 # Quantum Numbers and Electronic Configuration of Elements

### Quantum Numbers :

• a. Principal quantum number (n)
• b. Azimuthal quantum number (l)
• c. Magnetic quantum number (m)
• d. Spin quantum number (s)

a. Principal quantum number (n)
r_{n} = 0.54\frac{n^{2}}{Z}
Indicates size of the orbit.
Indicates energy of electron

b. Azimuthal quantum number (l)
Denoted by letter ' l ' and can have value from 0,1 to (n − 1)
l = 0 → s orbital → spherical
l = 1 → p orbital → dumb-bell
l = 2 → d orbital → double dumb-bell
l = 3 → f orbital → fore fold

c. Magnetic quantum number (m)
can have values −l to +l
total values (2l + 1)

d. Spin quantum number (s)
It can have values s = +½ and s = −½

### Exchange Energy :

Exchange Energy = nC2
=\frac{n!}{(n - 2)! \ 2!}
n = no.of unpaired electrons
Cr = 3d5 4s1 n = 6
6C2 = 15

Magnetic \ moment (\mu) = \sqrt{n(n + 2)} BM

 n μ=\sqrt{n(n + 2)} BM 1 \sqrt{3}=1.732 BM 2 \sqrt{8}=2.823 BM 3 \sqrt{15}=3.89 BM 4 \sqrt{24}=4.88 BM 5 \sqrt{35}=5.89 BM

### Electronic configuration :

nlx method
moeller diagram : 1s < 2s < 2p <3s <3p < 4s < 3d < 4p < 3s < 4d < 5p < 6s < 4f < < 5d < 6p < 7s < 5f < 6d < 7p < 8s

### Part2: View the Topic in this Video from 1:17 to 18:35

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1. The number of electrons in subshell = 2(2l + 1).
2. Number of orbitals in main energy level = n2.
3. Maximum number of electrons in nth shell = 2n2
4. The orbital angular momentum of an electron = \tt \sqrt{l\left(l + 1\right)}\frac{h}{2\pi}

5. Spin angular momentum = \tt \sqrt{s\left(s + 1\right)}\frac{h}{2\pi}

6. Magnetic moment = \tt \sqrt{n\left(n + 2\right)} B.M. (Bohr magneton) of n unpaired e-