(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?

(a) n = 4 [Given]

For a given value of ‘n’, ‘L’ can have values from zero to [n-1].

∴ L = 0, 1, 2, 3

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

(b) Number of orbitals in the n^th shell = n²

For n = 4

Number of orbitals = 16

Each orbital has one electron with m_s = -1/2

Hence there will be 16 electrons with m_s = -1/2