Which of the following elements has the most negative electron gain enthalpy?

Options

A. `K`
B. `Cl`
C. `Br`
D. `Cs`

Explanation

To determine which of the given elements has the most negative electron gain enthalpy, we need to analyze the trends in electron gain enthalpy across the periodic table. Here’s a step-by-step solution:

### Step 1: Understand Electron Gain Enthalpy
Electron gain enthalpy refers to the amount of energy released when an electron is added to a neutral atom in the gas phase. A more negative value indicates that more energy is released during the process, meaning the atom has a stronger tendency to gain an electron.

### Step 2: Identify the Elements
The question provides us with four elements: potassium (K), cesium (Cs), chlorine (Cl), and bromine (Br).

### Step 3: Group and Period Trends
- **Group Trends**: As we move down a group in the periodic table, the size of the atoms increases due to the addition of electron shells. This generally leads to a decrease in electron gain enthalpy (becomes less negative) because the added electron is further from the nucleus and experiences less attraction.
- **Period Trends**: As we move from left to right across a period, the atomic size decreases, and the effective nuclear charge increases, leading to a more negative electron gain enthalpy (more energy is released).

### Step 4: Analyze the Given Elements
- **Potassium (K)** and **Cesium (Cs)** are alkali metals (Group 1). They have low electron gain enthalpy values (less negative) because they readily lose an electron rather than gain one.
- **Chlorine (Cl)** and **Bromine (Br)** are halogens (Group 17). They have high electron gain enthalpy values (more negative) because they readily gain an electron to achieve a stable noble gas configuration.

### Step 5: Compare Electron Gain Enthalpy
Among the halogens, chlorine is higher up in the group than bromine, which means chlorine will have a more negative electron gain enthalpy compared to bromine. Therefore, we can conclude:
- Chlorine (Cl) has the most negative electron gain enthalpy among the given options.

### Conclusion
The element with the most negative electron gain enthalpy is **Chlorine (Cl)**.

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