The electric potential between a proton and as electron is given by `V= V_(0) ln (r )/(r_(0))` , where `r_(0)` is a constant . Assuming Bohr's model to be applicable , write variation of `r_(n)` with `n,n` being the principal quantum number ?

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`.