How do atomic radius vary in a period and in a group? How do you explain the variation?

Variation of atomic radii in a group. As we move down a group in the periodic table, the atomic radii go on increasing.
Reasons :
(i) Down a group, the nuclear charge goes on increasing. As a result, atomic radii must decrease.

(ii) As we move down a group, a new enthalpy shell is added at each succeeding element though the number of electrons in the valence shell the remain the same. As a result, atomic radii must increase.
The effect of the progressive addition of a new shell outweighs the effect of increased nuclear charge. Hence atomic radii of elements increase with the increase in atomic number as we move from top to bottom down a group.

Variation of atomic radii in a period. As we move from left to right in a period, atomic radii go on decreasing.

Reason: As we move from left to right in a particular period, the atomic number i.e. nuclear charge increases by one unit in each succeeding element but the corresponding addition of electron takes place in the same enthalpy shell. As a result, electrons are pulled little closer to the nucleus thereby making each individual shell smaller and smaller.