The electirc potential between a proton and an electron is given by `V = V_0 ln (r /r_0)` , where r_0 is a constant. Assuming Bhor model to be applicable, write variation of `r_n` with n, being the principal quantum number. (a) `r_n prop n` (b) `r_n prop (1)/(n)` (c ) `r_n^2` (d)`r_n prop (1)/(n^2)`

Options

A. `r_(n) prop n`
B. `r_(n) prop 1//n`
C. `r_(n) prop n^(2)`
D. `r_(n) prop 1//n^(2)`

Answer

A

Explanation

`|F| = |(-d U)/(d r)| = (m v^(2))/( r) implies v = sqrt((U_(0)/(m))` , which is a constant.
So, mv _(n) r_(n) = (n h)/(2 pi) implies r_(n) prop n`.