The increasing order of atomic radii is F<O<N. This is because electronegativities of these elements decrease in the same order. With increase in electronegativity, the tendency of an atom to attract electron cloud towards the itself increases. Hence, with increase in electronegativity, atomic size decreases. Florine has the highest electronegativity of 4, oxygen has an electronegativity of 3.5 and Nitrogen has an electronegativity of 3. Hence, the atomic size order is F<O<N.

NOTE: Electronegativity is the ability of an atom to attract a shared pair of electron towards itself. It is generally measured in Pauling scale.