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Question

The wavelength of photons emitted by electron transition between two similar levels in H and He+ are λ1 and λ2 resepectively. Then the relation between λ1 and λ2 is:

A
λ2=λ1
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B
λ2=2λ1
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C
λ2=λ1/2
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D
λ2=λ1/4
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Solution

The correct option is D λ2=λ1/4
According to Planck’s quantum theory, energy emitted by electron due to transition can be given by:
ΔE=hv=hcλ ...(i)
where h=Planck’s constant=6.63×1034 J s
v=frequency
λ=wavelength
c=velocity of light

Given: wavelength of photon in H atom =λ1
wavelength of photon in He+ ion =λ2

For hydrogen like species,
Energy of an electron =13.6Z2n2 eV ...(ii)

As the transition is between the same set of 2 energy levels, but in different species (H and He+ ion), we can conclude from eq. 1 and 2:

ΔEHΔEHe+=Z2HZ2He+=λ2λ1
(ZH=1 ; ZHe=2)
λ2=14λ1

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