on either of the two ions : As the charge on the ion increases, the electrostatic attraction
of the cation for the outer electrons of the anion also increases with the result its ability for forming the
covalent bond increases. FeCl3 has a greater covalent character than FeCl2. This is because Fe3+ ion
has greater charge and smaller size than Fe2+ ion. As a result Fe3+ ion has greater polarizing power.
Covalent character of lithium halides is in the order LiF < LiCl < LiBr < LiI.

(iv) Electronic configuration of the cation : For the two ions of the same size and charge, one with a
pseudo noble gas configuration (i.e. 18 electrons in the outermost shell) will be more polarizing than a
cation with noble gas configuration (i.e., 8 electron in outer most shell). CuCl is more covalent than
NaCl, because Cu+ contains 18 electrons in outermost shell which brings greater polarization of the
anion.

Important tips

∆en (Electronegativity difference) ∝ Ionic character
Covalent character

Increase of polarization brings more of covalent character in an ionic compound. The increased covalent character is indicated by the
decrease in melting point of the ionic compound

Decreasing trends of melting points with increased covalent character

NaF < NaCl < NaBr < NaI (size of anion increases)

M.Pt (oC) 988 801 755 651

BaCl2 < SrCl2 < CaCl2 < MgCl2 < BeCl2 (size of cation decreases)

M.Pt (oC) 960 872 772 712 405

Lithium salts are soluble in organic solvents because of their covalent character

Sulphides are less soluble in water than oxides of the same metal due to the covalent nature of sulphur.

Quantum theory (Modern theory) of covalent bond and overlapping.

(1) A modern Approach for covalent bond (Valence bond theory or VBT)

(i) Heitler and London concept.

(a) To form a covalent bond, two atoms must come close to each other so that orbitals of one overlaps
with the other.

(b) Orbitals having unpaired electrons of anti spin overlaps with each other.

(c) After overlapping a new localized bond orbital is formed which has maximum probability of finding
electrons.

(d) Covalent bond is formed due to electrostatic attraction between radii and the accumulated electrons
cloud and by attraction between spins of anti spin electrons.

(e) Greater is the overlapping, lesser will be the bond length, more will be attraction and more will be
bond energy and the stability of bond will also be high.

(ii) Pauling and slater extension
(a) The extent of overlapping depends upon: Nature of orbitals involved in overlapping, and nature of

overlapping.

(b) More closer the valence shells are to the nucleus, more will be the overlapping and the bond energy
will also be high.

(c) Between two sub shells of same energy level, the sub shell more directionally concentrated shows more
overlapping. Bond energy : 2s − 2s < 2s − 2p < 2p − 2p

(d) s -orbitals are spherically symmetrical and thus show only head on overlapping. On the other hand,

p -orbitals are directionally concentrated and thus show either head on overlapping or lateral

overlapping.

(iii) Energy concept

(a) Atoms combine with each other to minimize their energy.

(b) Let us take the example of hydrogen molecule in which the bond between two hydrogen atoms is

quite strong. ••
(c) During the formation of hydrogen molecule, when two
Attraction

hydrogen atoms approach each other, two types of + Repulsion +
interaction become operative as shown in figure. The force Attraction ••

of attraction between the molecules of one atom and

electrons of the other atom. The force of repulsion between the nuclei of reacting atoms and electrons

of the reacting atoms

(d) As the two hydrogen atoms approach each other from the O+ve
infinite distance, they start interacting with each other when –ve
the magnitude of attractive forces is more than that of E P.E. decreases as
repulsive forces a bond is developed between two atoms. d0

(e) The decrease in potential energy taking place during formation
of hydrogen molecule may be shown graphically (→)

)

(f) The inter nuclear distance at the point O have minimum

energy or maximum stability is called bond length.

(g) The amount of energy released (i.e., decrease in potential energy) is known as enthalpy of formation.

(h) From the curve it is apparent that greater the decrease in potential energy, stronger will be the bond
formed and vice versa.

(i) It is to be noted that for dissociation of hydrogen molecule into atoms, equivalent amount of energy is
to be supplied.

(j) Obviously in general, a stronger bond will require greater amount of energy for the separation of
atoms. The energy required to cleave one mole of bonds of the same kind is known as the bond
energy or bond dissociation energy. This is also called as orbital overlap concept of covalent bond.

(2) Overlapping

(i) According to this concept a covalent bond is formed by the partial overlapping of two half filled atomic
orbitals containing one electron each with opposite spins then they merge to form a new orbital known
as molecular orbital.

(ii) These two electrons have greater probability of their presence in the region of overlap and thus get
stabilised i.e., during overlapping energy is released.

Examples of overlapping are given below :
Formation of hydrogen molecule : Two hydrogen atoms having electrons with opposite spins come close to
each other, their s-orbitals overlap with each other resulting in the union of two atoms to form a molecule.

+ –+– + ++

H-atom H-atom H2-molecule

Formation of fluorine molecule : In the formation of F2 molecule p-orbitals of each flourine atom having
electrons with opposite spins come close to each other, overlapping take place resulting is the union of two atoms.

