The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest interger) is (a) 802 nm (b) 823 nm
(c ) 1882 nm (d) 1648 nm.

Answer

B

Explanation

The series in U-V region is Lyman series. Largest
wavelength correspond to minimum energy which
occurs in transition from n= to n=1.
`:. 122 = ((1)/(R))/(((1)/(1^2)-(1)/(2^2))) ....(i)`
The smallest wavelength in the infrared region
corresponds to maximum energy of Paschen series.
`122 = ((1)/(R))/(((1)/(1^2)-(1)/(2^2))) ....(i)`
The smallest wavelength in the infrared region
corresponds to maximum energy of Paschen series.
`:. ((1)/(R))/(((1)/(3^2)-(1)/(oo) .....(ii)`
Solving Eqs. (i) and (ii) we get
`lambda = 823.5 nm`
`:.` Correct option in (b).