Which of the following physical transformations is an exothermic?

Enthalpy of ionisation of one mole of gaseous sodium atom is the energy required to remove an electron from an isolated gaseous atom, which is always an endothermic process ($\Delta H > 0$).

Electron gain enthalpy of one mole of gas phase atoms of chlorine is the energy released when an electron is added to an isolated gaseous chlorine atom. Halogens have highly negative electron gain enthalpies, making this process exothermic ($\Delta H < 0$).

Enthalpy of atomization of one mole of methane gas involves breaking all the C-H bonds to form individual gaseous atoms. Bond breaking requires energy, so it is an endothermic process ($\Delta H > 0$).

Enthalpy of solution of one mole of sodium chloride in water is slightly endothermic ($\Delta H_{sol} = +4 \text{ kJ/mol}$) because the lattice enthalpy is slightly greater than the hydration enthalpy.

Therefore, the only exothermic transformation is the electron gain enthalpy of chlorine.

Answer: Electron gain enthalpy of one mole of gas phase atoms of chlorine.