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)propn`
C. `T_(n) prop (1)/(n), r_(n)propn`
D. `T_(n) prop(1)/(n)propn^(2)`

Answer

B

Explanation

`(mv^(2))/(r_(n))=(k)/(r_(n))` given `mvr_(n)=(nh)/(2pi)` from Bohr's theory.
Solving `r_(n) propn and T_(n)` is independent of n.