Magnetic moment of `O_(2)` is nearly 

Options

A. 1.8 BM
B. 2.8 BM
C. 3.8 BM
D. Zero

Answer

To determine the magnetic moment of \( O_2 \), we will follow these steps:

### Step 1: Determine the Electron Configuration of Oxygen
Oxygen has an atomic number of 8. Its electron configuration is:
\[ 1s^2 2s^2 2p^4 \]

### Step 2: Identify the Valence Electrons
For molecular orbital theory, we focus on the valence electrons. The valence shell of oxygen has:
- 2 electrons in the 2s orbital
- 4 electrons in the 2p orbitals

Thus, the total number of valence electrons is \( 2 + 4 = 6 \).

### Step 3: Construct the Molecular Orbital Diagram
1. **Molecular Orbitals Formation**:
- The 2s orbitals combine to form:
- One bonding molecular orbital (\( \sigma_{2s} \))
- One antibonding molecular orbital (\( \sigma^*_{2s} \))
- The 2p orbitals combine to form:
- One bonding molecular orbital (\( \sigma_{2p_z} \))
- Two degenerate pi bonding molecular orbitals (\( \pi_{2p_y} \) and \( \pi_{2p_x} \))
- One antibonding molecular orbital (\( \sigma^*_{2p_z} \))
- Two degenerate pi antibonding molecular orbitals (\( \pi^*_{2p_y} \) and \( \pi^*_{2p_x} \))

2. **Filling the Molecular Orbitals**:
- Fill the molecular orbitals with the total of 12 electrons (6 from each oxygen atom).
- The filling order is:
- \( \sigma_{2s}^2 \)
- \( \sigma^*_{2s}^2 \)
- \( \sigma_{2p_z}^2 \)
- \( \pi_{2p_y}^2 \)
- \( \pi_{2p_x}^1 \)
- \( \pi^*_{2p_y}^1 \)

### Step 4: Count the Unpaired Electrons
From the filling:
- The \( \pi_{2p_x} \) and \( \pi_{2p_y} \) orbitals each contain 1 unpaired electron.
- Thus, there are **2 unpaired electrons** in \( O_2 \).

### Step 5: Calculate the Magnetic Moment
The formula for the magnetic moment (\( \mu \)) is given by:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

Substituting \( n = 2 \):
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{2 \times 4} = \sqrt{8} = 2\sqrt{2} \text{ Bohr magneton} \]

### Step 6: Calculate the Numerical Value
The value of \( 2\sqrt{2} \) is approximately:
\[ 2\sqrt{2} \approx 2.8 \text{ Bohr magneton} \]

### Conclusion
The magnetic moment of \( O_2 \) is nearly **2.8 Bohr magneton**.

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