According to Bohr’s first postulate, the centripetal force required for electron to revolve around the central positive nucleus is provided by the electrostatic force of attraction between the electron and the nucleus.

If m is the mass of the electron moving with a velocity v in a circular orbit of radius r, then the necessary centripetal force F = mv² / r

The electrostatic force of attraction between the nucleus of charge +Ze, and the electron of charge (-e) is F = 1/4∏ε₀ (Ze)(e) /r²

Hence, mv² / r = 1/4∏ε₀ (Ze)(e) /r²    ----------------------Eqn (1)

According to Bohr’s second postulate, the electron revolve only in certain discrete non radiating orbits for which the angular momentum of the revolving electron is an integral multiple of h/2∏ where h is Plancks constant

mvr  = nh / 2∏ 

Hence, v = nh / 2∏ mr         ---------------------------- Eqn (2)

This gives the speed of the electron in the n th orbit.

Now put eqn (2) in eqn (2), we get

r = n²h² / 4∏² mKZe²

Thus the radius is directly proportional to n² and inversely proportional to Z.