2px 2px

2py 2py

2pz + 2pz

F-atom F-atom F2-molecule
Formation of fluorine molecule

Types of overlapping and nature of covalent bonds (σ - and π - bonds) : overlapping of different type

gives sigma (σ) and pi (π) bond. Various modes of overlapping given below :

s – s overlapping : In this type two half filled s-orbitals overlap along the internuclear axis to

form σ-bond. +

s-orbital s-orbital s-s overlap
s-s overlapping σ-bond

s-p overlapping : It involves the overlapping of half filled s-orbital of one atom with the half filled p-orbital of
other atom This overlapping again gives σ-bond e.g., formation of H – F molecule involves the overlapping of 1s
orbital of H with the half filled 2pz – orbital of Fluorine.

+

s-orbital p-orbital s–p overlap

p-p overlapping : p-p overlapping can take place ins –thp eovfeorlallpopwinigng two wayσs-.bond

(i) When there is the coaxial overlapping between p-orbitals of one atom with the p-orbitals of the

other then σ-bond formation take place e.g., formation of F2 molecule in which 2pz orbital of one F

atom overlap coaxially with the 2pz orbitals of second atom. σ-bond formation take place as shown
below :

+

pz-orbital pz -orbital pz – pz overlap
p – p overlapping σ-bond

(ii) When p–orbitals involved in overlapping are parallel and perpendicular to the internuclear axis. This
types of overlapping results in formation of pi bond. It is always accompanied by a σ bond and consists
of two charge clouds i.e., above and below the plane of sigma bond. Since overlapping takes place on
both sides of the internuclear axis, free rotation of atoms around a pi bond is not possible.

++ π

+→ Internuclear axis
π -bond
– – π
p-p overlapping
p-orbital p-orbital

Table : Difference in σ and π bonds

Sigma (σ) bond Pi (π) bond

It results from the end to end overlapping of two s- It result from the sidewise (lateral) overlapping of two p-
orbitals or two p-orbitals or one s and one p-orbital. orbitals.
Stronger Less strong
Bond energy 80 kcals Bond energy 65 kcals
More stable Less stable
Less reactive More reactive
Can exist independently
The electron cloud is symmetrical about the internuclear Always exist along with a σ-bond
axis. The electron cloud is above and below the plane of
internuclear axis.

Important Tips

 To count the σ and π bonds in molecule having single, double and triple bond first we write its expanded structure.

H C≡N H −C H
H | | |
ex. H − H , O σ O , N σ N, H \ C = C − C ≡ N , | C All the single
/ H −C
σ = ≡ N ≡C− C−C ≡ N C−H
π 2π ||
| C−H
(3π , 6σ ) C
C≡N |

(8π , 8σ )

H

(3π ,12σ )

bonds are σ-bond. In a double bond, one will be σ and the other π type while in a triple bond, one will be σ and other two π.

OH

|

The enolic form of acetone has 9σ, 1π and two lone pairs CH2 = C − CH3 (enol form of acetone)

HH H H
\ σ /
It is the π bond that actually takes part in reaction, / C C \ + H2 → H − |σ |
=
C− C − H , but the shape of molecule is decided by
π
HH | |
HH

σ-bond.
 The number of sp2-s sigma bonds in benzene are 6.
 When two atoms of the element having same spin of electron approach for bonding, the orbital overlapping and bonding both does

not occur.
 Head on overlapping is more stronger than lateral, or sidewise overlapping.

p-p > s-p > s-s > p-p

overlapping

Hybridization.

The concept of hybridization was introduced by Pauling and Slater. It is defined as the intermixing of
dissimilar orbitals of the same atom but having slightly different energies to form same number of new orbitals of
equal energies and identical shapes. The new orbitals so formed are known as hybrid orbitals.

Characteristics of hybridization
(1) Only orbitals of almost similar energies and belonging to the same atom or ion undergoes hybridization.
(2) Hybridization takes place only in orbitals, electrons are not involved in it.
(3) The number of hybrid orbitals produced is equal to the number of pure orbitals, mixed during
hybridization.
(4) In the excited state, the number of unpaired electrons must correspond to the oxidation state of the central
atom in the molecule.
(5) Both half filled orbitals or fully filled orbitals of equivalent energy can involve in hybridization.
(6) Hybrid orbitals form only sigma bonds.

(7) Orbitals involved in π bond formation do not participate in hybridization.
(8) Hybridization never takes place in an isolated atom but it occurs only at the time of bond formation.
(9) The hybrid orbitals are distributed in space as apart as possible resulting in a definite geometry of molecule.
(10) Hybridized orbitals provide efficient overlapping than overlapping by pure s, p and d-orbitals.

(11) Hybridized orbitals possess lower energy.

