`N_(0)//2` atoms of `X_((g))` are converted into `X_((g))^(o+)` by energy `E_(1), N_(0)//2` atoms of `X_((g))` are converted inot `X_((g))^(ɵ)` by energy `E_(2)`. Hence ionisation potential and electron affinity of `X_((g))` per atom are

Options

A. `(2E_(1))/(N_(0)),(2(E_(2)-E_(1)))/(N_(0))`
B. `(2E_(1))/(N_(0)), (2E_(2))/(N_(0))`
C. `((E_(1)-E_(2)))/(N_(0)), (2E_(2))/(N_(0))`
D. None is correct.

Explanation

To solve the problem, we need to determine the ionization potential and electron affinity of the element \( X \) based on the given energies \( E_1 \) and \( E_2 \) and the number of atoms \( N_0/2 \).

### Step-by-Step Solution:

1. **Understanding Ionization Potential**:
- Ionization potential (IP) is the energy required to remove one mole of electrons from one mole of gaseous atoms.
- In the problem, \( N_0/2 \) atoms of \( X \) are converted into \( X^+ \) by energy \( E_1 \).
- Therefore, the energy required to ionize \( N_0/2 \) atoms is given as \( E_1 \).

2. **Relating Energy to Ionization Potential**:
- The total energy \( E_1 \) for \( N_0/2 \) atoms can be expressed in terms of the ionization potential \( I \):
\[ E_1 = \frac{N_0}{2} \times I \]
- Rearranging this gives:
\[ I = \frac{2E_1}{N_0} \]

3. **Understanding Electron Affinity**:
- Electron affinity (EA) is the energy released when one mole of electrons is added to one mole of gaseous atoms.
- In the problem, \( N_0/2 \) atoms of \( X \) are converted into \( X^- \) by energy \( E_2 \).
- Thus, the energy required to add electrons to \( N_0/2 \) atoms is given as \( E_2 \).

4. **Relating Energy to Electron Affinity**:
- The total energy \( E_2 \) for \( N_0/2 \) atoms can be expressed in terms of the electron affinity \( E \):
\[ E_2 = \frac{N_0}{2} \times E \]
- Rearranging this gives:
\[ E = \frac{2E_2}{N_0} \]

5. **Final Expressions**:
- Therefore, we have the following expressions for ionization potential and electron affinity:
\[ I = \frac{2E_1}{N_0} \]
\[ E = \frac{2E_2}{N_0} \]

### Summary of Results:
- Ionization Potential \( I = \frac{2E_1}{N_0} \)
- Electron Affinity \( E = \frac{2E_2}{N_0} \)