Question

The magnetic moment of a trivalent ion of a metal with Z = 24 in aqueous solution is

• A. 3.87 BM
• B. 2.84 BM
• C. 1.73 BM
• D. 4.90 BM
• E. 5.92 BM

Answer 1

The Correct Option is A

The magnetic moment (\(\mu\)) for a metal ion can be calculated using the formula:

\(\mu = \sqrt{n(n + 2)}\) 

where \(n\) is the number of unpaired electrons. Now, for Z = 24, the electronic configuration of the element is:

Cr (Z = 24) → [Ar] 3d⁵ 4s¹

The trivalent ion (Cr³⁺) has an electronic configuration of:

Cr³⁺ → [Ar] 3d³

This indicates there are 3 unpaired electrons in the d-orbital. Hence, \(n = 3\).

Now, we substitute this value into the magnetic moment formula:

\(\mu = \sqrt{3(3 + 2)} = \sqrt{3 \times 5} = \sqrt{15} \approx 3.87 \, \text{BM}\)

This matches the value given in option (1), so the correct magnetic moment for Cr³⁺ is 3.87 BM.