If `m` is mass of electron, `v` its velocity, `r` the radius of stationary circular orbit around a nucleus with charge `Ze`, then from Bohr's first postulate, the kinetic energy `k = (1)/(2)mv^(2)` of the electron is

Options

A. `(1)/(2)(Ze^(2))/(r )`
B. `(1)/(2)(Ze^(2))/(r^(2))`
C. `(Ze^(2))/(r )`
D. `(Ze)/(r^(2))`

Answer

A

Explanation

In the revolution of electron, coulomb force provides the necessary centripetal force
`rArr (ze^(2))/(r^(2)) = (mv^(2))/(r ) rArr mv^(2) = (ze^(2))/(r )`
`:. K.E. (1)/(2)mv^(2) = (ze^(2))/(2r)`