Depending upon the type and number of orbitals involved in intermixing, the hybridization can be of various
types namely sp, sp2, sp3, sp3d, dsp2, sp3d2, sp3d3. The nature and number of orbitals involved in the above
mentioned types of hybridization and their acquired shapes are discussed in following table

Type of hy- Character Geometry of molecules as No. of No. of Actual Example
brisation per VSPER theory bonded lone shape of
s-character=50%, atoms pairs molecules CO2, HgCl2, BeF2, ZnCl2 ,
sp p -character= 50% 180o MgCl 2 , C2 H 2 , HCN, BeH 2
A 2 0 Linear C2 H 2 , CS2 , N 2O, Hg 2Cl 2 ,

Linear 0 Trigonal [Ag{NH 3 )2 ]+
Planar
sp 2 s-character= 3 1 BF3 , AlCl3 , SO3−− , C2 H 4 ,
33.33%, 0 V-shape
p-character=66.67% 120o 2 (bent) NO3−, CO32−, HCHO
A 4 1
2 Tetrahedra C6 H 6 , CH + graphite,
Trigonal Planar, 120o 0 l 3

<120o Trigonal C2Cl4 , C2H2Cl2,[HgI3]−,
pyramidal
V-shape [Cu(PMe3 )3 ]−

(bent) NO2− , SO2 , SnCl2
Square
sp 3 s-character = 25%, planar CH 4 , SiH 4 , SO42− , SnCl4 ,
p-character = 75%
ClO4−, BF4−, NH4+, CCl4,
109o28′
A SiF4 , H2 − NH2,

Tetrahedral , 109.5o [BeF4 ]− , XeO4 ,

< 109.5o 3 [AlCl4 ]−, SnCl4, PH4+ ,
104.5o 2 Diamond, silica,
4
90o Ni(CO)4 , Si(CH 3 )4 , SiC,
SF2, [NiCl4 ]2, [MnO4 ]−[VO4 ]3−

NH 3 , PCl3 , PH 3 , AsH 3

ClO3− , POCl3 H 3O + , XeO3

dsp 2 s-character = 25% H2O, H2S, PbCl2, OF2, NH2−
p – character = 50% ClO2
d – character = 25%
[Cu(NH 3 )4 ]2+ ,[Ni(CN)4 ]2+
[Pt(NH3)4 ]2+

sp 3d s-character = 20%, Square planar 5 0 Trigonal PCl5 , SbCl5 , XeO3 F2 , PF5
p-character = 60%, 90o bipyramid AsF5, PCl4+, PCl6−,[Cu(Cl)5]3−
d-character = 20%
120o A al [Ni(CN)5 ]3− , [Fe(CO)5 ]

Trigonal bipyramidal

4 1 Irregular TeCl 4 , SF4
3 tetrahedra
l

2 T-shaped ClF3 , IF3

2 3 Linear I − , XeF2
3

sp 3d 2 s-character = 25% 6 0 Octahedra SF6 , PF6− , SnCl − , MoF6 ,
p – character = 50% l 6
d – character = 25%
(BaCl6)−, (PF6)−,

[Fe(CN)6 ]4− ,[Fe(H 2O)6 ]3+

Octohedral

5 1 Square ICl5 , BrF5 , IF5 XeOF4
pyramidal

4 2 Square XeF4 , ICl −
planar 4

sp 3d 3 s-character= 7 0 Pentagona IF7, [ZrF7]3−[UF7]3−
14.28%, l [UO2 F5 ]3−
p-character=
42.86%, bipyramid
d-character= al
42.86%
90o

A 72o

Pentagonal bipyramidal

6 1 Distorted XeF6
octahedral

Short trick to find out hybridization : The structure of any molecule can be predicted on the basis of

hybridization which in turn can be known by the following general formulation. H= 1 (V +M −C+ A)
2

Where H = Number of orbitals involved in hybridization viz. 2, 3, 4, 5, 6 and 7, hence nature of hybridization
will be sp, sp2, sp3, sp3d, sp3d2, sp3d3 respectively.

V = Number electrons in valence shell of the central atom, M = Number of monovalent atom

C = Charge on cation, A = Charge on anion

Few examples are given below to illustrate this:

Type : (A) When the central atom is surrounded by monovalent atoms only, e.g. BeF2, BCl3, CCl4, NCl3,

PCl5, NH3, H2O, OF2, TeCl4, SCl2, IF7, ClF3, SF4, SF6, XeF2, XeF4, etc. Let us take the case of PCl5.

H = 1 (5 + 5 − 0 + 0) = 5. Thus, the type of hybridization is sp3d.
2

Type : (B) When the central atom is surrounded by divalent atoms only; e.g. CO2, CS2, SO2, SO3, XeO3 etc.

Let us take the case of SO3. H = 1 (6 + 0 − 0 + 0) = 3 . Thus, the type of hybridization in SO3 is sp2.
2

Type : (C) When the central atom is surrounded by monovalent as well as divalent atoms, e.g. COCl2, POCl3,

XeO2F2 etc. Let us take the case of POCl3. H = 1 (5 + 3 − 0 + 0) = 4. Thus, the nature of hybridization in POCl3 is sp3.
2

Type : (D) When the species is a cation, e.g. NH4+, CH3+, H3O+ etc. Let us take the case of CH3+.

H = 1 (4 + 3 −1+ 0) = 3. Thus, the hybridization in CH3+ is sp2.
2

Type : (E) When the species is an anion, e.g. SO42–, CO32–, PO43–, NO2–, NO3–, etc. Let us take the case of

SO42–. H = 1 (6 + 0 − 0 + 2) = 4 . Thus, hybridization in SO42 − is sp3 .
2

Type : (F) When the species is a complex ion of the type ICl4–, I3–, ClF2–, etc. Let us take the case of ClF2–.

