The potential of an atom is given by `V=V_(0)log_(e)(r//r_(0))` where `r_(0)` is a constant and r is the radius of the orbit Assumming Bohr's model to be applicable, which variation of `r_(n)` with n is possible (n being proncipal 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`