An element M belonging to the 3d transition series does not liberate hydrogen gas when treated with dilute HCl . The spin-only magnetic moment of its divalent cation ( M ²⁺ ) in aqueous solution is:

Step-by-step solution

Since the element M belongs to the 3d transition series and does not liberate hydrogen gas from dilute HCl , it must have a positive standard reduction potential. Copper is the only 3d metal with a positive E^ value ( +0.34 V ). Therefore, the element M is Copper ( Cu ). The electronic configuration of Cu is [ Ar ] ,3d¹⁰4s¹ . The electronic configuration of its divalent cation Cu ²⁺ is [ Ar ] ,3d⁹ . In the 3d⁹ configuration, there is 1 unpaired electron ( n = 1 ). The spin-only magnetic moment is given by: = n(n+2)