The electric potential between a proton and an electron is given by V = V 0 ln r r 0 where r 0 is a constant. Assuming Bohr's model to be applicable, write a variation of r n with n , n being the principal quantum number.

Step-by-step solution

U = e V = e V 0 ln r r 0 F = - d U d r = e V 0 r This force provides the necessary centripetal force. Hence m v 2 r = e V 0 r or v = e V 0 m ...(1) Moreover, mvr = nh 2 π ...(2) Dividing Eq. (2) by Eq. (1), we have mr = nh 2 π m e V 0 or r n ∝ n