Teacher’s Information
Shafikul Islam
Lecturer (Chemistry)
Morning Glory School & College
Savar Cantonment, Dhaka.
Let’s Observe the Figure
What is the topic to be
discussed today?
Atomic Structure
Concept
of
Quantum Numbers
Learning Outcomes
After completion of this lesson learners will be able to --1. Explain quantum numbers;
2. Draw the shape of different orbitals;
3. Calculate maximum electron holding capacity for a shell and
4. Justify possible and impossible orbitals.
Quantum Numbers
The numbers by which the size and shape of shell, size and
shape of sub-shells, orientations of atomic orbitals and the spin
of the rotating electron are defined are called quantum numbers.
Four quantum numbers are required to describe the position
and direction of rotation of an electron in an atom..
1. Principal quantum number (n)
2. Subsidiary or azimuthal quantum number (l)
3. Magnetic quantum number (m)
4. Spin quantum number
* First three are related to orbits – orbitals.
Principal Quantum Number, n
The principal quantum number (n) describes the size and shape of
shell, or energy level, of an atom. The value of n ranges from 1 to
infinity.
n = 1, 2, 3, 4, …….
With increasing value of n…..
1. Size of shell becomes larger;
2. Energy of shell increases;
3. Maximum electron holding
capacity increases
* Maximum electron holding capacity of any shell = 2n2
Subsidiary Quantum Number, l
The subsidiary or azimuthal quantum number (ℓ)) describes
the size and shape of sub-shell.
Value of l = upto (n-1) including zero
Number of values of l = Number of sub-shells present in that shell
Maximum electron holding capacity of a sub-shell = 2(2l+1)
Examples
For 1st shell (K-shell) : n = 1, l = 0;
K-shell has only one sub-shell.
For 2nd shell (L-shell) : n = 2, l = 0, 1;
L-shell has two sub-shells.
For 3rd shell (M- shell): n = 3, l = 0, 1, 2;
M- shell has three sub-shells.
For 4th shell (N- shell): n = 4, l = 0, 1, 2, 3; N- shell has four sub-shells.
Identity of shells
Representation of a sub-shell
Numerical value of principal
quantum number + English letter
corresponds to the value of l.
Value of
l
0
1
Representation of
Sub-shell
s
p
2
3
d
f
Examples
For 1st shell (K-shell) : n = 1,
l = 0;
K-shell: 1s
For 2nd shell (L-shell) : n = 2,
l = 0, 1;
L-shell: 2s 2p
For 3rd shell (M- shell): n = 3, l = 0, 1, 2;
For 4th shell (N- shell): n = 4,
M- shell: 3s 3p 3d
l = 0, 1, 2, 3; N- shell: 4s 4p 4d 4f
Possible and Impossible sub-shells
Problem: Justify whether the following sub-shells are possible or not?
i. 1p
ii. 2s
iii. 3f
iv. 2d
v. 3d
vi. 4f
vii. 4p
Sample solution:
i. For 1p sub-shell, n = 1, l = 0
We know that, for p-subshell the value of l should be 1 which is not present
when n = 1. Therefore 1p is not possible.
Sample solution:
ii. For 2s sub-shell, n = 2, l = 0,1.
We know that, for s-subshell the value of l should be 0 which is possible
when n = 1. Therefore 2s is possible.
Magnetic Quantum Number, m
Magnetic quantum number, m, expresses the orientation of
different orbitals in 3D space.
Value of m = From −l to +l (0 inclusive)
Number of values of m = Number of orbitals in the subshell
For s-subshell; l = 0, m = 0;
s-subshell has 1 orbital
For p-subshell; l = 1, m = -1, 0, +1;
p-subshell has 3 orbitals
For d-subshell; l = 2, m = -2,-1, 0, +1, +2;
d-subshell has 5 orbitals
For f-subshell; l = 3, m = -3, -2, -1, 0, +1, +2 +3 ;
f-subshell has 7 orbitals
* Any orbital can hold maximum 2 electrons.
Size, shape & orientation of orbitals
Calculation of Maximum Electron Holding
Capacity by a Shell
Problem- Calculate the maximum electron holding capacity for M- shell.
Solution: For M-shell, n = 3.
n
l
m
Number
of
orbitals
Max. No
of
Electron
3
0
1
0
-1, 0, +1
1
3
2
6
2
-2, -1, 0, +1, +2
5
10
Total
18
Spin Quantum Number, s
North
e
South
N
S
Electron aligned with
magnetic field,
ms = + ½
e
Electron aligned against
magnetic field,
ms = - ½
The electron behaves like a tiny charged particle spinning about an axis
through its center. This electron spin generates a magnetic field, the
direction of which depends on the direction of the spin.
Think and answer……..
 Express the sub-shell for which n = 3 and l = 1.
 Show that every shell has s-subshell.
 Why 2d is not possible?
Make a visible models for s, p and
d- subshells.
Home Work
Problem-1: Calculate the maximum electron holding
capacity of K, L and N shells mentioning the quantum
numbers and justify this number by 2n2 rule.
THANKS
FOR
YOUR
ATTENTION
Do Not Panic; Just
Practice…….
Goodbye