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` I sthe charge on the electron and is the permittivity of vacuum, the speed of the elctron is :

Options

A. `0`
B. `(e)/(sqrt(epsilon_(0)a_(0)m)`
C. `(e)/(sqrt(4pi epsilon_(0)a_(0) m)`
D. `sqrt((4pi epsilon_(0)a_(0)m)/(e))`

Answer

C

Explanation

`(mv^(2))/(a_(0)) = (1)/(4pi epsilon_(0))(e^(2))/(a_(0)^(2))`
`:. v = (e)/(sqrt(4pi epsilon_(0)a_(0)m)`