The electric potential between a proton and an electron is given by `V = V_0 " In" r/r_0` where `r_0` is a constant . Assuming Bohr's model to be applicable, write a variation of `r_n` with n, n being the principal quantum number.

Options

A. `r_(n)oon`
B. `r_(n)1//oon`
C. `r_(n)oon^(2)`
D. `r_(n)1//n^(2)`

Answer

a

Explanation

Given that `V=V_(0)log_(e)(r//R_(0))`
Field `E=-(dV)/(dr)=V_(0)(r )/(r_(0))`
`eE=(mV^(2))/(r )or (eV_(0)r_(0))/(r )=(mv^(2))/(r )rArr V=(eV_(0)r_(0))/(m)^(1)/(2)`
`mV=(m_(e)V_(0)r_(0))^(1)/(2)=constant`
`therefore mvr=(nh)/(2pi),Bohr'squantum condition or r prop n`