This document discusses the structure of the atom. It begins by describing Bohr's model of the atom and its limitations. It then introduces shells and subshells, as well as quantum numbers and the shapes of atomic orbitals. Rules for filling electrons into orbitals, such as the Aufbau principle and Pauli exclusion principle, are also covered. The document discusses atomic spectra, photoelectric effect, and the dual wave-particle nature of light and matter. It provides an overview of concepts like de Broglie wavelength, Heisenberg uncertainty principle, and atomic electron configuration.

1. Chapter:2
• Structure of Atom
• CLASS:11 CBSE
• SHORT NOTES
BY
S.ARUNKUMAR

2. • Bohr's model and its limitations, concept of shells
and subshells, dual nature of matter and light.
• de Broglie's relationship, Heisenberg uncertainty
principle, concept of orbitals, quantum Numbers,
shapes of s, p and d orbitals, rules for filling
electrons in orbitals ‐ Aufbau principle.
• Pauli's exclusion principle and Hund's rule,
electronic configuration of atoms, stability of half
filled and completely filled orbitals.

5. • Findings:
• (i) The positive charge and most of the mass
of the atom was densely concentrated in an
extremely small region. This very small
portion of the atom was called nucleus by
Rutherford.
• (ii) The nucleus is surrounded by electrons
that move around the nucleus with a very
high speed in circular paths called orbits.
• (iii) Electrons and nucleus are held together
by electrostatic forces of attraction.

6. • Disadvantages:
(i) When a body is moving in an orbit, it
achieves acceleration. Thus, an electron moving
around nucleus in an orbit is under
acceleration.
(ii) Rutherford’s model does not give any idea
about distribution of electrons around the
nucleus and about their energies.

7. • Atomic Number
The number of protons present in the
nucleus is equal to the atomic number (z).
• Mass Number
Number of protons and neutrons present in
the nucleus are collectively known as
nucleons. The total number of nucleons is
termed as mass number (A) of the atom.
Mass Number (A) = Number of protons (p) +
Number of neutrons (n).

8. Planck's quantum theory
• . According to Planck's quantum theory,
• Different atoms and molecules can emit
or absorb energy in discrete quantities
only. The smallest amount of energy
that can be emitted or absorbed in the
form of electromagnetic radiation is
known as quantum.

9. Bohr’s Model of Atom
• Niels Bohr in 1913, proposed a new model of
atom on the basis of Planck’s Quantum Theory.
The main points of this model are as follows:
• (i) In an atom, the electrons revolve around
the nucleus in certain definite circular paths
called orbits.
• (ii) Each orbit is associated with definite
energy and therefore these are known as
energy levels or energy shells. These are
numbered as 1, 2, 3, 4… or K, L, M, N…

10. • (iii) Only those energy orbits are
permitted for the electron in which
angular momentum of the electron is a
whole number multiple of h/2π
• Angular momentum of electron
(mvr) = nh/2π (n = 1, 2, 3, 4 etc).
m = mass of the electron.
v = tangential velocity of the revolving
electron.
r = radius of the orbit.
h = Planck’s constant.
n is an integer.

11. • (iv) As long as electron is present in a particular
orbit, it neither absorbs nor loses energy and
its energy, therefore, remains constant.
• (v) When energy is supplied to an electron, it
absorbs energy only in fixed amounts as
quanta and jumps to higher energy state away
from the nucleus known as excited state. The
excited state is unstable, the electron may
jump back to the lower energy state and in
doing so, it emits the same amount of energy.
(∆E = E2 – E1).

12. Achievements of Bohr’s Theory
• 1. Bohr’s theory has explained the
stability of an atom.
• 2. Bohr’s theory has helped in
calculating the energy of electron in
hydrogen atom and one electron
species.(He+, Li2+,Be3+, B4+, C5+) The
mathematical expression for the energy
in the nth orbit

14. • Limitations of Bohr’s Model
(i) The theory could not explain the atomic
spectra of the atoms containing more than one
electron or multi electron atoms.
• (ii) Bohr’s theory failed to explain the fine
structure of the spectral lines.
• (iii) Bohr’s theory could not offer any satisfactory
explanation of Zeeman effect and Stark effect.
.

