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)^(-)`

Answer

To determine the stability of the species \( \text{Li}_2 \), \( \text{Li}_2^- \), and \( \text{Li}_2^+ \), we will analyze their bond orders using molecular orbital theory. The bond order is a measure of the stability of a molecule; higher bond order indicates greater stability.

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

1. **Determine the number of electrons**: \( \text{Li}_2 \) has a total of 6 electrons (3 from each lithium atom).
2. **Molecular orbital configuration**: The electronic configuration of \( \text{Li}_2 \) is:
\[ \sigma_{1s}^2 \sigma_{1s}^* \sigma_{2s}^2 \sigma_{2s}^* \]
3. **Count bonding and antibonding electrons**:
- Bonding electrons: 4 (from \( \sigma_{1s}^2 \) and \( \sigma_{2s}^2 \))
- Antibonding electrons: 2 (from \( \sigma_{1s}^* \) and \( \sigma_{2s}^* \))
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 of \( \text{Li}_2^- \)

1. **Determine the number of electrons**: \( \text{Li}_2^- \) has a total of 7 electrons (6 from \( \text{Li}_2 \) plus 1 extra electron).
2. **Molecular orbital configuration**: The electronic configuration of \( \text{Li}_2^- \) is:
\[ \sigma_{1s}^2 \sigma_{1s}^* \sigma_{2s}^2 \sigma_{2s}^* \sigma_{2p}^1 \]
3. **Count bonding and antibonding electrons**:
- Bonding electrons: 4 (from \( \sigma_{1s}^2 \) and \( \sigma_{2s}^2 \))
- Antibonding electrons: 3 (from \( \sigma_{1s}^* \), \( \sigma_{2s}^* \), and \( \sigma_{2p}^1 \))
4. **Calculate bond order**:
\[ \text{Bond order} = \frac{4 - 3}{2} = \frac{1}{2} = 0.5 \]

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

1. **Determine the number of electrons**: \( \text{Li}_2^+ \) has a total of 5 electrons (6 from \( \text{Li}_2 \) minus 1).
2. **Molecular orbital configuration**: The electronic configuration of \( \text{Li}_2^+ \) is:
\[ \sigma_{1s}^2 \sigma_{1s}^* \sigma_{2s}^2 \sigma_{2s}^1 \]
3. **Count bonding and antibonding electrons**:
- Bonding electrons: 3 (from \( \sigma_{1s}^2 \) and \( \sigma_{2s}^2 \))
- Antibonding electrons: 2 (from \( \sigma_{1s}^* \) and \( \sigma_{2s}^1 \))
4. **Calculate bond order**:
\[ \text{Bond order} = \frac{3 - 2}{2} = \frac{1}{2} = 0.5 \]

### Step 4: Compare the bond orders and determine stability

- \( \text{Li}_2 \): Bond order = 1 (most stable)
- \( \text{Li}_2^- \): Bond order = 0.5
- \( \text{Li}_2^+ \): Bond order = 0.5

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

- \( \text{Li}_2 \) has the highest bond order and is therefore the most stable.
- Between \( \text{Li}_2^- \) and \( \text{Li}_2^+ \), \( \text{Li}_2^- \) has 4 bonding electrons compared to 3 in \( \text{Li}_2^+ \), making \( \text{Li}_2^- \) more stable than \( \text{Li}_2^+ \).

### Final Order of Stability

The increasing order of stability is:
\[ \text{Li}_2^+ < \text{Li}_2^- < \text{Li}_2 \]