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What are Quantum Numbers?
These are certain numbers which are used to locate electrons in an atom or in other words these are address of electrons. They are of four types out of which three are obtained by mathematical solution of the Schrödinger wave equation.
4 Quantum Numbers
(i) Principal Quantum Number (n):
It is obtained by mathematical solution of r-part of 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 sub shells or energy sub-levels
When ℓ = 0 It means s-sub shell (spherical shaped)
s stands for sharp
ℓ = 1
It means p-sub shell (dumbbell-shaped)
p stands for principal
ℓ = 2
It means d-sub shell
d stands for diffused
ℓ = 3
It means f-sub shell
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
- 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-sub shell and for p-sub shell,
Values of mℓ = 2ℓ + 1 = 2 x 1 +1 = 3
These values of mℓ = -1,0,+1
It means that p-sub shell 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-sub shell, 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-sub shell 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 clock wise spin (↑)
ms = + ½ electron shows anti-clock wise spin (↓)
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