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

`V=V_(0) " In " (r//r_(0))`
P.E. `U=-eV=-eV=-eV_(0) " In " (r//r_(0))`
`F=-(dU)/(dr)=(eV_(0))/((r//r_(0))).(1)/(r_(0))=(eV_(0))/(r )`
`(mv^(2))/(r ) =(eV_(0))/(r ) implies v=sqrt((eV_(0))/(m))`
`mvr=(nh)/(2pi)`
`r=(nh)/(2 pi mv)=(nh)/(2 pi msqrt(eV_(0))/(m))=(nh)/(2pi sqrt(meV_(0)))`
` r=r_(n) prop n`