Atomic radii vary in a predictable manner across the periodic table. Radii generally decrease along each period (row) of the table from left to right and increase down each group (column). These trends in atomic radii (as well as trends in various other chemical and physical properties of the elements) can be explained by the electron shell theory of the atom.
The increase in atomic radius with increasing atomic number can be explained by the arrangement of electrons in shells of fixed capacity. The shells are generally filled in order of increasing radius, since the negatively charged electrons are attracted by the positively charged protons in the nucleus. As the atomic number increases along each row of the periodic table, the additional electrons go into the same outermost shell, whose radius gradually contracts due to the increasing nuclear charge. In a noble gas, the outermost shell is completely filled; therefore, the additional electron of the next alkali metal will go into the next outer shell, accounting for the sudden increase in the atomic radius (as can be seen in the jump between each period for the first 100 elements in Figure 1).
The increasing nuclear charge is partly counterbalanced by the increasing number of electrons, a phenomenon known as shielding, which explains why atom size usually increases down each column.