Question

The magnetic moment of a complex having 3 unpaired electrons is closest to: \[ \mu = \sqrt{n(n+2)}\ \text{BM} \]

• A. \(1.73\ \text{BM}\)
• B. \(2.84\ \text{BM}\)
• C. \(3.87\ \text{BM}\)
• D. \(4.90\ \text{BM}\)

Hint:

Common magnetic moments: \(1\) unpaired electron \(\to1.73\) BM, \(2\) unpaired electrons \(\to2.84\) BM, \(3\) unpaired electrons \(\to3.87\) BM.

Answer 1

The Correct Option is C

Concept: The spin-only magnetic moment of a coordination complex is calculated using: \[ \mu = \sqrt{n(n+2)}\ \text{BM} \] where \(n\) is the number of unpaired electrons.

Step 1: Identify the number of unpaired electrons.
The complex contains: \[ n=3 \] unpaired electrons.

Step 2: Substitute the value into the formula.
Using the formula: \[ \mu=\sqrt{n(n+2)} \] Substituting \(n=3\): \[ \mu=\sqrt{3(3+2)} \] \[ \mu=\sqrt{3\times5} \] \[ \mu=\sqrt{15} \]

Step 3: Calculate the numerical value.
\[ \sqrt{15}\approx3.87 \] Therefore: \[ \boxed{\mu\approx3.87\ \text{BM}} \]