15. • The splitting of spectral lines by magnetic field
Zeeman effect.
• The splitting of spectral lines by electric field
Stark effect.
• (iv) Bohr’s theory failed to explain the ability
of atoms to form molecule formed by
chemical bonds.
• (v) It was not in accordance with the
Heisenberg’s uncertainty principle

16. • Shells
• Electrons orbit the nucleus of an atom at
different ranges, called shells.
• Each shell has a different energy level,
increasing the further it is from the nucleus.
• Each energy level is given a number called the
principal quantum number, n. The closest shell
has a value of n=1. The next shell has a value of
n=2, etc.

17. • The maximum number of electrons possible in
the first four energy levels are:

18. • Using the above you can work out the
maximum number of electrons that can
occupy a shell is 2n2.
• Electrons are placed into available shells,
starting with the lowest energy level. Each
shell must be full before the next starts to fill.
This model breaks down at the n=3 shell
because each shell has subshells.

19. • Subshells:
There are 4 subshells, s, p, d, and f. Each subshell
can hold a different number of electrons.
• The n number determines how many of the
subshells make up the shell. For example, the
1st shell is made up of 1 subshell, s. It can
therefore contain only 2 electrons.
• The 2nd shell is made up of 2 subshells, s and p.
It can therefore contain 2+6=8 electrons.
SubShell Electrons
s 2
p 6
d 10
f 14

20. • A complete table for the first four shells looks like:
• The number before each subshell specifies which shell it
belongs to.
• As an example, Lithium has 3 electrons. 2 will first fill up
the 1st shell in subshell 1s. The remaining electron will
appear in the second shell in the 2s subshell.
• You can write the full electron configuration in terms of
subshells.
• Going back to the above example, Lithium is 1s22s1 (1s has
2 electrons, 2s has 1 electron).
shell Subshell
Total Number of
Electrons in Shell
1st Shell 1s 2
2nd Shell 2s, 2p 2 + 6 = 8
3rd Shell 3s, 3p, 3d 2 + 6 + 10 = 18
4th Shell 4s, 4p, 4d, 4f 2 + 6 + 10 + 14 = 32

21. • Lithium 1s22s1 can be simplified to [He]2s1 as
Helium (He) has an electron configuration of
1s2.
• Note: subshells have different energy levels
which can confuse the order they fill.

22. • Subshells and Periodic Table
Elements are grouped in blocks that refer to the subshell that
contains the highest energy electron.
For example, any element in the row 3d will have it's highest
energy electron in sub-shell d of the 3rd shell, whereas an
element in row 4d will have the highest energy electron in sub-
shell d of the 4th shell.

23. Spectra
• When a ray of white light is passed through
the prism it spread into series of coloured
bands called spectrum.
• The spectrum of white light, that we can see,
ranges from violet 7.5x1014 HZ to red at
4x1014Hz . Such a spectrum is called
continuous spectrum.
• VIBGYOR (V) = Shortest wavelength 400nm; R
= Longest wavelength 750 nm

24. • A similar spectrum is produced when a
rainbow forms in the sky.
• When electromagnetic radiations
interacts with matter, atoms and
molecules may absorb energy and reach
to a higher energy state.

25. Emission spectra
• The spectrum of radiation emitted by a
substance that has absorbed energy is called an
emission spectrum.
It is noticed when radiations emitted from
source are passed through a prism & received
on photographic plate.
Emission spectrum is produced by supplying
energy to a sample by heating it or irradiating it
and the wavelength (or frequency) of the
radiation emitted, as the sample gives up the
absorbed energy, is recorded.

