In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If `a_(0)` is the radius of the ground state orbit, m is the mass and e is the chargeon the electron and `varepsilon_(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(4pi epsi_(0) a_(0) m))`
D. `(sqrt(4 pi epsi_(0)a_(0)m))/(e)`

Answer

C

Explanation

As `F_(e)= F_(c) rArr (1)/(4pi epsi_(0)) (e^(2))/(a_(0)^(2))= (mv^(2))/(a_(0)) rArr v= (e)/(sqrt(4pi epsi_(0) m a_(0)))`