The ratio of spin-only magnetic moment values eff [ Cr ( CN ) 6 ] 3 - / eff [ Cr ( H 2 O ) 6 ] 3 + is _________. [2023]

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Solution

Q.
The ratio of spin-only magnetic moment values $μ_{eff} {[Cr {(CN)}_{6}]}^{3 -} / μ_{eff} {[Cr {(H_{2} O)}_{6}]}^{3 +}$ is _________. [2023]

Ans.
(1)

${[Cr {(CN)}_{6}]}^{3 -}$ ${Cr}^{3 +} \to 3 d^{3} \Rightarrow t_{2 g}^{1, 1, 1} e_{g}^{0, 0},$ $μ = \sqrt{n (n + 2)} BM$ $= \sqrt{3 (3 + 2)} = \sqrt{15} BM$

${[Cr {(H_{2} O)}_{6}]}^{3 +}$ ${Cr}^{3 +} \to 3 d^{3} \Rightarrow t_{2 g}^{1, 1, 1} e_{g}^{0, 0},$ $μ = \sqrt{n (n + 2)} BM$ $= \sqrt{3 (3 + 2)} = \sqrt{15} BM$

$Ratio of magnetic moments = \frac{\sqrt{15}}{\sqrt{15}} = 1$

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