Question

What is the value of effective magnetic moment found in +3 oxidation state of Chromium (Z=24)?

• A. 1.73 BM
• B. 3.87 BM
• C. 4.90 BM
• D. 2.84 BM

Hint:

To calculate the effective magnetic moment, use the formula \(\mu_{\text{eff}} = \sqrt{n(n+2)}\), where \(n\) is the number of unpaired electrons.

Answer 1

The Correct Option is B

Step 1: Understanding the calculation of magnetic moment.
The magnetic moment \(\mu_{\text{eff}}\) for a transition metal ion can be calculated using the formula: \[ \mu_{\text{eff}} = \sqrt{n(n+2)} \, \text{BM} \] where \(n\) is the number of unpaired electrons. In the +3 oxidation state, Chromium (Cr\(^{3+}\)) has an electron configuration of [Ar] 3d\(^3\), meaning there are 3 unpaired electrons.

Step 2: Calculation.
Using \(n = 3\), the magnetic moment is: \[ \mu_{\text{eff}} = \sqrt{3(3+2)} = \sqrt{15} \approx 3.87 \, \text{BM} \]
Step 3: Conclusion.
The effective magnetic moment for Cr\(^{3+}\) is (B) 3.87 BM.