Question

The ratio of spin-only magnetic moment values \( \mu_{\text{eff}}[Cr(CN)_6]^{3-}/\mu_{\text{eff}}[Cr(H_2O)_6]^{3+} \) is_____

Hint:

For transition metal complexes, the spin-only magnetic moment depends on the number of unpaired electrons.

Answer 1

Correct Answer: 1

The spin-only magnetic moment is calculated using the formula: \[ \mu_{\text{eff}} = \sqrt{n(n+2)} \, \text{BM} \] For \( [Cr(CN)_6]^{3-} \) (d$^3$): \[ \mu_1 = \sqrt{3(3+2)} = \sqrt{15} \, \text{BM} \] For \( [Cr(H_2O)_6]^{3+} \) (d$^3$): \[ \mu_2 = \sqrt{3(3+2)} = \sqrt{15} \, \text{BM} \] Since both have the same electronic configuration, the ratio is: \[ \frac{\mu_1}{\mu_2} = \frac{\sqrt{15}}{\sqrt{15}} = 1 \] Thus, the ratio of magnetic moments is 1. The correct answer is (1).