Why does an increase in the number of protons in the nucleus of an atom
increase the ionization energy of atoms within a period?

As you move left to right, reactivity gets lowered-protons gets increased which results in more attraction therefore less reactivity .

Explanation:

Ionization energy gets increased while going across through a period as the number of protons gets increased, therefore there is more attraction to the nucleus. The more attraction to the nucleus requires the huge energy for the valence e- to be removed.

While moving left to right, reactivity drops - increase in protons therefore more attraction therefore less reactivity .

As you go across, the nuclear charge increases so there is a stronger attraction for electrons therefore it is harder to lose electrons so reactivity decreases.