Question

Which ion shows the highest magnetic moment?

• A. \(\text{Ti}^{3+}\)
• B. \(\text{V}^{3+}\)
• C. \(\text{Cr}^{3+}\)
• D. \(\text{Mn}^{2+}\)

Hint:

The magnetic moment depends only on the number of unpaired electrons, so write the d-electron configuration of each ion and count them.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Spin-only magnetic moment is \(\mu = \sqrt{n(n+2)}\) BM, where \(n\) is the number of unpaired electrons. More unpaired electrons means a larger moment.

Step 2: Electronic configurations
\(\text{Ti}^{3+}\): \(3d^1\), \(n=1\)
\(\text{V}^{3+}\): \(3d^2\), \(n=2\)
\(\text{Cr}^{3+}\): \(3d^3\), \(n=3\)
\(\text{Mn}^{2+}\): \(3d^5\), \(n=5\)

Step 3: Calculation
\(\mu(\text{Mn}^{2+}) = \sqrt{5 \times 7} = \sqrt{35} \approx 5.92\) BM, which is larger than \(\sqrt{15}\approx 3.87\) BM for \(\text{Cr}^{3+}\) and the others.

Final Answer:
\(\text{Mn}^{2+}\) has the highest magnetic moment. \[ \boxed{\text{(D) }\text{Mn}^{2+}} \]