The energy of electron in hydrogen atom is `E_n=(-13.6)/(n^(2)) eV`, Where n=1, 2,3,......Show that (i) the electron in hydrogen atom cannot have an energy of -6.8eV. (ii) spacing between the lines (consecutive energy levels) within the given set of observed hydrogen spectrum decreases as n increases.

Explanation

Here, `E_n=(-13.6)/(n^2) eV`
Putting n=1,2,3,.....we get
`E_1=(-13.6)/(1^2)eV=-13.6eV,`
`E_2=(-13.6)/(2^2)eV=-3.4eV,`
`E_3=(-13.6)/(3^2)eV=-1.51 eV,`
`E_4=(-13.6)/(4^2)eV=-0.85 eV, E_(oo)=0.`
Clearly, an electron in hydrogen atom cannot have energy of -6.8eV.
(ii) As the value of n increase, energy diff. between two consecutive energy level decreases.