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The transitions He^(o+) ion that would ...

The transitions `He^(o+)` ion that would have the same wavelength as the first Lyman line in hydrogen spectrum is

A

`2 rarr 1`

B

`5 rarr 3`

C

`4 rarr 2`

D

`6 rarr 4`

Text Solution

Verified by Experts

The correct Answer is:
C
`bar(v)_(H) = R[(1)/(1^(2))-(1)/(2^(2))] cm^(-1)` ...(i)
`bar(v)_(He^(+)) = R(2)^(2)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]` ....(ii)
Now, `bar(v)_(He^(+)) = R[(1)/(1^(2))-(1)/(2^(2))] = R xx ((2)^(2))/((2)^(2)) [(1)/(1^(2))-(1)/(2^(2))]`
`= R(2)^(2)[(1)/(2^(2))-(1)/(4^(2))]` ...(iii)
Comparing (ii) and (iii), it is clear that
`n_(2) = 4, n_(1) = 2`.
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