Question

The value of the 'spin only' magnetic moment for one of the following configurations is \( 2.84 \, \mathrm{BM} \). The correct one is:

• A. \( d^5 \, (\text{in strong ligand field}) \)
• B. \( d^3 \, (\text{in weak as well as strong fields}) \)
• C. \( d^4 \, (\text{in weak ligand fields}) \)
• D. \( d^4 \, (\text{in strong ligand fields}) \)

Hint:

The magnetic moment of a complex depends on the number of unpaired electrons. In strong ligand fields, electron pairing reduces the number of unpaired electrons, lowering the magnetic moment.

Answer 1

The Correct Option is D

The spin-only magnetic moment is calculated using the formula: \[ \mu = \sqrt{n(n+2)} \, \text{BM}, \] where \( n \) is the number of unpaired electrons. 
Configurations and calculations: 
- \( d^5 \) (strong ligand field): \( n = 1 \), \( \mu = \sqrt{3} = 1.73 \, \text{BM} \), 
- \( d^3 \) (weak/strong field): \( n = 3 \), \( \mu = \sqrt{15} = 3.87 \, \text{BM} \), 
- \( d^4 \) (weak field): \( n = 4 \), \( \mu = \sqrt{24} = 4.89 \, \text{BM} \), 
- \( d^4 \) (strong field): \( n = 2 \), \( \mu = \sqrt{8} = 2.82 \, \text{BM} \). 
Thus, the configuration \( d^4 \) in a strong ligand field corresponds to a magnetic moment of \( \mu = 2.82 \, \text{BM} \). 

Final Answer: \[ \boxed{d^4 \, (\text{in strong ligand fields})} \]