Suppose an electron is attracted towards 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

`k/r=(mv^(2))/r implies mv^(2) =k` (independent or r)
`n(h/(2pi))=mvrimplies r prop n` and `T=1/2 mv^(2)` is independent of n.