Which of the following pairs of ions will have the same value of spin-only magnetic moment? (Given atomic numbers: V =23 , Mn =25 , Fe =26 , Co =27 , Pr =59 , Sm =62 , Dy =66 , Er =68 )

Step-by-step solution

The spin-only magnetic moment is given by = n(n+2) BM, where n is the number of unpaired electrons. Electronic configurations and the number of unpaired electrons ( n ) for the given ions are: Fe ²⁺ ( Z=26 ): [ Ar ] 3d^6 n = 4 Dy ³⁺ ( Z=66 ): [ Xe ] 4f^9 n = 5 Co ²⁺ ( Z=27 ): [ Ar ] 3d^7 n = 3 Er ³⁺ ( Z=68 ): [ Xe ] 4f¹¹ n = 3 V ²⁺ ( Z=23 ): [ Ar ] 3d^3 n = 3 Pr ³⁺ ( Z=59 ): [ Xe ] 4f^2 n = 2 Mn ³⁺ ( Z=25 ): [ Ar ] 3d^4 n = 4 Sm ³⁺ ( Z=62 ): [ Xe ] 4f^5 n = 5 Since Co ²⁺ and Er ³⁺ both have 3 unpaired electrons, th