How many orbitals are singly occupied in `O_(2)` molecule ?

Options

A. 2
B. 1
C. 3
D. 4

Explanation

To determine how many orbitals are singly occupied in the O₂ molecule, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Total Number of Electrons**:
- Oxygen (O) has an atomic number of 8, which means each oxygen atom has 8 electrons. Therefore, in O₂, the total number of electrons is:
\[ 2 \times 8 = 16 \text{ electrons} \]

2. **Write the Molecular Orbital Configuration**:
- The molecular orbital (MO) configuration for O₂ can be written as:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^1 \]
- This configuration indicates how the 16 electrons are distributed among the molecular orbitals.

3. **Fill the Molecular Orbitals**:
- According to the Aufbau principle and Hund's rule, we fill the orbitals in the following order:
- Fill the lower energy orbitals first (σ and π).
- Each orbital can hold a maximum of 2 electrons.
- For the degenerate π orbitals (π₂p_x and π₂p_y), we place one electron in each before pairing them.

4. **Identify the Singly Occupied Orbitals**:
- From the configuration:
- The σ_{2p_z} orbital is fully occupied with 2 electrons.
- The π_{2p_x} and π_{2p_y} orbitals are fully occupied with 2 electrons each.
- The π^*_{2p_x} and π^*_{2p_y} orbitals each have 1 electron.
- Therefore, the singly occupied orbitals are:
- π^*_{2p_x} (1 electron)
- π^*_{2p_y} (1 electron)

5. **Count the Singly Occupied Orbitals**:
- There are 2 orbitals that are singly occupied:
- π^*_{2p_x}
- π^*_{2p_y}

### Final Answer:
Thus, the number of orbitals that are singly occupied in the O₂ molecule is **2**.

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