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(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)) rArr v = (e)/(sqrt(4pi epsilon_(0)a_(0)m))`