In the Bohr model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electrons. If `a_(0)` is the radius of the ground state orbit, `m` is the mass and `e` is the charge on the electron and `e_(0)` is the vacuum permittivity, the speed of the electron is

Options

A. `0`
B. `(e )/(sqrt( epsi_0 a_0 m ))`
C. `(e )/( sqrt((4 pi epsi_0 a_0 m))`
D. `sqrt((4 pi epsi_0 a_0 m)/(e ))`

Answer

C

Explanation

Centripetal force = coulombin force
` (mv^2 )/(a_0 ) = (1 )/( 4 pi epsi_0 ) .(e xx e )/( a_(0)^(2))`
` implies v^2 = (e^2 )/( 4 pi epsi_0 .a_0 ) . ( e xx e)/( a_(0)^(2))`
`implies v^2 = ( e^2) /( 4 pi epsi_0 .a_0 m ) implies v= (e )/( sqrt( 4 pi epsi_0 . a_0 . m ))`