The longest wavelength in the ultraviolet region of the hydrogen spectrum is 120nm. What is the smallest wavelength in the infrared region of the hydrogen spectrum ?

Options

A. 510 nm
B. 810 nm
C. 700nm
D. 950 nm

Answer

B

Explanation

Lyman series lies in the ultraviolet region and for this series
`1/lamda = R (1/1^2 -1/n^2)`
For largest wavelength n =2
`therefore 1/lamda_1 = R [ 1-1/4] = (3R)/(4) " "…(1)`
and for the smallest wavelength in infrared region , we have to consider paschen series, for which `n_1 = oo " and " n_2 =3`
`1/lamda_2 = R [1/3^2 - 1/oo]`
`therefore 1/lamda_2 = R/9 " "...(2)`
`therefore` from (1) and (2)
`(1/lamda_1)/(l/lamda_2)= lamda_2/lamda_1 = (3R)/(4) xx 9/R = 27/4`
`therefore lamda_2 = 27/4 xx120 = 810 nm`