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 (most endothermic first and most exothermic last) for the elements beryllium (Be), boron (B), carbon (C), and nitrogen (N), we will analyze the electron gain enthalpy of each element based on their electronic configurations and periodic trends.

### Step-by-Step Solution:

1. **Understanding Electron Gain Enthalpy**:
- Electron gain enthalpy is defined as the amount of energy released when an electron is added to an isolated gaseous atom. A more negative value indicates a more exothermic process, while a less negative or positive value indicates a more endothermic process.

2. **Periodic Trends**:
- As we move from left to right across a period, the electron gain enthalpy generally becomes more negative (more exothermic) because the atomic size decreases and the effective nuclear charge increases, leading to a greater attraction for the added electron.
- Conversely, as we move down a group, the atomic size increases, and the electron gain enthalpy becomes less negative (more endothermic) because the added electron is farther from the nucleus and experiences less attraction.

3. **Analyzing the Elements**:
- **Beryllium (Be)**: Electronic configuration is 1s² 2s². It has a completely filled outer shell, making it less favorable to gain an electron. Thus, it has a positive or less negative electron gain enthalpy.
- **Boron (B)**: Electronic configuration is 1s² 2s² 2p¹. It is more favorable than beryllium but still has a relatively less negative electron gain enthalpy.
- **Carbon (C)**: Electronic configuration is 1s² 2s² 2p². Carbon has a higher tendency to gain an electron compared to boron and beryllium, leading to a more negative electron gain enthalpy.
- **Nitrogen (N)**: Electronic configuration is 1s² 2s² 2p³. Nitrogen has a half-filled stable configuration, making it less favorable to gain an additional electron. Therefore, it has a less negative electron gain enthalpy than carbon.

4. **Ordering the Elements**:
- Based on the analysis:
- Beryllium (Be) has the least negative (most endothermic) electron gain enthalpy.
- Boron (B) comes next.
- Nitrogen (N) has a less negative electron gain enthalpy than carbon.
- Carbon (C) has the most negative (most exothermic) electron gain enthalpy.

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