Question

Hydrogen atom in its ground state is excited by means of a monochromatic radiation of wavelength 975 Å

(a) How many different lines are possible in the resulting spectrum? 

(b) Calculate the longest wavelength amongst them. Given that the ionization energy for hydrogen atom is 13.6 eV

Answer 1

Energy of the ground state (n = 1) = – (ionization energy) = –13.6 eV

The wavelength of the incident radiation = λ = 975 Å 

∴ Energy of the incident photon=  hc/λ

Let electron is exerted to nth orbit

The quantum transitions to the less excited states give six possible lines as follows:

The longest wavelength emitted is for the transition (4 → 3) where energy difference is minimum