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(4 pi epsilon a_(0) m))/(e)`

Answer

C

Explanation

`(mv^(2))/(r )=(1)/(4pi epislon _(0))(e.e)/(r^(2))`
`v=sqrt((e^(2))/(4pi epsilon_(0) mr))=(e)/(sqrt(4 pi epsilon_(0) ma_(0)))`