Question

An electron an a hydrogen like species makes a transition from the oth Bohr orbit to the next outer Bohr `(-=n + 1)` .Find an appocimate relation between the dependence of the frequency of the photon abserbed as a function of n .Assume n its to have a large value `(ngt gt1)`

Answer 1

`overset(Delta E_("energy difference"))underset((n rarr n + 1))=hv`
`= 2.18 xx 10^(-18) xx Z^(2)((1)/(n^(2)) - (1)/((n+1)^(2)))J`
`rArr hv = 2.18 xx 10^(-18) xx Z^(2)((2n + 1)/(n^(2)(n+1)^(2))) J`
Since `n gt gt1` (given)
`n + 1~ n, 2n +1 ~~ 2n`
`rArr hv= 2.18 xx 10^(-18)Z^(2) xx (2n)/(n^(4)) J`
`rArr v prop n^(-3)`