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Question

In a mixture of HHe+ gas, H atom and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer its excitation energy to He+ ions by collision.
If Bohr model is applicable then the wavelength of the light emitted in the visible region by He+ ions after collisions with He+ ions are:

A
400 A
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B
344 A
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C
244 A
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D
375 A
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Solution

The correct option is C 244 A
The energy difference between ground state and first excited state for H atom is
E=21.79×1019[112122]......(1)
The energy difference between ground state and first excited state for He+ ion is
E=21.79×1019×22[112122]......(2)
Total energy difference is obtained by adding (1) and (2)
E"=E+E=21.79×1019×3.75J/atom
Wavelength of light emitted is λ=hcE"=6.63×1034×3×10821.79×1019×3.75=2.44×108m=244A.

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