The first `(Delta_(i)H_(1)` and second `(Delta_(i)H_(2)` ionization enthalpies (in kJ/mol) and electron gain enthalpy (in kJ/mol) of few elements are given below:
`{:("Elements",Delta_(i)H_(1),Delta_(i)H_(2),Delta_(eg)H),(I,520,7300,-60),(II,1681,3374,-328),(III,899,1757,-48),(IV,2372,5251,+48):}`
Which of the following is likely to be an alkali metal?

Options

A. (a) I and IV
B. (b) IV and III
C. (c) II and IV
D. (d) I and III

Explanation

To determine which of the given elements is likely to be an alkali metal based on their ionization enthalpies and electron gain enthalpy, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Ionization Enthalpy and Electron Gain Enthalpy**:
- **Ionization Enthalpy**: The energy required to remove an electron from an atom. Alkali metals have low first ionization enthalpy because they can easily lose their single valence electron.
- **Electron Gain Enthalpy**: The energy change when an electron is added to an atom. Alkali metals typically have a negative electron gain enthalpy, indicating they do not favor gaining electrons.

2. **Analyze the Given Data**:
- The data provided is:
- Element I: \( \Delta_iH_1 = 520 \, \text{kJ/mol}, \Delta_iH_2 = 7300 \, \text{kJ/mol}, \Delta_{eg}H = -60 \, \text{kJ/mol} \)
- Element II: \( \Delta_iH_1 = 1681 \, \text{kJ/mol}, \Delta_iH_2 = 3374 \, \text{kJ/mol}, \Delta_{eg}H = -328 \, \text{kJ/mol} \)
- Element III: \( \Delta_iH_1 = 899 \, \text{kJ/mol}, \Delta_iH_2 = 1757 \, \text{kJ/mol}, \Delta_{eg}H = -48 \, \text{kJ/mol} \)
- Element IV: \( \Delta_iH_1 = 2372 \, \text{kJ/mol}, \Delta_iH_2 = 5251 \, \text{kJ/mol}, \Delta_{eg}H = +48 \, \text{kJ/mol} \)

3. **Identify Low First Ionization Enthalpy**:
- Alkali metals have low first ionization enthalpy. From the data:
- Element I: 520 kJ/mol (low)
- Element II: 1681 kJ/mol (high)
- Element III: 899 kJ/mol (moderate)
- Element IV: 2372 kJ/mol (very high)
- The lowest values are for Element I and Element III.

4. **Identify Negative Electron Gain Enthalpy**:
- Alkali metals typically have negative electron gain enthalpy. From the data:
- Element I: -60 kJ/mol (negative)
- Element II: -328 kJ/mol (negative)
- Element III: -48 kJ/mol (negative)
- Element IV: +48 kJ/mol (positive)
- Elements I, II, and III have negative values, but Element IV has a positive value, indicating it is not likely to be an alkali metal.

5. **Conclusion**:
- Based on the low first ionization enthalpy and negative electron gain enthalpy, Elements I and III are potential candidates for being alkali metals. However, Element I has the lowest first ionization enthalpy and a negative electron gain enthalpy, making it the most likely candidate.
- Therefore, the correct answer is **Option D: Element I and Element III**.