Oxygen molecule is paramagnetic in nature . What is the paramagnetic content in terms of magnetic moment is `O_(2)^(-)` ? (a) 1.732 (b) 3 (c) 1.5 (d) 2.5

Options

A. `1.732`
B. 3
C. `1.5`
D. `2.5`

Explanation

To determine the paramagnetic content in terms of magnetic moment for the O2^- ion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electronic Configuration of O2:**
- The molecular oxygen (O2) has 16 electrons. Its electronic configuration can be represented as:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p_z)², π(2p_x)², π(2p_y)², π*(2p_x)¹, π*(2p_y)¹
- The two unpaired electrons are in the π* (2p) antibonding orbitals.

2. **Understanding the Electronic Configuration of O2-:**
- The O2^- ion has 17 electrons. The additional electron will occupy one of the π* orbitals:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p_z)², π(2p_x)², π(2p_y)², π*(2p_x)¹, π*(2p_y)², π*(2p_x)¹
- Now, O2^- has one unpaired electron in the π* orbital.

3. **Calculating the Magnetic Moment (μ):**
- The magnetic moment (μ) can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]
- Where \( n \) is the number of unpaired electrons. For O2^-, \( n = 1 \).

4. **Substituting the Value of n:**
- Substitute \( n = 1 \) into the formula:
\[ \mu = \sqrt{1(1 + 2)} = \sqrt{1 \times 3} = \sqrt{3} \]

5. **Calculating the Value:**
- The numerical value of \( \sqrt{3} \) is approximately 1.732.

6. **Conclusion:**
- Therefore, the paramagnetic content in terms of magnetic moment for O2^- is 1.732.

### Final Answer:
The correct answer is (a) 1.732.