The electric potential between a proton and an electron is given by V = V0ln⁡rr0, where r0 is a constant. Assuming Bohr’s model to be applicable, write variation of rn with n, n being the principal quantum number.

Potential energy U=eV=eV0ln⁡rr0 ∴ Force F=dUdt=eV0r ∴ The force will provide the necessary centripetal force.  Hence, mv2r=eV0r⇒v=eV0m ---- (i)  and mvr=nh2π-----(ii)  From equations (i) and (ii), mr=nh2πmeV0 or r∝n.