A gas sample of hydrogen like atoms has some atoms in the lowest (ground) energy level A and some atoms in a particular upper (excited) energy level B and there are no atoms in any other energy level. The atoms of the gas make transition to a higher level by absorbing monochromatic light of photon energy 2.7 eV. Subsequently, the atoms emit radiation of only six different photon energies. Some of the emitted photons have energy 2.7 eV. Some have energy more and some have less than 2.7 eV.
(i) Principal quantum number of the initially excited level B is –
Text Solution
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Ans.
(i)
Sol.
n = 2 to 4
(ii)
Sol. 13.6 Z 2 
= 2.7
⇒ 13.6 Z 2 = 2.7 × 
eV
= 2.3 × 10 –18 J
(iii)
Sol. 
= 13.6 Z 2 
= 13.6 Z 2 × 
= 2.2 × 10 –18 J
E min = 13.6 Z 2 
= 13.6 Z 2 × 
= 1.1 × 10 –19 J
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