(a) how many sub-shells are associated with n = 4? (b) how many electrons will be present in the sub-shells having m_s value of -1/2 for n = 4?

Answer:

(a) For a given value of ‘n’, ‘l’ can have values from zero to (n – 1). i.e., 0,1,2,3

The four sub-shells are associated with n = 4, which are s, p, d and f.

(b) For n=4

The number of orbitals will be = n²

The number of orbitals = 16.

Two electrons will go to each orbital with spins -1/2 and +1/2

∴ Number of electrons having spin -1/2 will be 16.