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 Lyman series. Longest wavelength corresponds to minimum energy which occurs in transition from n=2 to n=1.
`therefore 122=((1)/(R))/((1)/((1)^(2))-(1)/((2)^(2)))` . .. (i)
the smallest wavelength in the infrared region
corresponds to maximum energy of paschen series.
`therefore lamda=((1)/(R))/((1)/((3)^(2))-(1)/(oo))` . . .(ii)
Solving Eqs. (i) and (ii), we get `lamda=823.5` nm