Why does atomic size tend to decrease with increasing atomic number across a row of the periodic table?

Because of greater nuclear attraction on valance shell.

Explanation:

The atomic size tend to decrease in same period of periodic table with increase of atomic number because the electrons are added with in the same shell. When the electron are added, at the same time protons are also added in the nucleus. The positive charge is going to increase and this charge is greater in effect than the charge of electrons. This effect lead to the greater nuclear attraction. The electrons are pull towards the nucleus and valance shell get closer to the nucleus. As a result of this greater nuclear attraction atomic radius decreases with increase of atomic number in period.

c (diamond),

sio2 (quartz)