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)/(2)`
C. `r_(n) prop n^(2)`
D. `r_(n) prop (1)/(n^(2))`

Answer

A

Explanation

Given that `v = v_(o) log_(e) (r//r_(o))`
field `E = (-dv)/(dr)` or `E = -V_(o) ((r_(o))/(r ))`
Now `eE = (mv^(2))/(r )` or `(eV_(o)r_(o))/(r ) = (mv_(o)^(2))/(r )`
`:. V = ((ev_(o)r_(o))/(m))^(1//2)`
Now `mv = (mev_(o)r_(o))1^(1//2) =` constant
`:. mvr = (nh)/(2 pi)` Bohr's quantum condition
or `r prop n`