Stability of the species `Li_(2), Li_(2)^(-)` and `Li_(2)^(+)` increases in the order of

Options

A. `Li_(2)^(-) lt Li_(2) lt Li_(2)^(+)`
B. `Li_(2) lt Li_(2)^(+) lt Li_(2)^(-)`
C. `Li_(2)^(-) lt Li_(2)^(+) lt Li_(2)`
D. `Li_(2) lt Li_(2) lt Li_(2)^(+)`

Explanation

To determine the stability of the species \( \text{Li}_2 \), \( \text{Li}_2^- \), and \( \text{Li}_2^+ \), we need to calculate the bond order for each species. The bond order is a measure of the stability of a bond; higher bond orders indicate greater stability.

### Step 1: Calculate the bond order for \( \text{Li}_2 \)

1. **Identify the number of electrons**: \( \text{Li}_2 \) has 6 electrons (3 from each lithium atom).
2. **Write the molecular orbital configuration**:
- \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \)
3. **Count bonding and antibonding electrons**:
- Bonding electrons = 4 (from \( \sigma_{1s}^2 \) and \( \sigma_{2s}^2 \))
- Antibonding electrons = 2 (from \( \sigma_{1s}^*^2 \))
4. **Calculate bond order**:
\[ \text{Bond Order} = \frac{\text{Bonding Electrons} - \text{Antibonding Electrons}}{2} = \frac{4 - 2}{2} = 1 \]

### Step 2: Calculate the bond order for \( \text{Li}_2^+ \)

1. **Identify the number of electrons**: \( \text{Li}_2^+ \) has 5 electrons.
2. **Write the molecular orbital configuration**:
- \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^1 \)
3. **Count bonding and antibonding electrons**:
- Bonding electrons = 3 (from \( \sigma_{1s}^2 \) and \( \sigma_{2s}^1 \))
- Antibonding electrons = 2 (from \( \sigma_{1s}^*^2 \))
4. **Calculate bond order**:
\[ \text{Bond Order} = \frac{3 - 2}{2} = 0.5 \]

### Step 3: Calculate the bond order for \( \text{Li}_2^- \)

1. **Identify the number of electrons**: \( \text{Li}_2^- \) has 7 electrons.
2. **Write the molecular orbital configuration**:
- \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^1 \)
3. **Count bonding and antibonding electrons**:
- Bonding electrons = 4 (from \( \sigma_{1s}^2 \) and \( \sigma_{2s}^2 \))
- Antibonding electrons = 3 (from \( \sigma_{1s}^*^2 \) and \( \sigma_{2s}^*^1 \))
4. **Calculate bond order**:
\[ \text{Bond Order} = \frac{4 - 3}{2} = 0.5 \]

### Step 4: Compare the bond orders

- \( \text{Li}_2 \) has a bond order of 1 (most stable).
- \( \text{Li}_2^+ \) has a bond order of 0.5.
- \( \text{Li}_2^- \) also has a bond order of 0.5.

### Step 5: Determine stability based on bond order

Since both \( \text{Li}_2^+ \) and \( \text{Li}_2^- \) have the same bond order, we need to consider the number of electrons in the antibonding molecular orbitals:
- \( \text{Li}_2^+ \): 2 antibonding electrons.
- \( \text{Li}_2^- \): 3 antibonding electrons.

The species with fewer antibonding electrons is more stable.

### Final Order of Stability

Thus, the order of stability is:
\[ \text{Li}_2 > \text{Li}_2^+ > \text{Li}_2^- \]