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 ?

Answer

A

Explanation

`v=v_(0)ln(r/(r_(0)))`. Magnitude of force on electron
`F=|-(dv)/(dr)|e=(v_(0)r_(0)e)/r`. if v is the orbital speed of the electron and `m` its mass, then `(mv^(2))/r=(v_(0)r_(0)e…..(i)`
Bohr's quantum condition is `mvr=(nh)/(2pi) Rightarrow v=(nh)/(2pimr)....(ii)` using in (i), we get
`r^(2)=(h^(2)/(4pi^(2)mv_(0)r_(0)e))n^(2)Rightarrowrpropn`