27. Absorption Spectra:
Absorption spectrum is the spectrum obtained
when radiation is passed through a sample of
material.
The sample absorbs radiation of certain
wavelengths.
The wavelengths which are absorbed are
missing and come as dark lines.
An absorption spectrum is like the
photographic negative of an emission spectrum

29. • Line Spectrum of hydrogen:
• When an electric discharge is passed through
gaseous hydrogen, the hydrogen molecules
dissociate and the energetically excited
hydrogen atoms produced emit
electromagnetic radiation of discrete
frequencies.

30. Line spectrum of hydrogen atom
• Hydrogen – hydrogen ion

32. • Johannes Rydberg noted all series of lines in
the hydrogen spectrum could be described by
the following expression:

34. Dual nature of matter and light
• Albert Einstein a German scientist, in 1905
developed a theory stating that light has a dual
nature. He proposed that light can exist as a wave
or a particle.

35. • Derivation of de-Broglie Equation
The wavelength of the wave associated with
any material particle was calculated by analogy
with photon.
• In case of photon, if it is assumed to have wave
character, its energy is given by
• E = hv …(i)
• (According to the Planck’s quantum theory)
• Where nth frequency of the wave and ‘h’ is
Planck’s constant
• If the photon is supposed to have particle
character, its energy is given by
• E = mc2 ….… (ii)

36. • According to Einstein’s equation
• where ‘m’ is the mass of photon, ‘c’ is the velocity of light.
• By equating (i) and (ii)
• hv = mc2
• But v = c/λ
• h
𝐶
λ
= mc2
• (or) λ = h /mc
• The above equation is applicable to material particle if the
mass and velocity of photon is replaced by the mass and
velocity of material particle. Thus for any material particle
like electron.
• λ =
ℎ
𝑚𝑣
or λ =
ℎ
𝑝
where mv = p is the momentum of the
particle.
• m=mass of particle, v=velocity of particle, p=moment of
particle

37. • Derivation of Angular Momentum from de Broglie
Equation:
According to Bohr’s model, the electron revolves around the
nucleus in circular orbits. According to de Broglie concept,
the electron is not only a particle but has a wave character
also.
• If the wave is completely in phase,
the circumference of the orbit must be equal to an
integral multiple of wave length (λ)
• Therefore 2πr = nλ
• where ‘n’ is an integer and ‘r’ is the radius of the orbit
• But λ = h/mv
• ∴ 2πr = nh /mv or mvr = n h/2π

38. • which is Bohr’s postulate of angular
momentum, where ‘n’ is the principal quantum
number.
• “Thus, the number of waves an electron makes
in a particular Bohr orbit in one complete
revolution is equal to the principal quantum
number of the orbit”.

39. Photo electric effect:
• H. Hertz performed a experiment in which
electrons were ejected when certain metals
(K, Ru, Cs) were exposed to a beam of light.
• This phenomenon is called photoelectric
effect.
• The electrons are ejected from the metal
surface as soon as the beam of light strikes the
surface, there is no time lag between the
striking of light beam and the ejection of
electrons from the metal surface.

40. • The number of electrons ejected is
proportional to the intensity or brightness of
light.
• For each metal, there is a characteristic
minimum frequency (Threshold frequency)
below which photoelectric is not observed.

41. • It has been observed that the number of
electrons ejected does depend upon the
brightness of light, the kinetic energy of the
ejected electrons does not.
• Ex: red light- 4.3to 4.6x1014 HZ may shine on
a piece of potassium metal for hours but no
photoelectrons ejected.
• But a very weak yellow light
• v=5.1 to5.2x1014HZ shines the potassium
metal, the photoelectric effect is observed.
• The threshold frequency for potassium metal
is 5.0x1014HZ.

42. • Einstein (1905) explain photoelectric effect
using the planck’s quantum theory of
electromagnetic radiation.
• Shining a beam of light on to a metal surface
can, therefore be viewed as shooting a beam
of particles, the photons.
• The kinetic energy of the ejected electron is
proportional to the frequency of
electromagnetic radiation.

