Variation of ionization energy down the group:
On moving down the group, the ionization enthalpy decreases. This is because the electron is to be removed from the larger valence shell. Screening due to core electrons goes on increasing and the effective nuclear charge decreases down the group. As a result, the removal of the outer electron becomes easier down the group.
Variation of ionization energy across a period:
The screening effect is the same while the effective nuclear charge increases across a period. As a result, the outer electron is held more tightly, and hence, the ionization enthalpy increases across a period. Therefore, the alkali metal shows the lowest first ionization enthalpy while the inert gas shows the highest first ionization enthalpy across a period.