In which of the following molecules, ` sigma 2p_(z)` molecular orbital is filled after `pi 2p_(x) and pi 2p_(y)` molecular orbitals ?

Options

A. `O_(2) `
B. `Ne_(2)`
C. `N_(2)`
D. `F_(2)`

Explanation

To determine in which of the following molecules the `sigma 2p_(z)` molecular orbital is filled after the `pi 2p_(x)` and `pi 2p_(y)` molecular orbitals, we need to analyze the molecular orbital (MO) filling order based on whether there is sp mixing or not.

### Step-by-step Solution:

1. **Understanding Molecular Orbital Theory**:
- In molecular orbital theory, atomic orbitals combine to form molecular orbitals. These molecular orbitals can be bonding or antibonding.
- The order in which these orbitals are filled depends on the presence of sp mixing.

2. **Identify sp Mixing**:
- Sp mixing occurs in diatomic molecules up to nitrogen (N2). In these cases, the energy levels of the molecular orbitals change due to the mixing of the s and p orbitals.
- For molecules beyond nitrogen (like O2 and F2), sp mixing does not occur, and the filling order changes.

3. **Filling Order with sp Mixing**:
- For molecules with sp mixing (like N2), the filling order is:
- `sigma 2s` < `sigma* 2s` < `pi 2p_(x)` = `pi 2p_(y)` < `sigma 2p_(z)`
- Here, the `sigma 2p_(z)` orbital is filled after the `pi 2p_(x)` and `pi 2p_(y)` orbitals.

4. **Filling Order without sp Mixing**:
- For molecules without sp mixing (like O2), the filling order is:
- `sigma 2s` < `sigma* 2s` < `sigma 2p_(z)` < `pi 2p_(x)` = `pi 2p_(y)`
- In this case, the `sigma 2p_(z)` orbital is filled before the `pi 2p_(x)` and `pi 2p_(y)` orbitals.

5. **Conclusion**:
- Since we are looking for a molecule where the `sigma 2p_(z)` orbital is filled after the `pi 2p_(x)` and `pi 2p_(y)` orbitals, we need to identify a molecule that exhibits sp mixing.
- The only molecule from the provided options that shows sp mixing is nitrogen (N2).

### Final Answer:
The molecule in which the `sigma 2p_(z)` molecular orbital is filled after the `pi 2p_(x)` and `pi 2p_(y)` molecular orbitals is **Nitrogen (N2)**.