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The electric potential between a proton ...

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. Assume that Bohr atom model is applicable to potential, then variation of radius of `n^(th)` orbit `r_(n)` with the principal quantum number n is

A

`r_(n) prop (1)/(n)`

B

`r_(n) prop n`

C

`r_(n) prop (1)/(n^(2))`

D

`r_(n) prop n^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`r_(n) prop n`
Electric potential between proton and electron in `n^(th)` orbit is given as ,
`V = V_(0)` In `((r_(n))/(r_(0)))`
Thus the coulomb force `|F_(e)| = e((dv)/(dr)) = e ((v_(0))/(r_(n)))`
This coulomb force is balance by the centripetal force
`(mv^(2))/(r_(n)) = e ((v_(0))/(r_(n))) rArr V = sqrt((eV_(0))/(m))`
Now from
`mvr_(e) = (nh)/(2pi)`
`r_(n) prop n `
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