Question

Making use of the Hund rules, find the number of electrons in the only partially filled subshell of the atom whose basic term is

(a) ³F₂; (b) ²P_3/2; (c) ⁶S_5/2.

Answer 1

(a) ³F₂: The maximum value of spin is S = 1 here. This means there are 2 electrons. L = 3 so s and p electrons are ruled out. Thus the simplest possibility is d electrons. This is the correct choice for if we were considering f electrons, the maximum value of L allowed by Pauli principle will be L = 5 (maximum value of the magnitude of magnetic quantum number will be 3 + 2 = 5 .)

Thus the atom has two d electrons in the unfilled shell. 

(b) ²P_3/2 Here L=1, S=1/2 and J=3/2 

Since J = L + S, Hund’s rule implies the shell is more than half full. This means one electron less than a full shell. On the basis of hole picture it is easy to see that we have p electrons. Thus the atom has 5 p electrons. 

(c) ⁶S_5/2 Here L = 0 . We either have five electrons or five holes. The angular part is antisymmetric. For five d electrons, the maximum value of the quantum number consistent with Pauli exclusion principle is ( 2 + 1 + 0 - 1 - 2 ) = 0 so L = 0 . For f or g electrons L > 0 whether the shell has five electrons or five holes. Thus the atom has five d electrons.