The wavelength of the spectral line, for the transition n = 2 to n=1 in the hydrogen emission spectrum is .X.. Which of the following spectral line also has a wavelength of X

Options

A. `.H_(alpha).` line in the Balmer series of spectrum of .H.
B. `.H_(beta).` line in the Balmer series of spectrum of .H.
C. `.H_(alpha).` line in the Balmer series of spectrum of .He^(+).
D. `.H_(beta).` line in the Balmer series of spectrum of .He^(+).

Answer

D

Explanation

`bar(upsilon) = Z^2 R [1/(1^2) - 1/(2^2)] and lambda = 1/(bar(upsilon))`
`" "H " "He^(+)`
`(1)^2 (1/((1)^2) - 1/((2)^2)) = (2)^2 ((1)/(n_1^2) - 1/(n_2^2))`
on solving `n_1 = 2 , n_2 = 4`