Suppose an electron is attracted toward the origin by a force`(k)/(r )` where `k` is a constant and `r` is the distance of the electron from the origin .By applying Bohr model to this system the radius of the `n^(th)` orbital of the electron is found to be `r_(n)` and the kinetic energy of the electron to be `T_(n)` , Then which of the following is true ?

Options

A. `T_n prop (1)/(n^2),r_n prop n^2`
B. `T_n` independent of `n, r_n prop n`
C. `T_n prop (1)/(n) , r_n prop n`
D. `T_n prop (1)/(n) , r_n prop n^2 `

Answer

B

Explanation

when `F= (k )/(r ) =` centripetal force , then `(k )/(r ) (mv^2)/(r ) implies mv^2 = ` costant `implies ` kinetic energy is constant `implies ` T is independent of n .