Question

The magnetic moment of lanthanide ions is determined from which one of the following relation?

• A. \( \mu = \sqrt{n(n+1)} \)
• B. \( \mu = g \sqrt{J(J+1)} \)
• C. \( \mu = g \sqrt{n(n+1)} \)
• D. \( \mu = 2 \sqrt{J(J+1)} \)

Hint:

The magnetic moment for lanthanide ions is often calculated using the relation involving total angular momentum \( J \).

Answer 1

The Correct Option is B

Step 1: Understanding the relation for magnetic moment. The magnetic moment of lanthanide ions is typically given by the relation: \[ \mu = g \sqrt{J(J+1)} \] Where \( J \) is the total angular momentum quantum number, and \( g \) is the g-factor.
Step 2: Conclusion. Thus, the correct relation is \( \mu = g \sqrt{J(J+1)} \).