5.1 QUANTUM NUMBERS OF ELECTRON

CHAPTER 5

ELECTRONIC
CONFIGURATION

F2F: 6 HOURS
NF2F: 6 HOURS

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5.1
Quantum Numbers of

Electron

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Learning Outcomes

At the end of this topic students should be able to:

a) Define the term orbital.

b) State and describe all the four quantum numbers of an
electron in an orbital.
i. principal quantum number, n
ii. angular momentum quantum number, 
*other terms for  are azimuthal or subsidiary quantum number
iii. magnetic quantum number, m
iv. electron spin quantum number, s

c) Sketch the shapes of s, p and d orbitals with correct
orientation.

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Orbital

• An orbital is a three-dimensional region in
space around the nucleus where there is a
high probability of finding an electron.

• The nucleus is described as being surrounded
by an electron cloud

• In quantum mechanics, the electron is
described as occupying a three dimensional
space around the nucleus , called orbitals.

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The Quantum Numbers

Each electron in an atom is described and
characterised by a set of four quantum
numbers:

a) principal quantum number, n
b) angular momentum quantum number, 
c) magnetic quantum number, m
d) electron spin quantum number, s

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Principal Quantum Number, n

 n determines the energy of an orbital and

thereby the energy of the electron in that
particular orbital.
 The principal quantum number have only
integer values :

n = 1, 2, 3, …, .

• When n increase (↑), energy increase(↑),
orbital size bigger(↑)

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Angular Momentum Quantum
Number, 

•  defines the shapes of orbital.
•  have integral values from 0 to (n-1) for each

value of n.
• Each value of  corresponds to particular

orbital designated as s, p, d and f

Value of  0 1 2 3
Letter used s p d f
Shape of orbital
spherical Dumb-bell Cloverleaf

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Angular Momentum Quantum
Number, 

• When n = 1,  = 0 only.
At n = 1, there is only 1s orbital

• When n = 2,  = 0 and 1 only.
At n = 2, there are 2s and 2p orbital

• When n = 3,  = 0, 1 and 2 only.
At n = 3, there are 3s, 3p and 3d orbital.

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Angular Momentum Quantum
Number, 

n Orbital/s
10 1s
2 0, 1 2s, 2p
3 0, 1, 2 3s, 3p, 3d

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Magnetic Quantum Number, m

 m describe the orientation in space of the

electron cloud surrounding the nucleus.
 The magnetic quantum number have

integral values from – until  (including 0):

m It means

00 One orientation in s orbital

1 -1, 0 , 1 Three orientation in p-orbital

2 -2, -1, 0, 1, 2 Five orientation in d-orbital

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Electron Spin Quantum Number, s

 s determines the direction of spinning motions of

an electron (either clockwise or anti clockwise)
which is spinning on its own axes, as earth does.

 The electron spin quantum number has a value

of : + 1 or - 1
2 2

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Shapes of Orbital

s-orbital

• s orbital only has one orientation. 12

• when n increase(↑), energy of electron

increase(↑), orbital size bigger(↑).

Shapes of Orbital

p-orbital

• Three p-orbitals px, py, and pz. correspond to
m = -1, 0, and +1.
• p-orbital lies on the stated axis.
• p-orbitals have a node at the nucleus.

• dumb-bell shape.

• Energy of electrons in 2px = 2py = 2pz

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Shapes of Orbital

p orbitals

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Shapes of Orbital

p orbitals

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Shapes of Orbital

p orbitals

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Shapes of Orbital

2px 3px

• When n increase(↑), energy of electron increase(↑),
orbital size bigger(↑).
• Atomic orbitals with the same energy (the same value
of n and ) are referred to as degenerate orbitals. 17

Shapes of Orbital

d-orbital

• Five d-orbital correspond to m = -2, -1, 0, 1 and 2.
• d-orbital lies in-between the stated axis (except dx2-y2

and dz2).
• Atomic orbitals with the same energy (the same value

of n and ) are referred to as degenerate orbitals.

• Cloverleaf shape.

• Energy of electrons in 3dxy = 3dxz = 3dyz = 3d 2 2 = 3dz2
x -y

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Shapes of Orbital

d orbitals x

y

z 19

ddxxyy

Shapes of Orbital

d orbitals x

y

z 20

ddxxzz

Shapes of Orbital

d orbitals x

y

z 21

ddyyzz

Shapes of Orbital

d orbitals x

y

z

ddxx2y22-y2

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Shapes of Orbital

d orbitals z

y

x 23

dd zz22

RELATIONSHIP BETWEEN n ,  , m

-n  m No. of Atomic Max. no of Max. no
Orbital
degenerate designation e- in each of e- in
( < n) (   m  + ) orbitals
 each n

10 0 1 1s 2 2

00 1 2s 2

21 -1, 0, 1 3 2px , 2py 6 8
0 0 , 2pz
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1 3s 2
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1 -1, 0, 1 3 3px , 3py , 6
3 3pz

2 -2 , -1, 0, 1 , 2 5 3dxy , 3dxz , 10
3dyz , 3dx2-y2,
3dz2

Example 1

For each of the following orbitals, state its
value of n,  and m;

a) 2s
b) 3px
c) 4dz2
d) 5py

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Answer 1

a) n = 2 ;  = 0 ; m = 0
b) n = 3 ;  = 1 ; m = -1 @ 0 @ 1
c) n = 4 ;  = 2 ; m = -2 @ -1 @ 0 @ 1 @ 2
d) n=5 ;  = 1 ; m = -1 @ 0 @ 1

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Example 2

Identify whether the following orbitals are
acceptable or not, and explain:

a) 7s
b) 2d
c) 3p
d) 1p

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Answer 2

a) Orbital 7s is acceptable.
When n = 7
 = 0, 1, 2, 3, 4, 5, 6.
7s orbital n = 7,  = 0

b) 2d orbital is not acceptable.
d orbital is designated by  =2.
When n = 2,  can be 0 and 1 only. The allowed
orbitals is only 2s and 2p.

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Answer 2

c) 3p orbital is acceptable.
When n = 3,  can be 0, 1 and 2.
3p orbital n= 3,  =1

d) 1p orbital is not acceptable.
When n = 1,  only can be 0
1p orbital n= 1,  =1
n≠

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Example 3

Explain why the following set of quantum
numbers are not accepted.

a) (2, 2, 0, +½)
b) (0, 0, 2, +½)
c) (3, 1, -2, -½)

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Answer 3

a) When n=2,  =0 and 1 only.  cannot be 2.
b) The value of n starts with 1. n cannot be zero.
c) When  =1, m must be -1 , 0 or 1 only.

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Example 4

1s2 2s2 2p6 3s2 3p6 4s2 3d1
Based on the electronic configuration above,
state the no. of electrons when:
a) n = 3
b)  = 0
c)  = 1
d) m = 2

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Answer 4

1s2 2s2 2p6 3s2 3p6 4s2 3d1

a) When n = 3, no of e = 2 + 6 + 1 = 9
b) When  = 0(s orbital), no of e = 2+2 +2 + 2 = 8
c) When  = 1(p orbital), no of e = 6 + 6 = 12
d) When m = 2 ( = 2, d orbital), no of e = 1

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