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

Answer

B

Explanation

` U=- (ke^2 )/(2R^2 ) , F=(dU ) /( dR )=- (3 ke ^2 )/( 2R^4 )`
but `F = ( mv^2)/(R ) implies (mv^2 ) /( R ) = ( 3 ke^2 )/(2R^4)`
also , mvR `=(nh )/(2 pi)`
solve to get `: R=( 6 pi ^2 ke^2 m)/( n^2 h^2)`