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

Electronic configuration :

nl^x method
moeller diagram :

1s < 2s < 2p <3s <3p < 4s < 3d < 4p < 3s < 4d < 5p < 6s < 4f < < 5d < 6p < 7s < 5f < 6d < 7p < 8s