Question

Is electron gain enthalpy inversely proportional to the atomic radius?

Answer 1

Electron gain enthalpy of an element is the energy released when a neutral isolated gaseous atom accepts an extra electron to form the gaseous negative ion or anion.

Moving across a period, the atomic radius decreases, but effective nuclear charge increases. This makes electron gain enthalpy more negative.
Or in other words, more energy is released.

Moving down a group, the atomic radius increases. But due to screening effect of inner electrons, the nuclear charge will not be enough to hold another electron. Hence, the electron gain enthalpy is less negative. Or less energy is released.

Therefore, in terms of energy released, electron gain enthalpy is inversely proportional to atomic radius.

But when considered in terms of pure mathematics, electron gain enthalpy is directly proportional to atomic radius. Since more negative the number, the less is its magnitude.