Which of the following molecules/ins does not contain unpaired electrons?

Options

A. `N_(2)^(+)`
B. `O_(2)`
C. `O_(2)^(2-)`
D. `B_(2)`

Explanation

To determine which of the given molecules or ions does not contain unpaired electrons, we will analyze each species using molecular orbital theory. The species we need to evaluate are N2+, O2, O2²⁻, and B2.

### Step-by-Step Solution:

1. **Identify the number of electrons in each species:**
- **N2+**: Nitrogen (N) has 7 electrons, so N2 has 14 electrons. N2+ has one less electron, giving it 13 electrons.
- **O2**: Oxygen (O) has 8 electrons, so O2 has 16 electrons.
- **O2²⁻**: O2 has 16 electrons, and the 2- charge means it has 2 additional electrons, totaling 18 electrons.
- **B2**: Boron (B) has 5 electrons, so B2 has 10 electrons.

2. **Determine the electron configuration using molecular orbital theory:**
- For species with less than 14 electrons (like N2+, B2):
- The molecular orbitals are filled as follows:
- **B2 (10 electrons)**:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p)², π(2p)²
- This results in 2 unpaired electrons in the π(2p) orbitals.
- **N2+ (13 electrons)**:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p)², π(2p)³
- This results in 1 unpaired electron in the π(2p) orbital.

- For species with 14 or more electrons (like O2 and O2²⁻):
- **O2 (16 electrons)**:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p)², π(2p)⁴
- This results in 2 unpaired electrons in the π(2p) orbitals.
- **O2²⁻ (18 electrons)**:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p)², π(2p)⁴, and 2 additional electrons filling the last π(2p) orbital.
- This results in all electrons being paired.

3. **Conclusion:**
- **N2+** has 1 unpaired electron.
- **O2** has 2 unpaired electrons.
- **B2** has 2 unpaired electrons.
- **O2²⁻** has all paired electrons.

Thus, the species that does not contain unpaired electrons is **O2²⁻**.