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What are Quantum Numbers?
4 Quantum Numbers
(i) Principal Quantum Number (n):
It is obtained by mathematical solution of r-part of the Schrödinger wave equation.
Its values are:
n = 1, 2, 3, ………..,∞
- It represents the shells or orbits or energy levels
When n = 1
It means 1st shell or K-shell
n = 2
It means 2nd shell or L-shell
n = 3
It means 3rd shell or M-shell
- It also indicates energy. Higher is the value of “n” more is the energy.
- It also indicates the distance of the electron from the nucleus. Higher is the value of “n” away is the electron from the nucleus.
- The numbers of electrons in a shell are calculated by it as 2n2.
(ii) Azimuthal Quantum Number (ℓ):
It is obtained by the mathematical solution of θ-part of the Schrödinger wave equation. It is also called a secondary quantum number. Its values are:
ℓ = 0, 1, 2, 3, ……….., n-1
- It represents the subshells or energy sub-levels
When ℓ = 0 It means s-sub shell (spherical shaped)
s stands for sharp
ℓ = 1
It means p-subshell (dumbbell-shaped)
p stands for principal
ℓ = 2
It means d-sub shell
d stands for diffused
ℓ = 3
It means f-subshell
f stands for fundamental
- It also indicates energy up to some extent. Higher is the value of “ℓ” more is the energy.
- It also represents the shapes of orbitals.
- The number of orbitals in a sub-shell can be calculated by it.
- Number of orbitals in a sub-shell = 2 ℓ + 1
- The number of electrons in a sub-shell can be calculated by it.
Number of electrons in a sub-shell = 2(2 ℓ + 1)
(iii) Magnetic Quantum Number (mℓ ):
It is obtained by mathematical solution of Ø-part of Schrödinger wave equation. Its values are:
Values of mℓ = – ℓ , …,0 ,……..,+ ℓ
The number of values of mℓ = 2 ℓ + 1
- It represents orbitals and their orientations
e.g ( i) if ℓ = 1 It means p-subshell and for p-subshell,
Values of mℓ = 2ℓ + 1 = 2 x 1 +1 = 3
These values of mℓ = -1,0,+1
It means that the p-subshell has three orbitals with three different orientations.
orbitals px py pz
mℓ +1 -1 0
e.g(ii) if ℓ = 2 It means d-sub shell
and for d-subshell, number of values of mℓ = 2ℓ + 1 = 2 x 2 +1 = 5
these values of mℓ are = -2, -1, 0, +1, +2
It means that d-subshell has five orbitals with five different orientations.
dxy dyz dz2 dxz dx2-y2
mℓ -2 -1 0 +1 +2
Spin Quantum Number (ms):
It describes the spin of electrons. Its values are
ms = + ½ , – ½
When ms = – ½ electron shows clockwise spin (↑)
ms = + ½ electron shows anti-clockwise spin (↓)
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