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Question

The wavelength of certain electronic transition in hydrogen atom is 91.2 nm. Calculate the corresponding wavelength of He+ atom:

A
22.8 nm
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B
45.60 nm
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C
91.20 nm
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D
32 nm
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Solution

The correct option is A 22.8 nm
For hydrogen like atom:
1λ=Z2RH(1n211n22)
where Z = atomic number of an element
As given, n1 and n2 for H and He+ are same.
For Hydrogen,
1λH=(1)2×RH(1n211n22) (i)
For He+
1λHe+=(2)2×RH(1n211n22) (ii)
on dividing eqn (i) by eqn (ii), we get
λHe+=22.8 nm

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