The correct order of electron gain enthalpy (most endothermic first and most exothermic last) is:

Options

A. `Be lt B lt C lt N`
B. `Be lt N lt B lt C`
C. `N lt Be lt C lt B`
D. `N lt C lt B lt Be`

Explanation

To determine the correct order of electron gain enthalpy for the elements beryllium (Be), boron (B), carbon (C), and nitrogen (N), we need to analyze their electronic configurations and the stability of the resulting anions after gaining an electron.

### Step-by-Step Solution:

1. **Identify the Electronic Configurations:**
- Beryllium (Be): 1s² 2s²
- Boron (B): 1s² 2s² 2p¹
- Carbon (C): 1s² 2s² 2p²
- Nitrogen (N): 1s² 2s² 2p³

2. **Understand Electron Gain Enthalpy:**
- Electron gain enthalpy refers to the energy change when an electron is added to a neutral atom to form a negative ion.
- A more exothermic (negative) value indicates that energy is released when an electron is added, while a more endothermic (positive) value indicates that energy is absorbed.

3. **Analyze Stability of the Resulting Anions:**
- **Beryllium (Be):** The 2s² configuration is stable and completely filled. Adding an electron would lead to a less stable configuration (1s² 2s² 2p¹), requiring energy input. Thus, Be has a very endothermic electron gain enthalpy.
- **Boron (B):** The addition of an electron to boron (1s² 2s² 2p¹) results in a configuration (1s² 2s² 2p²) that is less stable than the neutral atom, but more stable than Be. Therefore, it has a less endothermic value than Be.
- **Carbon (C):** The addition of an electron to carbon (1s² 2s² 2p²) results in (1s² 2s² 2p³), which is a half-filled stable configuration. This means it releases energy, making it more exothermic than both Be and B.
- **Nitrogen (N):** The addition of an electron to nitrogen (1s² 2s² 2p³) results in (1s² 2s² 2p⁴), which is less stable than the half-filled state. However, it is still more stable than Be and B, resulting in a less exothermic value than C.

4. **Order the Elements:**
- Based on the analysis:
- Most endothermic: Beryllium (Be)
- Next: Boron (B)
- Then: Nitrogen (N)
- Most exothermic: Carbon (C)

5. **Final Order:**
- The correct order of electron gain enthalpy from most endothermic to most exothermic is:
- Be > B > N > C

### Conclusion:
The correct order of electron gain enthalpy is: **Be > B > N > C**.