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

`U = e V = e V_(0) ln (( r)/(r_0))`
`F= (-d U)/(dr) rArr F= -(e V_(0) r_0)/( r) rArr F = -(K)/( r)`
`(mv^2)/( r_n) = (K)/( r_n) rArr mv = sqrt(m K), mvr_(n) =(nh)/( 2pi)`
`sqrt( m K ) r_(n) = (nh)/(2pi) rArr r_(n) prop n`.