H = 1 (7 + 2 − 0 + 1) = 5 . Thus, in ClF2–, Cl is sp3d hybridized.
2

Type : (G) When the species is a complex ion of the type [PtF6]2 –, [Co(NH3)6]2+, [Ni(NH3)4Cl2] etc. In such
cases nature of hybridization is given by counting the co-ordination number.

Important Tips

 The sequence of relative energy and size of s – p type hybrid orbitals is sp < sp2 < sp3.
 The relative value of the overlapping power of sp, sp2 and sp3 hybrid orbitals are 1.93, 1.99 and 2.00 respectively.
 An increase in s-character of hybrid orbitals, increases the bond angle. Increasing order of s-characters and bond angle is sp3 < sp2 < sp.
 Normally hybrid orbitals (sp, sp2, sp3, dsp2, dsp3 etc.) form σ-bonds but in benzyne lateral overlap of sp2-orbitals forms a π-bond.

 Some iso-structural pairs are [NF3, H3O+], [NO3−, BF3],[SO42−, BF4−] . There structures are similar due to same hybridization.

 In BF3 all atoms are co-planar.
In PCl5 the state of hybridization of P atom is sp3d. In its trigonal bipyramidal shape all the P-Cl bonds are not equal.

 The π bond formed between S and O atoms in SO2 molecule is due to overlap between their p-orbitals ( Pπ − Pπ bonding) or
between p orbital of O-atom with d-orbital of S-atom (called pπ – dπ bonding)

16 S = 1s 2 2s 2 2p6 3s 2 3 p 2 3 p1y 3 p1z (Ground state configuration)
x

= 1s 2 2s 2 2p6 3s 2 3p1x 3p1y 3p1z 3d1 (Excited state configuration)

8 O = 1s 2 2s 2 2p 2 2p1y 2p1z pπ- dπ pπ- pπ
x bonding 3p bonding

2p d 2p

S ••
S

d

S-atom undergoes sp2 hybridization leaving one half-filled 3pz orbital and one d-orbital unhybridized. Out of two half filled
orbitals of O-atom, one is involved in formation of σ-bond with S-atom and the other in forming π-bond.

Resonance.

The phenomenon of resonance was put forward by Heisenberg to explain the properties of certain
molecules.

In case of certain molecules, a single Lewis structure cannot explain all the properties of the molecule. The
molecule is then supposed to have many structures, each of which can explain most of the properties of the
molecule but none can explain all the properties of the molecule. The actual structure is in between of all these
contributing structures and is called resonance hybrid and the different individual structures are called
resonating structures or canonical forms. This phenomenon is called resonance.

To illustrate this, consider a molecule of ozone O3 . Its structure can be written as

O OO

OO OO OO

(a) (b) (c)

It may be noted that the resonating structures have no real existence. Such structures are only theoretical. In
fact, the actual molecule has no pictorial representation. The resonating structures are only a convenient way of
picturing molecule to account for its properties.

As a resonance hybrid of above two structures (a) and (b). For simplicity, ozone may be represented by
structure (c), which shows the resonance hybrid having equal bonds between single and double.

Resonance is shown by benzene, toluene, O3, allenes (>C = C = C<), CO, CO2, CO3− , SO3, NO, NO2 while
it is not shown by H2O2, H2O, NH3, CH4, SiO2.

(1) Conditions for writing resonance structures

The resonance contributing structures :

(i) Should have same atomic positions.

(ii) Should have same number of bond pairs and lone pairs.

(iii) Should have nearly same energy.

(iv) Should be so written such that negative charge is present on an electronegative atom and positive
charge is present on an electropositive atom.

(v) The like charges should not reside on adjacent atoms. But unlike charges should not greatly separated.

(2) Characteristics of resonance

(i) The contributing structures (canonical forms) do not have any real existence. They are only imaginary.

Only the resonance hybrid has the real existence.

(ii) As a result of resonance, the bond lengths of single and double E1

bond in a molecule become equal e.g. O–O bond lengths in E2

ozone or C–O bond lengths in CO32– ion. E3

(iii) The resonance hybrid has lower energy and hence greater Energy Resonance energy
stability than any of the contributing structures.
E0
(iv) Greater is the resonance energy, greater is the stability of the Resonating structures
molecule. Concept of resonance energy. Energies E1, E2
and E3 for three structures and E0 is the
(v) Greater is the number of canonical forms especially with nearly experimentally determined bond energy
same energy, greater is the stability of the molecule.

(3) Resonance energy

It is the difference between the energy of resonance hybrid and that of the most stable of the resonating
structures (having least energy). Thus,

Resonance energy = Energy of resonance hybrid – Energy of the most stable of resonating structure.

(4) Bond order calculation

In the case of molecules or ions having resonance, the bond order changes and is calculated as follows:

Bond order = Total no. of bonds between two atoms in all the structures
Total no. of resonating structures

e.g., (i) In benzene ←→

Bond order = double bond + single bond = 2 + 1 = 1.5
2 2

(ii) In carbonate ion O− ←→ O ←→ O−
| || |
C C C
// \ /\ / \\
O O− −O O− −O O

Bond order = 2+1+1 = 1.33
3

Important Tips

 Resonance structure (canonical form) must be planar.

 O 
 
 In case of formic acid H − C , the two C−O bond lengths are different but in formate ion

 O − H 
 

 O O − 
H −C ←→ H − C  the two C − O bond lengths are equal due to resonance.