44. Wave nature of Electromagnetic
Radiation
• He suggested that when electrically
charged particle moves under
acceleration, alternating electrical and
magnetic fields are produced and
transmitted.
• These fields are transmitted in the forms
of waves called electromagnetic waves or
electromagnetic radiation.

45. • Newton proposed that light was made up
of particles called corpuscules.
• Maxell reveal light waves are associated
with oscillating electric and magnetic
character.
• The oscillating electric and magnetic
fields produced by oscillating charged
particles are perpendicular to each other
and both are perpendicular to the
direction of propagation of the wave.

47. • (ii) Unlike sound waves or water waves electromagnetic
waves do not required medium and can move in vaccum.
• (iii) There are many types of electromagnetic radiations,
which differ form one another in wavelength(or
frequency).
• Ex: Radio frequency region -106hz- broadcasting
Microwave region- 1010hz – radar
Infrared region -1013hz-heating
Ultra violet region- 1016hz- sun’s radiation
Visible light- 1015hz
•

48. • The S.I unit of frequency is Hertz.(Hz/s)
• Frequency: it is defined as the number of
waves that pass a given point in one second.
• In vaccum all types of electromagnetic
radiations, travel at the same speed.
• 3.0 x108 ms-1. (Speed of light)
The frequency(ν), wavelength(ʎ) and velocity of
light (c) are related by the equation.
C=vʎ

49. • Wave number: (ṽ). It is defined as the number
of wavelengths per unit length.
• Unit : m-1

50. • Particle nature of electromagnetic
radiation:
• Wave nature of electromagnetic radiation
explains diffraction and interference.
• It can’t explain
• (i) The nature of emission of radiation of hot
bodies (black-body radiation)
• (ii) Ejection of electrons from metal surface
when radiation strikes it.
• (iii) Variation of heat capacity of solids as a
function of temperature.
• (iv) line spectra of atoms with special reference
to hydrogen.

51. • Black body: The ideal body, which emits and
absorbs radiations of all frequencies, is
called a black body and the radiation
emitted by such body is called black body
radiation.
• When iron rod is heated in furnance, it first
turns to dull red and then progressively
become more and more red as the
temperature increases.
• As this is heated further, the radiation
emitted becomes white and then becomes
blue as the temperature becomes very high.

52. • It means that the frequency of emitted radiation
goes from a lower frequency to a higher
frequency as the temperature increases.
• Red is lower frequency while blue colour belongs
to the higher frequency region of the
electromagnetic spectrum.

53. • At a given temperature intensity of radiation
emitted increases with decrease of
wavelength, reaches a maximum value at a
given wavelength and then starts decreasing
with further decrease of wavelength.
• Planck suggested that
• Atoms and molecules could emit(or absorb)
energy only in discrete quantities .(quantum)

54. Conclusion:
• The radiant energy is emitted or absorbed not
continuously but discontinuously in the form of
small discrete packets of energy called ‘quantum’.
In case of light, the quantum of energy is called a
‘photon’
• The energy of each quantum is directly
proportional to the frequency of the radiation,
• i.e. E α υ
• Or E = hυ
• Where h = Planck’s constant = 6.626 × 10-27 Js
• Energy is always emitted or absorbed as integral
multiple of this quantum,
i.e,E = nhυ Where n =1,2,3,4,.....

55. Heisenberg’s Uncertainty Principle:
• It states that it is impossible to determine
simultaneously, the exact position and exact
momentum (or velocity) of an electron. The
product of their uncertainties is always equal
to or greater than h/4π.

56. • Where, Δx = uncertainty in position
• Δp = uncertainty in momentum
• Δvx= uncertainty in momentum or velocity of
the particle.
• If the position of the electron is known with
high degree of accuracy, then the velocity of
the electron will be uncertain.
• On the other hand, if the velocity of the
electron is known precisely, then the position
of the electron will be uncertain .
• EX: Measurement taking in scale without
reading.

