Question

List the allowed quantum numbers m_l and m_s for the following subshells and determine the maximum occupancy of the subshells. a) 2p b) 3d c) 4f d) 5g

Answer 1

a) 2p

The value of l = 1, hence the value of ml will be either -1 or 0 or 1

ms (spin quantum number will be +1/2 or -1/2

maximum occupancy of the subshells is 6, i.e. 3 (ml values) * 2 (ms values) = 6 electrons

b) 3d

The value of l = 2, hence the value of ml will be either -2 or -1 or 0 or 1 or 2

ms (spin quantum number will be +1/2 or -1/2

maximum occupancy of the subshells is 10, i.e. 5 (ml values) * 2 (ms values) = 10 electrons

c) 4f

The value of l = 3, hence the value of ml will be either -3 or -2 or -1 or 0 or 1 or 2 or 3

ms (spin quantum number will be (+1/2 or -1/2)

maximum occupancy of the subshells is 14, i.e. 7 (ml values) * 2 (ms values) = 14 electrons

d) 5g

The value of l = 2, hence the value of ml will be either -4 or -3 or -2 or -1 or 0 or 1 or 2 or 3 or 4

ms (spin quantum number will be +1/2 or -1/2

maximum occupancy of the subshells is 18, i.e. 9 (ml values) * 2 (ms values) = 18 electrons