O− O 

 In resonance hybrid, the bond lengths are different from those in the contributing structure.
 Resonance arises due to delocalisation of π electrons. Resonating structures have different electronic arrangements.
 The resonating structures do not have real existence.
 Resonance energy = [Experimental heat of formation]–[Calculated heat of formation of most stable canonical form].

 Three contributing structure of CO2 molecule are – O = C = O ↔ O+ ≡ C − O− ↔ O− − C ≡ O+

Resonance structure of carbon monoxide is • •• •• C ← O••
 • C O
= ↔ =
••

 Resonance energy of benzene is 152.0 kJ / mol .

Bond characteristics.

(1) Bond length

“The average distance between the centre of the nuclei of the two bonded atoms is called bond length”.

It is expressed in terms of Angstrom (1 Å = 10–10 m) or picometer (1pm = 10–12 m). It is determined
experimentally by X-ray diffraction methods or spectroscopic methods. In an ionic compound, the bond length is
the sum of their ionic radii (d = r++ r–) and in a covalent compound, it is the sum of their covalent radii (e.g., for HCl, d
= rH + rCl).

Factors affecting bond length

(i) Size of the atoms : The bond length increases with increase in the size of the atoms. For example, bond
length of H − X are in the order , HI > HBr > HCl > HF

(ii) Electronegativity difference : Bond length × 1 .
∆EN

(iii) Multiplicity of bond : The bond length decreases with the multiplicity of the bond. Thus, bond length

of carbon–carbon bonds are in the order , C ≡ C < C = C < C – C

(iv) Type of hybridisation : As an s-orbital is smaller in size, greater the s-character shorter is the hybrid

orbital and hence shorter is the bond length. For example, sp 3 C – H > sp 2 C – H > sp C – H

(v) Resonance : Bond length is also affected by resonance as in benzene and CO2 . In benzene bond

length is 1.39 Å which is in between C − C bond length 1.54 Å and C = C bond length 1.34 Å

In CO2 the C-O bond length is 1.15 Å .
(In between C ≡ O and C = O )

O = C = O ↔ O − C ≡ O+ ↔ O+ ≡ C − O
(vi) Polarity of bond : Polar bond length is usually smaller than the theoretical non-polar bond length.
(2) Bond energy
“The amount of energy required to break one mole of bonds of a particular type so as to separate them into
gaseous atoms is called bond dissociation energy or simply bond energy”. Greater is the bond energy, stronger
is the bond.

Bond energy is usually expressed in kJ mol –1 .

Factors affecting bond energy

(i) Size of the atoms : Bond energy ∝ 1 Greater the size of the atom, greater is the bond length and
atomic size

less is the bond dissociation energy i.e. less is the bond strength.

(ii) Multiplicity of bonds : For the bond between the two similar atoms, greater is the multiplicity of the
bond, greater is the bond dissociation energy. This is firstly because atoms come closer and secondly,
the number of bonds to be broken is more, C − C < C = C < C ≡ C , C ≡ C < C ≡ N < N ≡ N

(iii) Number of lone pairs of electrons present : Greater the number of lone pairs of electrons present on
the bonded atoms, greater is the repulsion between the atoms and hence less is the bond dissociation
energy. For example for a few single bonds, we have

Bond C–C N–N O–O F–F
Lone pair of electrons 0 1 2 3
Bond energy (kJ mol–1)
348 163 146 139

(iv) Percentage s–character : The bond energy increases as the hybrid orbitals have greater amount of s
orbital contribution. Thus, bond energy decreases in the following order, sp > sp 2 > sp3

(v) Bond polarity : Greater the electronegativity difference, greater is the bond polarity and hence greater
will be the bond strength i.e., bond energy, H − F > H − Cl > H − Br > H − I ,

(vi) Among halogens Cl – Cl > F – F > Br – Br > I – I, (Decreasing order of bond energy)

(vii) Resonance : Resonance increases bond energy.

(3) Bond angle

In case of molecules made up of three or more atoms, the average angle between the bonded orbitals (i.e.,
between the two covalent bonds) is known as bond angle θ.

Factors affecting bond angle

(i) Repulsion between atoms or groups attached to the central atom : The positive charge, developed due
to high electronegativity of oxygen, on the two hydrogen atoms in water causes repulsion among
themselves which increases the bond angle, H–O–H from 90º to 105º.

(ii) Hybridisation of bonding orbitals : In hybridisation as the s character of the s hybrid bond increases,
the bond angle increases.

Bond type sp3 sp2 sp

Bond angle 109º28′ 120o 180o

(iii) Repulsion due to non-bonded electrons : Bond angle ∝ No. of lone 1 of electrons . By increasing
pair

lone pair of electron, bond angle decreases approximately by 2.5%.

Bond angle CH4 NH3 H2O
109º 107o 105o

(iv) Electronegativity of the atoms : If the electronegativity of the central atom decreases, bond angle

decreases.

Bond angle H2O > H2S > H 2Se > H 2Te
104.5 o 92.2o 91.2o 89.5 o

In case the central atom remains the same, bond angle increases with the decrease in electronegativity
of the surrounding atom, e.g.