57. • To observe an electron , we can illuminate it with
light or electromagnetic radiation. The light used
must have a wavelength smaller than the
dimensions of an electron.
• The high momentum photons of such light (p=
𝒉
ʎ
)
would change the energy of electrons by collisions.
• In this process we can calculate the position of the
electron, but we would know very little about the
velocity of the electron after the collision.

58. Significance of Uncertainty principle
• 1. It rules out existence of definite paths or
trajectories of electrons and other similar
particles.
• The effect of Heisenberg Uncertainty Principle is
significant only for motion of microscopic objects
and is negligible for that of macroscopic objects.
• If we find the exact position of electron then its
velocity is infinite.
• If we find the exact velocity then its location is
infinite.

59. Reason for the failure of the Bohr
model
• It ignores the dual behavior of matter.
• It also contradicts with Heisenberg
uncertainty principle.

60. • Concept of orbitals:
Orbit Orbital
An orbit is a well defined circular
path in which electron revolves. These
are numbered as 1,2,3,4 or K,L,M,N
An orbital is the region of space
around the nucleus where the
probability of finding the electron is
maximum. It may be spherical or
dumbshell in shape.
It represents the movement of electron
around the nucleus in one plane.
It represents the three dimensional
motion of electron around the nucleus.
An orbit means that the position as
well as momentum of an electron can
be known with certainty.
An orbital does not represent the
position and momentum of electron
with complete certainty.

61. • The Shape of s Orbitals:
• The boundary surface diagram for the s orbital
looks like a sphere having the nucleus as its
centre which in two dimensions can be seen as
a circle.
• Hence, we can say that s-orbitals are
spherically symmetric having the probability of
finding the electron at a given distance equal in
all the directions.
• The size of the s orbital is also found to
increase with the increase in the value of the
principal quantum number (n), thus, 4s > 3s> 2s
> 1s.

63. • The Shape of P Orbitals:
• Each p orbital consists of two sections better known
as lobes which lie on either side of the plane passing
through the nucleus.
• The three p orbitals differ in the way the lobes are
oriented whereas they are identical in terms of size
shape and energy.
• As the lobes lie along one of the x, y or z-axis, these
three orbitals are given the designations 2px, 2py, and
2pz. Thus, we can say that there are three p orbitals
whose axes are mutually perpendicular.
• Similar to s orbitals, size, and energy of p orbitals
increase with an increase in the principal quantum
number (4p > 3p > 2p).

64. • The shape of P orbitals

65. • The shape of d orbitals:
• The magnetic orbital quantum number for d
orbitals is given as (-2,-1,0, 1,2). Hence, we
can say that there are five d-orbitals.
• These orbitals are designated as dxy, dyz, dxz,
dx
2
–y
2 and dz
2.
• Out of these five d orbitals, shapes of the
first four d-orbitals are similar to each other,
which is different from the dz
2 orbital
whereas the energy of all five d orbitals is
the same.

69. Nodes in orbitals
• The 1s orbital has no nodes, the entire orbital is the
same phase. The 2s orbital is larger and has one
radial node separating two phases.
• The 3s orbital has two radial nodes separating three
phases.
• All the 2p orbitals have a single angular node, a
plane, separating the positive and negative phases of
the orbitals.
• All the 3d orbitals have two angular nodes. In four of
the orbitals, these nodes are planes separating the
positive and negative phases of the orbitals. In the
fifth orbital, the nodes are two conical surfaces.

70. • The number of nodes is always one less
than the principal quantum number:
Nodes = n - 1.
• In the first electron shell, n = 1. The 1s
orbital has no nodes.
• In the second electron shell, n = 2. The 2s
and 2p orbitals have one node.
• In the third electron shell, n = 3. The 3s,
3p, and 3d orbitals have two nodes, etc.

