How the radius of atoms changes in periods and in groups, the main subunits of the periodic system. justify the answer?

The radius of atoms of chemical elements belonging to the same period of the main subgroup of the Periodic Table of D.I.Mendeleev increases from left to right. This is due to the fact that the number of electrons on the outer electron shell of the atom increases from left to right in the period (the number of energy levels remains unchanged).
The radius of atoms of chemical elements belonging to one group of the main subgroup of the table of D.I.Mendeleev increases from top to bottom. From top to bottom in the group, the number of energy levels increases (the number of electrons at the external energy level is unchanged), therefore, the size of the atom increases.