In a period, from left to right, with an increase in the atomic number, the oxidizing character increases due to the presence of vacant d orbitals in their valence shells.
Hence, the decreasing order of oxidizing character is F > O > N.
On moving down the group, the oxidizing character decreases. hence, F > Cl.
But O has higher oxidizing character than Cl thus, O > Cl.
Thus, the correct order of chemical reactivity of F, Cl, O, and N in terms of their oxidizing property is F > O > Cl > N.