Increasing nuclear charge pulls the electrons closer to the nucleus.
Explanation:Increasing nuclear charge pulls the electrons closer to the nucleus.
Now, assuming that this one sentence didn't actually make anything clearer, let's break this down:
Elements in the same period have electrons with roughly the same amount of energy.
As you move across a period from left to right, the elements have an increasing number of protons.
Protons pull electrons closer to the nucleus because positive and negative charges attract.
Because the electrons of all the elements in a period have the same amount of energy (i.e. they're pretty much equal) and an increasing number of protons gives the nucleus more "pulling power", the electrons are pulled more tightly to the nucleus. This makes the atom smaller.