If potential energy between a proton and an electron is given by `| U | = k e^(2)//2 R^(3)`, where `e` is the charge of electron and `R` is the radius of atom , that radius of Bohr's orbit is given by `(h = Plank's constant, k = constant)`

Options

A. `(k e^(2) m)/(h^(2))`
B. `(6 pi^(2))/(n^(2)) (k e^(2) m)/(h^(2))`
C. `(2 pi)/(n) (k e^(2) m)/(h^(2))`
D. `(4 pi^(2) k e^(2) m)/(n^(2) h^(2))`

Answer

B

Explanation

`U = - (ke^(2))/(2 R^(3)) , F = - (dU)/(d R) = - (3 ke^(2))/(2 R^(4))`
Also `m v R = (n h)/(2 pi)`
Solved to get `R = (6 pi ^(2)ke^(2) m)/(n^(2) h^(2))`