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.