The spin only magnetic moment in strong Ligand field of $d^{6}$ ion of octahedral complex is:

Question

Accepted Answer

The question asks for the spin-only magnetic moment of a $d^6$ ion in an octahedral complex with a strong ligand field. Let's analyze why Option 1, which states the magnetic moment is 0, is correct.

### Explanation for Option 1:

1. **Strong Ligand Field and Low Spin Configuration:**
   - In an octahedral complex with a strong ligand field, the ligands cause a large splitting of the d-orbitals into two sets: the lower energy t2g orbitals and the higher energy eg orbitals.
   - For a $d^6$ ion, in a strong ligand field, the electrons will pair up in the lower energy t2g orbitals to minimize energy, resulting in a low spin configuration.
   - The electron configuration in this case will be t2g^6 eg^0, with all six electrons paired in the t2g orbitals.

2. **Spin-Only Magnetic Moment Calculation:**
   - The spin-only magnetic moment (μ) is calculated using the formula: μ = √(n(n+2)), where n is the number of unpaired electrons.
   - In the low spin configuration for a $d^6$ ion, there are 0 unpaired electrons (since all electrons are paired in the t2g orbitals).
   - Substituting n = 0 into the formula gives: μ = √(0(0+2)) = √0 = 0.

Thus, the spin-only magnetic moment is 0, which supports Option 1 as the correct answer.

### Explanation for Why Other Options are Incorrect:

- **Option 2 (1.73 D):**
  - This value corresponds to a system with 1 unpaired electron (μ = √(1(1+2)) = √3 ≈ 1.73).
  - In a strong ligand field for a $d^6$ ion, there are no unpaired electrons, making this option incorrect.

- **Option 3 (2.83 D):**
  - This value corresponds to a system with 2 unpaired electrons (μ = √(2(2+2)) = √8 ≈ 2.83).
  - Again, in the strong ligand field scenario, all electrons are paired, so this option is incorrect.

- **Option 4 (4.9 D):**
  - This value suggests a system with 4 unpaired electrons (μ = √(4(4+2)) = √24 ≈ 4.9).
  - Such a configuration is not possible for a $d^6$ ion in a strong ligand field, where all electrons are paired.

In conclusion, the correct answer is Option 1, as the strong ligand field results in a low spin configuration with no unpaired electrons, leading to a spin-only magnetic moment of 0.