71. • Types of Node
• There are two types of node: radial and
angular.
• The number of angular nodes is always equal
to the orbital angular momentum quantum
number, l.
• The number of radial nodes = total number of
nodes minus number of angular nodes
• = (n-1) - l

72. Example
• Second Shell
In the second electron shell, the 2s orbital has
n=2 and l=0.
• The number of angular nodes = l = 0.
• The number of radial nodes
• = [(n-1) - l] = [1 - 0] = 1
• In the second electron shell,
The 2p orbital has n=2 and l=1.
The number of angular nodes = l = 1.
The number of radial nodes = [(n-1) - l] = [1 - 1] = 0
•

73. • Third Shell
In the third electron shell, the 3s orbital has n=3
and l=0. The number of angular nodes = l = 0.
The number of radial nodes
• = [(n-1) - l] = [2 - 0] = 2
• In the third electron shell, the 3p orbital has n=3
and l=1. The number of angular nodes = l = 1.
The number of radial nodes
• = [(n-1) - l] = [2 - 1] = 1
• In the third electron shell, the 3d orbital has n=3
and l=2. The number of angular nodes = l = 2.
The number of radial nodes
• = [(n-1) - l] = [2 - 2] = 0

74. Energies of Orbitals
• Energies of orbitals of hydrogen and hydrogen
like particles depend upon the value of principal
quantum number(n) only, those of multi-
electrons atoms depend both upon principal
quantum number(n) as well as azimuthal
quantum number(l).

76. • The order of the increase in energy along the
various orbitals is stated as –
• 1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f

77. orbital n l n+l
1s 1 0 1
2s 2 0 2
2p 2 1 3
3s 3 0 3
3p 3 1 4
4s 4 0 4
3d 3 2 5
4p 4 1 5

78. • In hydrogen atom, the only force of
interaction is the force of attraction between
the negatively charged electron and the
positively charged nucleus.
• But in a multi electron atom, in addition to the
force of attraction between the electrons and
the nucleus, there are forces of repulsion
among the electrons.
• The atom is stable because the net forces of
attraction are greater than forces of repulsion.
• The repulsive forces are on the electrons of the
outer shell by the electrons of the inner shell.

79. • The attractive forces on the electron increases
with increase of the nuclear charge. But these
attractive forces on the outer shell electrons
are greatly reduced by the presence of inner
shell electrons which produce a screening
effect or shielding effect between the outer
shell electrons and the nucleus.

80. • The net positive charge experienced by the
electrons is does much less. This is known as
effective nuclear charge.
• S orbital being spherical in shape , shields the
electrons from the nucleus more effectively
then p orbital which in turn shields more
effectively then d orbital.
• S>p>d>f

81. • Quantum Numbers
• An atom contains a large number of orbitals.
These are distinguished from each other on the
basis of their shape ,size and orientation in
space. These characteristics of an orbital are
expressed in terms of three numbers, called
principal, azimuthal and magnetic quantum
number.

82. • Quantum numbers may be defined as a set of 4
numbers with the help of which we can get
complete information about all the electrons in
• An atom ,ie. location ,energy ,the type of
Orbital occupied, space and orientation of that
orbital.

83. • Principal quantum number:
• It tells the principal energy level or shell to
which the electron belongs.
• It is donated by the letter n and can have any
integral value except 0 ie. n=1,2,3,4…. etc.
• The various principal energy shells are also
designated by the letters K,L,M,N,O……starting
from the nucleus.
• This number helps to explain the main lines of
the spectrum on the basis of the electronic
jump between these shell.

84. • a)It gives the average distance of the electron from
the nucleus ,ie. it largely determined the size of the
electron cloud.
• b) It completely determine the energy of the electron
in hydrogen atom and hydrogen like particles.
• For the first principal shell( K) ,n=1 which means that
this energy shell is lowest energy and lies closest to
the nucleus.
• For the second principal shells( L) ,n=2 and for the
third principal shell( M), n=3 and so on.
• The energies of the various principal shells follow the
sequence:
• K<L<M<N<O…..
• 1<2<3<4<5…….

