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

Explanation

a. The atomic radius increases down the group `(darr)`. This is due to (i) decrease of `Z_(eff)` (effective nuclear charge) and (ii) increase of number of shells or principal quantum number `(n)`.
i. Effective nuclear charge `(Z_(eff))`: The `Z_(eff)` decreases down the group, due to increase in sreening constant `(sigma)` with the increase in number of inner electrons. Lesser is `Z_(eff)` lesser is the attraction between the nucleus and outer most electrons and consequently the size of the atom increases.
ii. Number of shells: As the total number of shells or principal quantrum number `(n)` increases, the outer electrons get farther and farther away from the nucleus adn hence atomic and ionic radii increase.
b. The atomic radius decreases along the period `(rarr)`. Along the period, the outer electrons remain in the same shell but the nuclear charge increses by one unit at each succeeding element. Thus, `Z_(eff)` also increases along the period. Due to this increased `Z_(eff)` the attraction between nucleus and the outermost electrons increase and atomic size decreases.