how does atomic radii changes from groups to periods?
The atomic radii increases as we go down within a group. It is simply because when we go down a group, the number of electrons of each element increases. The number of shells (n) increases. This is also caused by the increase in the shielding effect, hence the size of atom increases.
Atomic radius decreases across a period because valence electrons are being added to the same energy level at the same time the nucleus is increasing in protons. The increase in nuclear charge attracts the electrons more strongly, pulling them closer to the nucleus. Hence atomic radii decreases.