Question

Consider that a $d^6$ metal ion $\left(M^{2+}\right)$ forms a complex with aqua ligands, and the spin only magnetic moment of the complex is $4.9$$\mathrm{BM}$. The geometry and the crystal field stabilization energy of the complex is:

• A. Tetrahedral and $-0.6{∆}_t$
• B. Tetrahedral and $-1.6{∆}_t+1P$
• C. Octahedral and $-1.6{∆}_0$
• D. Octahedral and $-2.4{∆}_0+2P$

Answer 1

The correct option is A

Tetrahedral and $-0.6{∆}_t$

Explanation for correct option:

(A) tetrahedral and $\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{6}{\mathbf{∆}}_{\mathbf{t}}$

1. As it is given that spin only magnetic moment of the complex is $4.9BM$ so the number of the unpaired electron must be $4$.
2. The crystal field splitting for the tetrahedral complex is :
3. The crystal field splitting energy for the tetrahedral complex is: $$\begin{gathered} CFSE=-0.6\times 3{∆}_t+0.4\times 3{∆}_t \\ =-1.8{∆}_t+1.2{∆}_t \\ =-0.6{∆}_t \end{gathered}$$

Explanation for incorrect options:

(B) Tetrahedral and $\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{6}{\mathbf{∆}}_{\mathbf{t}}\mathbf{+}\mathbf{1}\mathit{P}$

1. As it can be observed from the calculations done for crystal field splitting that the crystal field energy for the tetrahedral complex is$-0.6{∆}_t$.
2. Hence, the present option is incorrect.

(C) Octahedral and $\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{6}{\mathbf{∆}}_{\mathbf{0}}$

1. The crystal field splitting for the tetrahedral complex is:
2. The crystal field splitting energy for the tetrahedral complex is: $$\begin{gathered} CFSE=-0.4\times 4{∆}_O+0.6\times 2{∆}_O \\ =\left[1.6+1.2\right]{∆}_o \\ =-0.4{∆}_o \end{gathered}$$
3. The calculated crystal field energy and geometry of the complex do not coincide with the given option.

(D) Octahedral and $\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{4}{\mathbf{∆}}_{\mathbf{0}}\mathbf{+}\mathbf{2}\mathit{P}$

1. As it can be observed from the calculations done for crystal field splitting that the crystal field energy for the octahedral complex is$-0.4{∆}_o$.
2. Hence, the present option is incorrect.

Hence option (A) is correct, The geometry of the given complex is tetrahedral and the crystal field splitting energy is $-0.6{∆}_t$.