A sample of hydrogen gas in its ground state is irradiated with photons of 10.02 eV energies. The radiation from the above sample is used to irradiate two other samples of excited ionized He + and excited ionized Li 2+ respectively. Both the ionized samples absorb the incident radiation.
(i) How many lines are obtained in the He + and Li 2+ emission spectra respectively?
(ii) What are the smallest and biggest wavelengths in their spectra?
Text Solution
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Sol. Consider energy level diagram of hydrogen atom. After absorbing photons of energy 10.2 eV it would reach the first excited state of – 3.4 eV, since energy difference corresponding to n = 1 and n = 2 is 10.2 eV. When this excited hydrogen atom de-excites, it would release 10.2 eV energy, which is absorbed by He + and Li 2+ .
Fig.
Energy of n th state of a hydrogen like atom with atomic number Z is given by
E n = 
eV
After absorbing 10.2 eV He + electron moves from n = 2 to n = 4 and Li 2+ electron moves from n = 3 to n = 6.
In the spectrum of He + there would be 4 C 2 = 6 lines.
Fig.
= 
= 
= 470 nm
= 
= 
= 24.4 nm
Fig.
Similarly in spectrum of Li 2+ there will be 6 C 2 = 15 lines.
= 
= 830.2 nm
= 
= 10.4 nm
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