The spin-only magnetic moment of a divalent cation ( M ²⁺ ) of a 3 d transition metal in aqueous solution is 3.87 BM . The possible atomic numbers of the metal M are:

Step-by-step solution

The spin-only magnetic moment ( ) is given by the formula = n(n+2) BM , where n is the number of unpaired electrons. Given = 3.87 BM , we have: n(n+2) = 3.87 Squaring both sides gives n(n+2) 15 , which corresponds to n = 3 . Thus, the M ²⁺ ion has 3 unpaired electrons in its 3 d subshell. This is possible for two configurations: 3 d ^3 and 3 d ^7 . Case 1: If M ²⁺ is 3 d ^3 , the neutral metal M must have the configuration [ Ar ] 4 s ^2 3 d ^3 . This corresponds to Vanadium, which has an atomic number of 23 . Case