The atomic radius of an atom is determined by the total number of electrons, electron shells and protons in an atom. Protons are located in the nucleus of an atom and create an effective nuclear charge. Electrons within a shell are attracted to the nuclear charge and vary accordingly.
The two major trends in atomic radii size seen across the periodic table are a decrease when traveling from left to right and an increase when traveling top to bottom. Each is explained by the specific interactions of electrons and protons. Traveling from left to right across a period of elements on the periodic table increases the number of protons and electrons simultaneously by one. The negatively charged electrons are added to the outermost electron shells first and become strongly attracted to the positively charged protons in the nucleus. As the number of electrons and protons increase, so does the total attractive forces within in the atom, causing a decrease in atomic radius.
When traveling from top to bottom of a family of elements on the periodic table, the total number of valence electrons remain the same, but the number of filled electron shells and total electrons increase. The further away from the nucleus an electron is located, the less it experiences the forces of attraction exhibited by the protons. Because the pull of attraction is weaker, the atom is not as compressed and the atomic radius increases.