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

Answer

C

Explanation

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