'Spin only' magnetic moment is same for which of the following ions? A. $\mathrm{Ti}{}^{3+}$ B. $\mathrm{Cr}{}^{2+}$ C. $\mathrm{Mn}{}^{2+}$ D. $\mathrm{Fe}{}^{2+}$ E. $\mathrm{Sc}{}^{3+}$ Choose the most appropriate answer from the options given below:

Solution & Explanation

\textbf{Answer:} (d) B and D only \textbf{Solution:} The spin-only moment is $\mu =\sqrt{n(n+2)}$ BM, where $n$ is the number of unpaired electrons. Ions with the same $n$ have the same moment. $\mathrm{Ti}{}^{3+}$ is $3\mathrm{d}{}^1$ ($n=1$); $\mathrm{Cr}{}^{2+}$ is $3\mathrm{d}{}^4$ ($n=4$); $\mathrm{Mn}{}^{2+}$ is $3\mathrm{d}{}^5$ ($n=5$); $\mathrm{Fe}{}^{2+}$ is $3\mathrm{d}{}^6$ ($n=4$); $\mathrm{Sc}{}^{3+}$ is $3\mathrm{d}{}^0$ ($n=0$). Only $\mathrm{Cr}{}^{2+}$ (B) and $\mathrm{Fe}{}^{2+}$ (D) have the same number of unpaired electrons ($n=4$), so they have the same spin-only magnetic moment.