Bond angle PCl 3 PBr3 PI 3 , AsCl 3 AsBr3 AsI 3
100 o 101.5 o 102o 98.4 o 100.5 o 101o

Example: Energy required to dissociate 4 grams of gaseous hydrogen into free gaseous atoms is 208 kcal at 25oC the bond

energy of H–H bond will be [CPMT 1989]

(a) 104 Kcal (b) 10.4 Kcal (c) 20.8 Kcal (d) 41.6 Kcal

Answer: (a) 4 gram gaseous hydrogen has bond energy 208 kcal

So, 2 gram gaseous hydrogen has bond energy = 208 kcal = 104 kcal.
2

Important Tips

 More directional the bond, greater is the bond strength and vice versa. For example :

sp3 − sp3 > sp2 − sp2 > sp − sp > p − p > s − p > s − s
 The hybrid orbitals with more p-character are more directional in character and hence of above order.
 The terms ‘bond energy’ and ‘bond dissociation’ energy are same only for di-atomic molecules.

 The order of O–O bond length in O2, H2O2 and O3 is H2O2 > O2 > O3
 Because of higher electron density and small size of F atom repulsion between electron of it two F atoms, weakens the F-F bond.
 The bond length increases as the bond order decreases.

 Carbon monoxide (CO) has the highest bond energy(1070 kJmol −1 ) of all the diatomic molecules. Bond energy of N2(946kJmol−1)
and that of H2(436 kJmol-1) are other diatomic molecules with very high bond energies.

VSEPR (Valence shell electron pair repulsion) theory.

The basic concept of the theory was suggested by Sidgwick and Powell (1940). It provides useful idea for
predicting shapes and geometries of molecules. The concept tells that, the arrangement of bonds around the central
atom depends upon the repulsion’s operating between electron pairs(bonded or non bonded) around the central
atom. Gillespie and Nyholm developed this concept as VSEPR theory.

The main postulates of VSEPR theory are

(i) For polyatomic molecules containing 3 or more atoms, one of the atoms is called the central atom to

(ii) The geometry of a molecule depends upon the total number of valence shell electron pairs (bonded or
not bonded) present around the central atom and their repulsion due to relative sizes and shapes.

(iii) If the central atom is surrounded by bond pairs only. It gives the symmetrical shape to the molecule.

(iv) If the central atom is surrounded by lone pairs (lp) as well as bond pairs (bp) of e− then the molecule
has a distorted geometry.

(v) The relative order of repulsion between electron pairs is as follows : Lone pair-lone pair>lone pair-
bond pair>bond pair-bond pair

A lone pair is concentrated around the central atom while a bond pair is pulled out between two bonded
atoms. As such repulsion becomes greater when a lone pair is involved.

Steps to be followed to find the shape of molecules :

(i) Identify the central atom and count the number of valence electrons.

(ii) Add to this, number of other atoms.

(iii) If it is an ion, add negative charges and subtract positive charges. Call the total N.

(iv) Divide N by 2 and compare the result with the following table and obtain the shape.

Total N/2 Shape of molecule or ion Example
2 Linear HgCl2 / BeCl2
3
3 Triangular planar BF3
4 Angular SnCl2 , NO2

4 Tetrahedral CH4, BF4−
4 NH 3 , PCl 3
5 Trigonal Pyramidal
5 Angular H2O
PCl5 , PF5
Trigonal bipyramidal
Irregular tetrahedral SF4 , IF4+

5 T-shaped CIF3 , BrF3

5 Linear XeF2 , I −
3

6 Octahedral SF6 , PF6

6 Square Pyramidal IF5

6 Square planar XeF4 , ICI 4

Geometry of Molecules/Ions having bond pair as well as lone pair of electrons

Type of No. of No. of lone Hybridi- Bond angle Expected Actual Examples
mole- bond pairs of zation geometry geometry
cule pairs of electrons SO2, SnCl2, NO2–
electron sp 2 < 120o Trigonal V-shape,
AX 3 1 planar Bent, H2O, H2S, SCl2, OF2, NH2–,
2 sp 3 < 109o 28′ ClO2–
2 sp 3 < 109o 28′ Tetrahedral Angular
AX 4 2 1 sp 3d V-shape, NH3, NF3 , PCl3, PH3, AsH3,
AX 4 3 1 Tetrahedral Angular ClO3– , H3O+
AX 5 4 sp 3d Pyramidal
2 sp 3d SF4, SCl4, TeCl4
AX 5 3 3 sp 3d 2 < 109o 28′ Trigonal Irregular
AX 5 2 1 sp 3d 2 bipyramidal tetrahedro ICl3, IF3, ClF3
AX 6 5 2 sp 3d 3 90o XeF2, I3–, ICl2–
AX 6 4 1 180o Trigonal n ICl5, BrF5, IF5
AX7 6 < 90o bipyramidal T-shaped
XeF4, ICl4–
– Trigonal Linear XeF6
– bipyramidal
Octahedral Square
pyramidal
Octahedral
Square
Pentagonal planar
pyramidal Distorted
octahedral

Molecular orbital theory.

Molecular orbital theory was given by Hund and Mulliken in 1932. When two or more constituent atomic
orbital merge together, they form a bigger orbital called molecular orbital (MO). In atomic orbital, the electron is
influenced by only one nucleus whereas in case of molecular orbital, the electron is influenced by two or more
constituent nuclei. Thus, atomic orbital is monocentric and molecular orbital is polycentric. Molecular orbitals follow
Pauli's exclusion principle, Hund’s rule, Aufbau's principle strictly.

