What transition in helium will have the same wavelength as the first line in Lyman series of hydrogen atom?

Text Solution

`2 rarr 1``5 rarr 3``4 rarr 2``6 rarr 4`

Answer : C

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