Before we jump straight in, we really need to define how we measure the radius of an atom …
This is a tricky one because electrons are not solid particles with a finite edge, their wave-like properties mean that electron density for an atom fades away gradually as we move away from the nucleus of an atom.
We can define the atomic radius of an element as
half the distance between the nuclei of neighbouring atoms
which in metals means the metallic radius
and in non-metals, the covalent radius.
The atomic radius decreases across Period 3 (and we see the same pattern across all periods) because there is an increase in effective nuclear charge as we move from one element to the next.
As we add one more proton to the nucleus, we add one more electron to the same shell (n=3 for Period 3).
The increasing nuclear charge pulls all the electrons closer to the nucleus and this outweighs any increase in electron / electron repulsions. Electrons in the same shell do not shield each other very effectively from this increasing nuclear charge and so the atomic radius decreases.
The trend in atomic radius is broken by the the elements in Group 18 (the Noble gases). Since they are monatomic there is no covalent or metallic radius so we must use the van der Waals radius …
half the distance between non-bonded nuclei
of neighbouring atoms in the solid
The van der Waals radius is significantly greater as there are no bonds in the solid structure pulling atoms closer together.
