Question

The spin-only magnetic moment of \( \text{Cr}^{3+} \) cation is ___________.

• A. 3.742 BM
• B. 3.755 BM
• C. 3.873 BM
• D. 3.633 BM

Hint:

Remember, the spin-only magnetic moment formula, $mu = sqrtn(n+2)$ BM, is essential for estimating the magnetic properties of transition metal ions based solely on their unpaired electrons.

Answer 1

The Correct Option is C

The spin-only magnetic moment, \( \mu \), for a transition metal ion is calculated using the formula: \[ \mu = \sqrt{n(n+2)} \text{ BM} \] where \( n \) is the number of unpaired electrons. For \( \text{Cr}^{3+} \), which has an electronic configuration of \( 3d^3 \) (reflecting the loss of three electrons from the neutral state of Cr), the number of unpaired electrons \( n \) is 3. Calculating the magnetic moment: \[ \mu = \sqrt{3(3+2)} = \sqrt{15} \approx 3.873 \text{ BM} \] Thus, the correct answer is \( \mu \approx 3.873 \text{ BM} \).