The energy of the electron in the hydrogen atom is known to be expressible in the form of `E_(n) = (-13.6 eV)/(n^(2))` [ where, n=1,2,3.. ]
Use this expression to show that the
electron in the hydrogen atom cannot have an energy of -2 eV.
(ii) spacing between the lines (consecutive energy levels) within the given set of the observed hydrogen spectrum decreases as n increases.

Explanation

For `E_(n) = -2 eV`
`implies -2 eV = (-13.6)/(n^(2)) eV `
`implies 13.6 = 2n^(2) `
`implies n^(2) =6.8`
n is necessarily non - integral value whereas it should be integer to satisfy quantisation condition . Therefore -2 eV energy of electron is not possible.
(ii) Energy of the electron `E_(n) = (-13.6)/(n^(2))`
`implies ` For n =1 `E_(1) = (13.6)/(1) = - 13.6 eV `
For n =2 `E_(2) = (13.6)/((2)^(2)) = - 3.4 eV `
For n =3 `E_(3) = (13.6)/((3)^(2))= - 1.51 eV `
For n =4 `, E_(4) = (13.6)/((3)^(2)) = - 0.85 `eV
`implies E_(n) - E_(n-1) lt E_(n-1) - E_(n-2) AA n inN `
So from above result we can say that spacing between spectral lines decreases .