Which of the following species absorb maximum energy in its `HOMO-LUMO` electronic transition?

Options

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

Answer

To determine which species absorbs maximum energy in its HOMO-LUMO electronic transition, we will analyze the molecular orbital (MO) diagrams for the given species: Oxygen (O2), Nitrogen anion (N2^-), Carbon (C2), and Nitrogen (N2). Here’s a step-by-step solution:

### Step 1: Identify the number of electrons in each species
- **Oxygen (O2)**: Each oxygen atom has 8 electrons (2s² 2p⁴), so O2 has a total of 16 electrons.
- **Nitrogen anion (N2^-)**: Each nitrogen atom has 7 electrons (2s² 2p³), so N2 has 14 electrons, plus 1 extra electron from the negative charge, totaling 15 electrons.
- **Carbon (C2)**: Each carbon atom has 6 electrons (2s² 2p²), so C2 has a total of 12 electrons.
- **Nitrogen (N2)**: Each nitrogen atom has 7 electrons, so N2 has a total of 14 electrons.

### Step 2: Draw the Molecular Orbital (MO) diagrams
1. **Oxygen (O2)**:
- The MO configuration is: (σ2s)² (σ*2s)² (σ2p)² (π2p)² (π*2p)² (σ*2p)²
- The highest occupied molecular orbital (HOMO) is π2p and the lowest unoccupied molecular orbital (LUMO) is π*2p.

2. **Nitrogen anion (N2^-)**:
- The MO configuration is: (σ2s)² (σ*2s)² (σ2p)² (π2p)² (π*2p)² (σ*2p)¹
- The HOMO is π*2p and the LUMO is σ*2p.

3. **Carbon (C2)**:
- The MO configuration is: (σ2s)² (σ*2s)² (σ2p)² (π2p)²
- The HOMO is π2p and the LUMO is σ*2p.

4. **Nitrogen (N2)**:
- The MO configuration is: (σ2s)² (σ*2s)² (σ2p)² (π2p)² (π*2p)²
- The HOMO is π2p and the LUMO is π*2p.

### Step 3: Calculate the energy gap between HOMO and LUMO
- The energy absorbed during the electronic transition is proportional to the energy gap between the HOMO and LUMO. The larger the energy gap, the more energy is absorbed.

### Step 4: Compare the energy gaps
- **Oxygen (O2)**: The energy gap between π2p and π*2p is moderate.
- **Nitrogen anion (N2^-)**: The energy gap between π*2p and σ*2p is larger due to the additional electron in the π* orbital.
- **Carbon (C2)**: The energy gap between π2p and σ*2p is smaller compared to nitrogen.
- **Nitrogen (N2)**: The energy gap between π2p and π*2p is moderate.

### Conclusion
The species that absorbs the maximum energy in its HOMO-LUMO electronic transition is **Nitrogen anion (N2^-)** due to the larger energy gap between its HOMO (π*2p) and LUMO (σ*2p).

**Final Answer**: Nitrogen anion (N2^-)

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