What is the relationship between atomic size and atomic number?

Atomic size is a periodic trend, meaning that it repeats in a regular pattern. Going from left to right across a period (horizontal row) of the periodic table the atomic radius or size decreases as the atomic number increases. However, moving from top to bottom within a group (vertical column) the atomic radius increases as the atomic number increases.

The reason for this has to do with the arrangement of electrons. The atomic number represents...

Atomic size is a periodic trend, meaning that it repeats in a regular pattern. Going from left to right across a period (horizontal row) of the periodic table the atomic radius or size decreases as the atomic number increases. However, moving from top to bottom within a group (vertical column) the atomic radius increases as the atomic number increases.

The reason for this has to do with the arrangement of electrons. The atomic number represents the number of protons, which equals the number of electrons in a neutral atom. The size of an atom is determined by the attraction of the electrons to the positive nucleus. When there's more attraction the electrons are pulled in closer. Inner electrons repel outer electrons, shielding the outer electrons from some of the nuclear charge. Within a period, each additional electron is added to the existing energy level. The addition of one proton and one electron with no change in the amount of shielding by inner electrons results in an increase in the amount of postive charge experienced by the outer electrons. This is called the effective nuclear charge. The effective nuclear charge is roughly equal to the atomic number minus the number of inner electrons. Here's an example of why fluorine is smaller than oxygen:

Effective nuclear charge of O = 8-2 = 6, number of electrons = 8

Effective nuclear charge of F = 9-2 = 7, number of electrons = 9

Nine electrons are more attracted by a charge of +7 than eight are by a charge of +6, so fluorine's electrons are pulled in close than oxgyen's. This is just an approximation, there's a little more that goes into calculating a shielding factor.

Moving down a group, the shielding factor increases because each row has an additional level of inner electrons. The electrons are thus less attracted to the nucleus and move further away, resulting in the observed increase in atomic radius going down a group.