The Magnetic Dipole Moment

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

where 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, .

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

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