the correct order of electron gain enthalpy with negative sign of `F,Cl,Br and I` , having atomic number `9,17,35 and 53` respectively is

Options

A. `F gt Cl gt Br gt I`
B. `Cl gt F gt Br gt I`
C. `Br gt Cl gt I gt F`
D. `I gt Br gt Cl gt F`

Explanation

To determine the correct order of electron gain enthalpy (with negative sign) for the halogens Fluorine (F), Chlorine (Cl), Bromine (Br), and Iodine (I), we need to consider the trends in the periodic table and the specific properties of these elements.

### Step-by-Step Solution:

1. **Understanding Electron Gain Enthalpy**:
Electron gain enthalpy refers to the energy change when an electron is added to a neutral atom in the gaseous state. A more negative value indicates a greater tendency to gain an electron.

2. **Group Trend**:
In general, as we move down a group in the periodic table, the size of the atoms increases. This increase in atomic size usually leads to a decrease in electron gain enthalpy because the added electron is further from the nucleus and experiences less attraction.

3. **Analyzing the Halogens**:
The halogens in question are:
- Fluorine (F, atomic number 9)
- Chlorine (Cl, atomic number 17)
- Bromine (Br, atomic number 35)
- Iodine (I, atomic number 53)

4. **Size and Electron Repulsion**:
- Fluorine is the smallest atom among these halogens. When an electron is added to fluorine, it experiences significant inter-electronic repulsion due to its small size and high electron density. This repulsion makes the electron gain enthalpy less favorable (less negative).
- Chlorine, being larger than fluorine, has less electron-electron repulsion when gaining an electron, making its electron gain enthalpy more negative than that of fluorine.

5. **Order of Electron Gain Enthalpy**:
Based on the above analysis, we expect the order to be:
- Chlorine (most negative, highest tendency to gain an electron)
- Fluorine (less negative due to electron repulsion)
- Bromine (less negative than fluorine)
- Iodine (least negative, lowest tendency to gain an electron)

6. **Final Order**:
Therefore, the correct order of electron gain enthalpy (with negative sign) is:
**Cl > F > Br > I**

### Conclusion:
The correct order of electron gain enthalpy with negative sign for F, Cl, Br, and I is Cl, F, Br, I.