• •• •• ••

Atomic orbital According to VBT Molecular orbital According to MOT
(AO) (MO)

The main ideas of this theory are : (i) When two atomic orbitals combine or overlap, they lose their identity
and form new orbitals. The new orbitals thus formed are called molecular orbitals. (ii) Molecular orbitals are the
energy states of a molecule in which the electrons of the molecule are filled just as atomic orbitals are the energy
states of an atom in which the electrons of the atom are filled. (iii) In terms of probability distribution, a molecular
orbital gives the electron probability distribution around a group of nuclei just as an atomic orbital gives the electron

probability distribution around the single nucleus. (iv) Only those atomic orbitals can combine to form molecular
orbitals which have comparable energies and proper orientation. (v) The number of molecular orbitals formed is
equal to the number of combining atomic orbitals. (vi) When two atomic orbitals combine, they form two new
orbitals called bonding molecular orbital and antibonding molecular orbital. (vii) The bonding molecular orbital has
lower energy and hence greater stability than the corresponding antibonding molecular orbital. (viii) The bonding
molecular orbitals are represented by σ,π etc, whereas the corresponding antibonding molecular orbitals are

represented by σ *, π * etc. (ix) The shapes of the molecular orbitals formed depend upon the type of combining

atomic orbitals.

Periodic classification of elements

Periodic table is an arrangement of elements with similar properties placed together. The periodic table

evolved largely as a result of experimental observations.

Earlier Attempt to Classify Elements.

(1) Dobereiner’s law of triads (1829) : It was the classification of elements into groups of three elements
each with similar properties such that the atomic weight of the middle element was the arithmetic mean of the other
two e.g. Ca, Sr, Ba ; Cl, Br, I etc.

(2) Telluric screw or Helix was proposed by Chancourtois in 1862.
(3) Newlands law of octaves (1864) : It was an arrangement of elements in order of increasing atomic
weights in which it was observed that every eighth element had properties similar to those of the first just like the
eighth note of an octave of music.
(4) Mendeleef’s period law (1869) : The first significant classification (arrangement of known elements in a
systematic way) was given by Mendeleeff (a Russian chemist) in 1869 in the form of periodic table, commonly
known as Mendeleeff's periodic table. His periodic table was based on periodic law, ''The physical and chemical
properties of elements are periodic functions of their atomic weights.''
In Mendeleef’s periodic table elements are arranged in order of their increasing atomic weights in such a way
that elements with similar properties are placed in the same group. It consists of seven horizontal rows called
periods. These are numbered from 1 to 7.
Mendeleef’s original table consists of 8 vertical columns called groups. These are numbered as I, II III….. VIII.
However, 9th vertical column called Zero group was added with the discovery of inert gases. Except for group VIII
and zero, each group is further divided into two sub-groups designated as A and B. Group VIII consists of 9
elements arranged in three sets each containing three elements.

Modern Periodic Law and Modern Mandeleeff's Periodic Table .

The recent work has established that the fundamental property of an atom is atomic number and not atomic
weight. Therefore, atomic number is taken as the basis of the classification of the elements. The modern periodic
law may be stated as : ''The properties of elements are periodic functions of their atomic number.'' (Moseley).
When atomic number is taken as the basis for classification of elements, many anomalies of Mendeleef's table disappear,
such as the,

(1) Position of hydrogen : Dual behaviour of hydrogen is explained on the fact that it has one electron in
its outermost orbit. When it loses its electron it gives H+ and behaves like alkali metals and when it gains an electron
it gives H– and behaves like halogens. Thus, it resembles with both the alkali metals and the halogens.

(2) Dissimilar elements placed together : The lengths of periods are determined by the arrangement of
electrons in different orbits. The period ends on the completion of last orbits (last members always being the inert
gas). Different periods contain 2, 8, 18 or 32 elements. Now out of the two elements which every long period adds
to the group, one resembles the typical elements while the other does not. This gives rise to formation of subgroups.
This explains the inclusion of dissimilar elements in the same group but different subgroups.

(3) Position of rare earth elements : The electronic arrangement of rare earths can be written as 2, 8, 18,
(18 + x), 9, 2 where x varies from 0 to 13, i.e., from Lanthanum to Lutecium. The number of electrons in valency
shell, in case of all the elements remains the same although the atomic number increases. Since they possess the

same number of valency electrons, the chemical behaviour is also similar. This justifies their positions in the same
group and in the same place of the periodic table.

(4) Anomalous pairs of elements : Now the basis of classification is atomic number, therefore, this
anomaly disappears as the elements occupy their normal position in the new periodic table.

(5) Position of isotopes : Since the isotopes of same element possess same atomic number they should
occupy one and the same position in the periodic table.

(6) Position of VIII group elements : In long periods 18 elements are to be distributed among 8 groups; 1
to 7 groups get 2 elements each and zero group accommodates inert elements, the rest three elements are placed at
one place in a new group, known as VIII group. This lack of space justifies the induction of VIII group in the periodic
table.

