JEE MAIN - Chemistry (2023 - 25th January Morning Shift - No. 20)
How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? ______________
(Given : Atomic number V, 23; Cr, 24; Fe, 26; Ni, 28)
V$$^{3+}$$, Cr$$^{3+}$$, Fe$$^{2+}$$, Ni$$^{3+}$$
Answer
2
Explanation
$\mu_{\mathrm{s}}=\sqrt{\mathrm{n}(\mathrm{n}+2)} \mathrm{BM} \quad(\mathrm{n}=\mathrm{no}$ of unpaired electrons)
$$ \begin{array}{ll} & n \\ \mathrm{V}^{3+}:[\mathrm{Ar}] 3 \mathrm{~d}^2 4 \mathrm{~s}^0 & 2 \\\\ \mathrm{Cr}^{3+}:[\mathrm{Ar}] 3 \mathrm{~d}^3 4 \mathrm{~s}^0 & 3 \\\\ \mathrm{Fe}^{2+}:[\mathrm{Ar}] 3 \mathrm{~d}^6 4 \mathrm{~s}^0 & 4 \\\\ \mathrm{Ni}^{3+}:[\mathrm{Ar}] 3 \mathrm{~d}^7 4 \mathrm{~s}^0 & 3 \end{array} $$
$\mathrm{Cr}^{3+} ~\&~ \mathrm{Ni}^{3+}$ have same value of $\mu_{\mathrm{s}}$
$$ \begin{array}{ll} & n \\ \mathrm{V}^{3+}:[\mathrm{Ar}] 3 \mathrm{~d}^2 4 \mathrm{~s}^0 & 2 \\\\ \mathrm{Cr}^{3+}:[\mathrm{Ar}] 3 \mathrm{~d}^3 4 \mathrm{~s}^0 & 3 \\\\ \mathrm{Fe}^{2+}:[\mathrm{Ar}] 3 \mathrm{~d}^6 4 \mathrm{~s}^0 & 4 \\\\ \mathrm{Ni}^{3+}:[\mathrm{Ar}] 3 \mathrm{~d}^7 4 \mathrm{~s}^0 & 3 \end{array} $$
$\mathrm{Cr}^{3+} ~\&~ \mathrm{Ni}^{3+}$ have same value of $\mu_{\mathrm{s}}$
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