Q. During the emission spectrum,the first line of Lyman series of H-atom occurs as `lambda` = ` ``x ` .The wavelength of the 1st line of Lyman series of `He^+` ion will occur at:-
The Rydberg equation for transition of an electron from n=2 to n=1 in hydrogen-like elements can be expressed as:
Where, lambda is the wavelength of the emitted radiation, R_oo is the Rydberg constant and Z is the atomic number of the element.
For hydrogen, Z=1, for the first line of transition of Lyman series, `n_2=2, n_1=1,`
So, `1/x=R_oo *1^2(1/ 1^2-1/ 2^2)`
Putting this value of `R_oo` in `He^(2+)(Z=2)` , for the first line of transition,
`1/lambda=4/(3x)*2^2(1/ 1^2-1/ 2^2)`
Hence the correct answer is option E).