The ratio of spin-only magnetic moment values $\mu_{\text {eff }}\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-} / \mu_{\text {eff }}\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ is ____.

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Coordination Compounds

The ratio of spin-only magnetic moment values

μ_{eff} [Cr (CN)_{6}]^{3 -} / μ_{eff} [Cr (H_{2} O)_{6}]^{3 +}

is ____.

Answer: 1

Solution

For

[Cr (CN)_{6}]^{3 -}

Cr^{3 +}

has electronic configuration

3 d^{3}

CN^{-}

is a strong field ligand, causing pairing. Configuration:

t_{2 g}^{3} e_{g}^{0}

, with 3 unpaired electrons.

μ_{1} = n (n + 2) = 3 (3 + 2) = 15

BM

For

[Cr (H_{2} O)_{6}]^{3 +}

H_{2} O

is a weak field ligand, no pairing occurs. Configuration:

t_{2 g}^{3} e_{g}^{0}

, with 3 unpaired electrons.

μ_{2} = 3 (3 + 2) = 15

\frac{μ _{1}}{μ _{2}} = \frac{15}{15} = 1

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Integer answer

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