(1) rn ∝ n
U = The electrostatic P.E of the electrons, at a distance r from the proton, = eV = eV0ln (r/r0)
∴ F = The magnitude of the force between the electron and proton = \(|-\frac{dU}{dr}|=\frac{eV_0r_0}{r}\)
The force, F, provides the centeripetal force for the electron, orbiting in its nth allowed orbit of radius rn .
From Bohr’s postulate, we also have mvnrn = n h/2π ......(2)
From Eqn. (1) and (2), we get, rn ∝ n