Question

Spin only magnetic moment is given by

\(\begin{array}{l} \mu = \sqrt{n(n+2)} \; B.M. \end{array}\)

where \(n\) = number of unpaired electrons.

\(Co^{3+}\)

\(\begin{array}{l} Co : [Ar]\,3d^7 4s^2 \end{array}\)

\(\begin{array}{l} Co^{3+} : 3d^6 \end{array}\)

\(n = 4\)

\(\begin{array}{l} \mu = \sqrt{4(4+2)} = \sqrt{24}\;B.M. \end{array}\)

\(Cr^{3+}\)

\(\begin{array}{l} Cr : [Ar]\,3d^5 4s^1 \end{array}\)

\(\begin{array}{l} Cr^{3+} : 3d^3 \end{array}\)

\(n = 3\)

\(\begin{array}{l} \mu = \sqrt{3(3+2)} = \sqrt{15}\;B.M. \end{array}\)

\(Fe^{3+}\)

\(\begin{array}{l} Fe : [Ar]\,3d^6 4s^2 \end{array}\)

\(\begin{array}{l} Fe^{3+} : 3d^5 \end{array}\)

\(n = 5\)

\(\begin{array}{l} \mu = \sqrt{5(5+2)} = \sqrt{35}\;B.M. \end{array}\)

\(Ni^{2+}\)

\(\begin{array}{l} Ni : [Ar]\,3d^8 4s^2 \end{array}\)

\(\begin{array}{l} Ni^{2+} : 3d^8 \end{array}\)

\(n = 2\)

\(\begin{array}{l} \mu = \sqrt{2(2+2)} = \sqrt{8}\;B.M. \end{array}\)

Hence, correct matching is

\(\begin{array}{l} a \rightarrow iv \\ b \rightarrow v \\ c \rightarrow ii \\ d \rightarrow i \end{array}\)

• A. a - iii , b - v , c - i , d - ii
• B. a - iv , b - v , c - ii , d - i
• C. a - iv , b - i, c - ii , d - iii
• D. a - i , b - ii , c - iii , d - iv

Answer 1

The Correct Option is B

Magnetic moment is given by 

\(\begin{array}{l} \mu = \sqrt{n(n+2)} \; \text{B.M.} \end{array}\)

where \(n\) = number of unpaired electrons.

\(Co^{3+}\)

\(Co : [Ar]\,3d^7 4s^2\)

\(\begin{array}{l} Co^{3+} : 3d^6 \end{array}\)

Number of unpaired electrons \(n = 4\)

\(\begin{array}{l} \mu = \sqrt{4(4+2)} = \sqrt{24}\,\text{B.M.} \end{array}\)

\(Cr^{3+}\)

\(Cr : [Ar]\,3d^5 4s^1\)

\(\begin{array}{l} Cr^{3+} : 3d^3 \end{array}\)

Number of unpaired electrons \(n = 3\)

\(\begin{array}{l} \mu = \sqrt{3(3+2)} = \sqrt{15}\,\text{B.M.} \end{array}\)

\(Fe^{3+}\)

\(Fe : [Ar]\,3d^6 4s^2\)

\(\begin{array}{l} Fe^{3+} : 3d^5 \end{array}\)

Number of unpaired electrons \(n = 5\)

\(\begin{array}{l} \mu = \sqrt{5(5+2)} = \sqrt{35}\,\text{B.M.} \end{array}\)

\(Ni^{2+}\)

\(Ni : [Ar]\,3d^8 4s^2\)

\(\begin{array}{l} Ni^{2+} : 3d^8 \end{array}\)

Number of unpaired electrons \(n = 2\)

\(\begin{array}{l} \mu = \sqrt{2(2+2)} = \sqrt{8}\,\text{B.M.} \end{array}\)

Hence, the correct matching is :

\(\begin{array}{l} Co^{3+} \rightarrow \sqrt{24} \\ Cr^{3+} \rightarrow \sqrt{15} \\ Fe^{3+} \rightarrow \sqrt{35} \\ Ni^{2+} \rightarrow \sqrt{8} \end{array}\)