The largest wavelength in the ultraviolet region of the hydrogen spectrum is `122` nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

Options

A. `802 nm`
B. `823 nm`
C. `1882 nm`
D. `1648 nm`

Answer

B

Explanation

The series in `U-V` region is Lymen series. Longest wavelength corresponding to minimum energy which occurs in transition from `n=2` to `n=1`.
`:. 122=(1/R)/((1/1^(2)-1/2^(2)))` …(i)
The samllest wavelength in the infrared region corresponds to maximum energy of Paschen series.
`:. lambda=(1/R)/((1/3^(2)-1/oo))` ...(ii)
Solving equation (i) and (ii), we get `lambda=823.5 nm`