1.

The electric potential between a proton and an electron is given byV= 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

Answer»

`r INFTY (1)/(n)`
`r_(n) infty n`
`r_(n) infty (1)/(n^(2))`
`r_(n) infty n^(2)`

Solution :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))) Rightarrow V = sqrt((eV_(0))/(m))`
Now from
`mvr_(n) = (NH)/(2pi)`
`r_(n) infty n`


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