Which one of the following molecules is expected to exhibit diamagnetic behaviour?
(i) `N_2` (ii) `O_2`
(iii) `S_2` (iv) `C_2`

Options

A. (i), (ii), (iii), (iv)
B. (ii), (iii)
C. (i), (iii)
D. (i), (iv)

Explanation

To determine which of the given molecules exhibits diamagnetic behavior, we need to analyze the molecular orbital (MO) electron configurations of each molecule and check for unpaired electrons. A molecule is diamagnetic if all its electrons are paired, while it is paramagnetic if it has unpaired electrons.

### Step-by-Step Solution:

1. **Identify the total number of electrons for each molecule:**
- (i) `N_2`: Each nitrogen atom has 7 electrons, so `N_2` has \( 2 \times 7 = 14 \) electrons.
- (ii) `O_2`: Each oxygen atom has 8 electrons, so `O_2` has \( 2 \times 8 = 16 \) electrons.
- (iii) `S_2`: Each sulfur atom has 16 electrons, so `S_2` has \( 2 \times 16 = 32 \) electrons.
- (iv) `C_2`: Each carbon atom has 6 electrons, so `C_2` has \( 2 \times 6 = 12 \) electrons.

2. **Write the molecular orbital electron configurations:**
- (i) **For `N_2` (14 electrons):**
- Configuration: \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \)
- All electrons are paired. **Diamagnetic.**

- (ii) **For `O_2` (16 electrons):**
- Configuration: \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^1 \pi_{2p_y}^1 \)
- There are 2 unpaired electrons in the \( \pi^* \) orbitals. **Paramagnetic.**

- (iii) **For `S_2` (32 electrons):**
- Configuration: \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{3s}^2 \sigma_{3s}^*^2 \sigma_{3p_z}^2 \pi_{3p_x}^1 \pi_{3p_y}^1 \)
- There are 2 unpaired electrons in the \( \pi^* \) orbitals. **Paramagnetic.**

- (iv) **For `C_2` (12 electrons):**
- Configuration: \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \)
- All electrons are paired. **Diamagnetic.**

3. **Conclusion:**
- From the analysis, `N_2` and `C_2` are both diamagnetic because they have all paired electrons.
- `O_2` and `S_2` are paramagnetic due to the presence of unpaired electrons.

### Final Answer:
The molecules expected to exhibit diamagnetic behavior are:
- (i) `N_2`
- (iv) `C_2`