Which of the following orderof energies of molecular orbitals of `N_(2)` is correct?

Options

A. `(pi2p_(y) lt (pi2p_(z))lt(pi2p_(x))=(pi2p_(y))`
B. `(pi2p_(y))gt(pi2p_(z))gt(pi2p_(x))=(pi2p_(y))`
C. `(pi2p_(y))lt(pi2p_(z)) lt(pi2p_(x))=(pi2p_(y))`
D. `(pi2p_(y))gt(pi2p_(z))lt(pi2p_(x))=(pi2p_(y))`

Explanation

To determine the correct order of energies of molecular orbitals for \( N_2 \), we will follow these steps:

### Step 1: Determine the total number of electrons in \( N_2 \)
- Nitrogen (N) has an atomic number of 7, which means each nitrogen atom has 7 electrons. Therefore, \( N_2 \) has a total of \( 7 + 7 = 14 \) electrons.

### Step 2: Write the order of molecular orbitals for 14 electrons
- According to molecular orbital theory, the order of energy levels for molecular orbitals in diatomic molecules like \( N_2 \) can be represented as follows (in ascending order of energy):
1. \( \sigma_{1s} \)
2. \( \sigma^*_{1s} \)
3. \( \sigma_{2s} \)
4. \( \sigma^*_{2s} \)
5. \( \sigma_{2p_z} \)
6. \( \pi_{2p_x} = \pi_{2p_y} \) (these two orbitals are degenerate)
7. \( \pi^*_{2p_x} = \pi^*_{2p_y} \) (these two orbitals are also degenerate)

### Step 3: Fill the molecular orbitals with the 14 electrons
- The filling of the molecular orbitals follows the Pauli exclusion principle and Hund's rule:
- \( \sigma_{1s} \) (2 electrons)
- \( \sigma^*_{1s} \) (2 electrons)
- \( \sigma_{2s} \) (2 electrons)
- \( \sigma^*_{2s} \) (2 electrons)
- \( \sigma_{2p_z} \) (2 electrons)
- \( \pi_{2p_x} \) (2 electrons)
- \( \pi_{2p_y} \) (2 electrons)

### Step 4: Identify the correct order of energies
- The correct order of energies for the molecular orbitals of \( N_2 \) is:
- \( \sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \sigma_{2p_z} < \pi_{2p_x} = \pi_{2p_y} < \pi^*_{2p_x} = \pi^*_{2p_y} \)

### Step 5: Check the options provided
- Based on the derived order, we can evaluate the options given in the question. The correct option should reflect the order we have established.

### Conclusion
- The correct order of energies of molecular orbitals for \( N_2 \) is:
- \( \sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \sigma_{2p_z} < \pi_{2p_x} = \pi_{2p_y} < \pi^*_{2p_x} = \pi^*_{2p_y} \)