85. • The maximum number of electrons present in any
principle shell is given by 2n2 Where n is the number
of principal shell.
• Azimuthal or angular momentum quantum number:
• Azimuthal quantum number tells about the :
• 1)Number of sub shells present in the main
shells.
• 2)The angular momentum of the electron
present in any sub shell.
• 3)The relative energies of the various sub shells.
• 4)The shapes of the various sub shells present
within the same principal Shell.

86. • For a given value of n, it can have any integral value
ranging from 0 to n-1.
• For 1st Shell (K) , n=1, l can have only one value i.e. , l=0
• For the 2nd Shell (L) , n=2 , l can have two values i.e. l
=0 and 1
• For the 3rd Shell ( M) , n= 3 , l can have three values i.e.
l=0, 1, 2
• For the 4th shells ( N ) , n=4 , l can have 4 values i.e. l= 0,
1, 2, 3
• Depending upon the values of l , i.e. l= 0, 1, 2 and 3 ,the
different sub shells are designated as s ,p ,d and f
.These notations are the initial letters of the words,
sharp, principal, diffused and fundamental formerly
used to describe different spectral lines.
• l= 4 is called g sub shell ,l = 5 is called is h sub shell.

87. • 1)First principal shell ( K shell or n=1 ) has only
one sub shell called the s sub shell.
• 2)Second principal shell ( L shell or n=2) has
only 2 sub shells i.e. s sub shell ( l = 0 ) and p
sub shell (l=1)
• 3)Third principal shell ( M shell or n= 3) has
three sub shells i.e. s sub shell ( l=0 ), p sub
shell (l= 1) and d sub shell (l=2 )
• 4)Fourth principal shell (N shell or n=4 ) has
four sub shell i.e. s sub shell ( l=0) , p sub shell
( l= 1) , d sub shell ( l=2) and f sub shell ( l=3).

88. • The energies of different sub shells present
within the same principal are found to be in
order
• s < p< d < f
• i.e. an electron in the s – sub shell has lower
energy than that in the p sub shell of the
same principal Shell.
• The maximum number of electrons in the s,
p, d and f sub shell are 2, 6,10 and 14.

90. • Magnetic quantum number:
• This quantum number is required to explain the
fact that when the source producing the line
spectrum is placed in a magnetic field each
spectral line splits up into a number of lines.
• An electron due to its orbital motion around the
nucleus generates an electric field. This electric
field in turn produces a magnetic field which can
interact with the external magnetic field. Thus
under the influence of external magnetic field ,the
electrons of a sub shell can orient themselves in
certain preferred regions of space around the
nucleus called orbitals.

91. • The magnetic quantum number determines the
number of orbitals present in any sub shell.
For every value of l, m has 2l + 1 values
1) For l= 0 , m can have only one value. This means
that s sub shell has only one orientation in space.
s sub shell has only one orbital called s – orbital.
2) For l= 1( p sub shell) , m can have three values i.e.
m = -1 ,0, +1.p sub shell has 3 orbitals. Since these
3 orbitals are oriented along x axis, y axis and z
axis ,therefore they are commonly referred to as
px , py and pz.
3)For l= 2( d sub shell) , m can have five values i.e.
m =-2, -1 ,0, +1, +2 .d sub shell has 5 orbitals.

92. • 4) For l= 3 (f sub shell ), m can have 7 values
i.e.m = -3, – 2, -1 ,0, +1, +2, +3 there are 7
different orientation of f sub shells. f sub shell
has 7 orbitals.
• All the three p orbitals of a particular principal
shell have the same energy in the absence of a
magnetic field. All the five d orbitals of a
particular shell have the same energy and all the
7 f orbitals have same energy.
• These orbitals of the same sub shell having
equal energy are called degenerate orbitals.

93. • In the presence of an external magnetic field,
this degeneracy is broken and orbitals of the
same sub shell acquire slightly different
energy. This cause the splitting of a given
spectral line into many.

