A `12.5eV` electron beam is used to bombard gaseous hydrogen at room temperature. What serious of wavelength will be emitted?

Explanation

First excitation energy
`E=E_2-E_1=-3.4-(-13.6)`=10.2 eV
Second excitation energy
`E=E_3-E_1=-1.51-(-13.6)`=12.09 eV
Third excitation energy
`E=E_4-E_1`=-0.85-(-13.6)=12.75 eV
Since incident beam has energy = 12.5 eV
So only first two lines in the Lyman series of wavelength 103 nm and 122 nm will be emitted .
Also , `E_3-E_2=-1.51-(-3.4)` =1.89 eV
i.e. first line in the Balmer series of wavelength 656 nm will also will be emitted.