(7) Transuranic elements : These elements form a series known as actinide series, it begins from actinium
and ends at lawrencium (89–103). Discovery of elements 104, 105 and 112 has recently been reported. This series
has been placed outside the periodic table. The electronic configuration of these elements can be written as 2, 8, 18,
32, (18 + x), 9, 2, where x varies from zero (for actinium) to 14 (for lawrencium). The number of valency electrons
remains the same for all these elements although atomic number increases. Therefore, their chemical behaviour is
similar. This justifies their position outside the periodic table at one place.

Extended or Long Form of Periodic Table .

Modern periodic table is also called long form of the periodic table or Bohr’s table. In this table, the
elements are arranged in order of their increasing atomic number. It consists of 4 blocks (s, p, d and f), 18 groups
numbered from 1 to 18 and 7 periods numbered from 1 to 7.

Blocks : The periodic table is divided into four main blocks (s, p, d and f) depending upon the subshell to
which the valence electron enters into.

(1) Elements of group 1 and 2 constitute s-Block.

(2) Elements of group 13, 14, 15, 16, 17, 18 constitute p-Block

(3) Elements of group 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 constitute d-Block

(4) The f-Block elements comprise two horizontal rows placed at the bottom of the periodic table to avoid its
unnecessary expansion.

Elements of s and p-blocks are called normal or representative elements, those of d-block are called transition
elements while the f-block elements are called inner transition elements.

Groups : The 18 vertical columns are called groups. The elements belonging to a particular group is known as a
family and is usually named after the first number. Apart from this some of the groups are given typical names as
examplified beneath ,

(1) Elements of group 1 are called Alkali-Metals.
(2) Elements of group 2 are called Alkaline Earths.
(3) Elements of group 3 are called Pnicogens.
(4) Elements of group 16 are called Chalcogens.
(5) Elements of group 17 are called Halogens.
(6) Elements of group 18 are called Noble Gases or Aerogens.
All the other groups are named after the first member of each group.
Periods : The horizontal rows are called periods. There are Seven Periods in the long form of the periodic table.
(1) Ist period 1 H →2 He) contains 2 elements. It is the shortest period.

(2) 2nd period (3 Li →10 Ne) and 3rd period (11 Na →18 Ar) contains 8 elements each. These are short periods.

(3) 4th period (19 K →36 Kr) and 5th period (37 Rb →54 Xe) contains 18 elements each. These are long periods.

(4) 6th period (55 Cs →86 Ra) consists of 32 elements and is the longest period.

(5) 7th period starting with 87 Fr is incomplete and consists of 19 elements.
Periodicity in Properties.

''The repetition of similar electronic configuration after a definite period is the cause of periodicity of the
properties of elements.''

It can be explained with the help of electronic arrangement of elements. According to the modern views, the
valency of an element is indicated by the number of electrons present in the outermost orbit. The chemical
properties of elements are dependent on valency electrons. Variation in electronic arrangement leads to the
variation in properties. After a definite interval, recurrence of similar electronic arrangement takes place when the
number of valency electrons is the same. Thus, there is a regular gradation and repetition in the properties of
elements. For example,

Alkali metals Halogens

Li3 2, 1 F9 2, 7

Na11 2, 8, 1 Cl17 2, 8, 7

K19 2, 8, 8, 1 Br35 2, 8, 18, 7

Rb37 2, 8, 18, 8, 1 I53 2, 8, 18, 18, 7

Cs55 2, 8, 18, 18, 8, 1 At85 2, 8, 18, 32, 18, 7

Therefore, in group IA all elements possess one valency electron and they have a tendency to lose this

electron. They are all monovalent and electropositive having similar chemical properties. Same is the case with

halogens. They had seven electrons in their outermost orbit and, have a tendency to gain one electron. Therefore,

they are all monovalent and electronegative and resemble each other in chemical properties. Thus, it is observed

that the same electronic arrangement of outermost orbit is repeated after regular intervals and that accounts for the

periodicity of the properties of the elements.

Periodic properties are directly or indirectly related to their electronic configuration and show a regular

gradation on moving from left to right in a period or from top the bottom in a group. Some period or from top to

bottom in a group. Some important periodic properties are : oxidation number, shielding effect, atomic radii,

ionization energy, electron affinity, electronegativity, valency, density, m.pt. and b.pt.

The Screening Effect or Shielding Effect.

A valence-electron in a multi-electron atom is attracted by the nucleus, and repelled by the electrons of inner-
shells. The combined effect of this attractive and repulsive force acting on the valence-electron experiences less
attraction from the nucleus. This is called shielding or screening effect. The magnitude of the screening effect
depends upon the number of inner electrons, i.e., higher the number of inner electrons, greater shall be the value of
screening effect. The screening effect constant is represented by the symbol 'σ ' is determined by the Slater's
rules.

The magnitude of screening constant in the case of s- and p- block elements increases in a
period as well as in a group as the atomic number increases.

Effective Nuclear Charge.

Due to screening effect the valency electron experiences less attraction towards nucleus. This brings decrease
in the nuclear charge (Z) actually present on the nucleus. The reduced nuclear charge is termed effective nuclear
charge and is represented by Z* . It is related to actual nuclear charge (Z) by the following formula,

Z* = (Z − σ ) where σ is screening constant.

Ajánló 2019. aug-okt
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