94. Spin quantum number
• The electron in an atom not only moves around
the nucleus but also spin about its own axis. This
number give the information about the direction
of spinning of the electron present in any orbital.
• It is represented by s or ms.
• Since the electron in an orbital can spin either in
clockwise direction or in the anticlockwise
direction, hence for a given value of m, s can have
only two values i.e. + ½ and – ½ or these are very
often represented by two arrows pointing in the
opposite direction i.e. ↑ or ↓.

95. • In an atom, if all the orbitals are fully filled, net
magnetic moment is zero and the substance is
diamagnetic.
• If some half filled orbitals are present, the
substance has a net magnetic moment and is
paramagnetic.

96. • This quantum number helps to explain the
magnetic properties of the substance. A
spinning electron behaves like a micro
magnet with a definite magnetic moment. If
an orbital contains 2 electrons, the two
magnetic moment opposes and cancel each
other.

97. • Aufbau Principle
• It states that electrons are filled into atomic
orbitals in the increasing order of orbital energy
level. According to the Aufbau principle, the
available atomic orbitals with the lowest energy
levels are occupied before those with higher
energy levels.
(Or).
• Electrons first occupy the lowest energy
orbital available to them and enter into
higher energy orbitals.

98. • Here, ‘n’ refers to the principal quantum
number and ‘l’ is the azimuthal quantum
number.

100. • The Aufbau principle can be used to
understand the location of electrons in
an atom and their corresponding energy
levels. For example, carbon has 6
electrons and its electronic
configuration is 1s22s22p2.

101. • Pauli exclusion principle states that in a single
atom no two electrons will have an identical
set or the same quantum numbers (n, l, ml,
and ms). To put it in simple terms, every
electron should have or be in its own unique
state (singlet state).
• There are two salient rules that the Pauli
Exclusion Principle follows:
• Only two electrons can occupy the same
orbital.
• The two electrons that are present in the
same orbital must have opposite spins or it
should be antiparallel.

103. • Hunds Rule of Maximum Multiplicity:
According to this rule electron pairing in p, d
and f orbitals cannot occur until each orbital
of a given subshell contains one electron each
or is singly occupied.
• It states that:
• 1. In a sublevel, each orbital is singly
occupied before it is doubly occupied.
• 2. The electrons present in singly occupied
orbitals possess identical spin.

106. Electronic configuration of atoms
• The distribution of electrons into different
shells, sub shells and orbitals of an atom is
called its electronic configuration.
• The electronic configuration of any orbital
can be represented as: nlx
• n is the number of principal shell, l = symbol
of the sub shell or orbital, x= number of
electrons present in the orbital
• 4p1 means that p- sub shell of the 4th main
shell contain one electron.

109. • In certain elements when the two sub shells
differ slightly in their energies, an electron may
shift from a sub shell of lower energy to a sub
shell of higher energy only if such a shift results
in the symmetrical distribution of the electrons
in the various orbitals of the sub shell of higher
energy.

110. • Symmetrical distribution: The electronic
configuration in which all the orbitals of the
same sub shell are either completely filled or
are exactly half filled are more stable because of
symmetrical distribution of electrons.
• The expected electronic configuration of
chromium
If one of the 4s electron shifts to the vacant 3d
orbital ,the distribution of the electron will
become more symmetrical and this will impart
extra stability.

111. The actual electronic configuration of chromium
The expected electronic configuration of copper
If one of the 4s electron shifts to the vacant 3d
orbital ,the distribution of the electron will
become more symmetrical and this will impart
extra stability.

112. • The actual electronic configuration of copper

113. Exchange energy
• The electrons with parallel spins present in the
degenerate orbitals tend to exchange their
position .The energy released during this
exchange is called exchange energy.
• The number of exchanges that can take place is
maximum when degenerate orbitals are exactly
half filled or completely filled. As a result, the
exchange is maximum and so is the stability.

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