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) "independent of n," r_(n) prop n`
B. `T_(n) prop (1)/(n), r_(n) prop n`
C. `T_(n) prop (1)/(n),r_(n) prop n^(2)`
D. `T_(n) prop (1)/(n^(2)), r_(n) prop n^(2)`

Answer

A

Explanation

`(mv^(2))/(r )=(k)/(r ) implies v=sqrt((k)/(m))`
`mvr =(nh)/(2pi)`
`msqrt((k)/(m)) r=(nh)/(2 pi)`
`r=r_(n)=(nh)/(2 pi sqrt(mk)), r_(n) prop n`
`T_(n)=(1)/(2) mv^(2)=(1)/(2)m(k)/(m)=(k)/(2)`
`T_(n) ` is independent of n