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Question
What is the minimum energy that must be given to a H atom in ground state so that it can emit an Hγ line in Balmer series. If the angular momentum of the system is conserved, what would be the angular momentum of such Hγ photon?
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Solution
We know that Hγ spectral line in the Balmer series is formed when an electron falls from n = 5 to n = 1.
Here the electron is in the ground state ie., n = 1 and must be taken to n = 5 for Hγ line.
So the energy of H? = `E_5 - E_1 = (13.6/5^2) - (- 13.6)`
= – 0.54 + 13.6
= 13.06 eV
Since angular momentum, is conserved, so the angular momentum of Hγ = change in angular momentum of the electron
= L5 – L2 – 5h – 2h
= 3h = 3 × 6.63 × 10–34
= 19.89 × 10–34 kg m2/s
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