What is the relationship between atomic size and atomic number of an atom?

When you look at the structure of the atom, you have a
dense, positive nucleus composed of protons and neutrons. Around the nucleus are a equal
number of negatively charged electrons.  There are two trends taking place when you look
at the elements in the periodic table.

As you go from left
to right in the same period (row) each new element adds one proton (its atomic number)
and one electron. Because the protons are densely packed their increasing positive
charge pulls on the electrons more strongly and the size of the atom gets smaller as you
go across any row.

When you go down a group (a column on
the periodic table) you are adding an additional layer or shell of electrons which are
further from the nucleus than the previous row.  Because Coulomb's law  (F = kQ1Q2/d^2)
says that the force between two particles in inversely proportional to the
square of the distance, the attraction between the positive
nucleus and the surrounding electrons quickly diminishes as the additional electrons are
added. As a result, as you go down a group, the size of the atom will
increase.

In summary, atomic size decreases in a given
period, and increases in a given row.