1. Meaning of positive electron gain enthalpy

Electron gain enthalpy is the enthalpy change when an electron is added to an isolated gaseous atom:

$X(g) + e^- \rightarrow X^-(g)$

• If energy is released, electron gain enthalpy is negative.
• If energy must be supplied, electron gain enthalpy is positive.

For inert gases, the valence shell is completely filled, so adding an extra electron is unfavorable. Hence, their electron gain enthalpy is positive.

2. Why does the value change down the group?

Among noble gases:

• He has configuration $1s^2$.
• Adding an electron means putting it into the next shell ($2s$), which is very unfavorable.
• So helium has the highest positive electron gain enthalpy.

As we move down the group from He to Xe:

• Atomic size increases.
• The incoming electron experiences less repulsion and enters a shell that is relatively less difficult to accommodate.
• Therefore, the positive electron gain enthalpy generally decreases down the group.

So the order is:

$\mathrm{He} > \mathrm{Ne} > \mathrm{Kr} > \mathrm{Xe}$

in terms of magnitude of positive electron gain enthalpy.

If written in increasing order of electron gain enthalpy value:

$\mathrm{Xe} < \mathrm{Kr} < \mathrm{Ne} < \mathrm{He}$

3. Check the options

• A: $\mathrm{He < Ne < Kr < Xe}$ ❌
• B: $\mathrm{He < Xe < Kr < Ne}$ ❌
• C: $\mathrm{Xe < Kr < Ne < He}$ ✅
• D: $\mathrm{He < Kr < Xe < Ne}$ ❌

4. Final answer

The correct order is:

$\boxed{\mathrm{Xe < Kr < Ne < He}}$

So, Option C is correct.