Which species is diamagnetic and have shortest bond length?

Options

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

Answer

To determine which species is diamagnetic and has the shortest bond length, we will analyze the given options: C2^(-2), N2^(-2), O2^(-2), and O2. We will do this by calculating the electronic configurations, bond orders, and checking for unpaired electrons.

### Step 1: Determine the electronic configuration of each species.

1. **C2^(-2)**:
- Total electrons: 2 (C) × 6 + 2 (from -2 charge) = 14 electrons.
- Molecular orbital filling:
- σ1s², σ*1s², σ2s², σ*2s², π2px², π2py², σ2pz²
- Configuration: σ1s² σ*1s² σ2s² σ*2s² π2px² π2py² σ2pz²
- Total bonding electrons = 10, Total antibonding electrons = 4.
- Bond order (BO) = (10 - 4) / 2 = 3.

2. **N2^(-2)**:
- Total electrons: 2 (N) × 7 + 2 (from -2 charge) = 16 electrons.
- Molecular orbital filling:
- σ1s², σ*1s², σ2s², σ*2s², π2px², π2py², σ2pz², π*2px¹, π*2py¹
- Configuration: σ1s² σ*1s² σ2s² σ*2s² π2px² π2py² σ2pz² π*2px¹ π*2py¹
- Total bonding electrons = 10, Total antibonding electrons = 6.
- Bond order (BO) = (10 - 6) / 2 = 2.
- Contains unpaired electrons (paramagnetic).

3. **O2^(-2)**:
- Total electrons: 2 (O) × 8 + 2 (from -2 charge) = 18 electrons.
- Molecular orbital filling:
- σ1s², σ*1s², σ2s², σ*2s², σ2pz², π2px², π2py², π*2px², π*2py²
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2pz² π2px² π2py² π*2px² π*2py²
- Total bonding electrons = 10, Total antibonding electrons = 8.
- Bond order (BO) = (10 - 8) / 2 = 1.
- All electrons are paired (diamagnetic).

4. **O2**:
- Total electrons: 2 (O) × 8 = 16 electrons.
- Molecular orbital filling:
- σ1s², σ*1s², σ2s², σ*2s², σ2pz², π2px¹, π2py¹
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2pz² π2px¹ π2py¹
- Total bonding electrons = 10, Total antibonding electrons = 6.
- Bond order (BO) = (10 - 6) / 2 = 2.
- Contains unpaired electrons (paramagnetic).

### Step 2: Identify the diamagnetic species and compare bond lengths.

- From the analysis:
- C2^(-2): Diamagnetic, BO = 3
- N2^(-2): Paramagnetic, BO = 2
- O2^(-2): Diamagnetic, BO = 1
- O2: Paramagnetic, BO = 2

### Step 3: Conclusion

Among the diamagnetic species, C2^(-2) has the highest bond order (3), which means it has the shortest bond length. Therefore, the answer to the question is:

**C2^(-2) is the species that is diamagnetic and has the shortest bond length.**

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