The electric potential between a proton and an 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| =|(-dU)/(dr)| = (mv^(2))/(r )`
`rArr v = sqrt((v_(0)r)/(m))` which is a constant
`mv_(n)r_(n) = (nh)/(2pi)`
`r_(n) prop n`