Question

Discuss how the Pauli exclusion principle, the aufbau principle, and Hund's rule work together to explain why vanadium has three unpaired electrons in the ground state.

Answer 1

Ans. According to Pauli exclusion principle, an orbital can contain maximum 2 electron of opposite spin. And Aufbao state that energy of an orbital increases with increase in value of n+l. And Hund's rule stated that electron will be filled singly first then pairing takes places. Apply these 3 rule

Vanadium (z=23) = [Ar] 3d3 4s^2

First we apply Aufbao principle, for 4s, n+l = 4, for 3d:- n+l = 5 and hence the electron will be first first filled in 4s and then 3d.

now apply paul exclusion principle, first 4s orbital will be filled by 2 electron with opposite spin.

now apply hund's rule, there are 5 d orbital and 3 electron left, so, we filled the first 3 electron singly to get stability