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 smallest frequency and largest wavelength in ultra violet region will be for transition of electron from orbit `2` to orbit `1`. Therefore ,
`(1)/(lambda) = R ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
`implies (1)/(122 xx 10^(-9) m) = R [(1)/(1^(2)) - (1)/(2^(2))] - R [1 - (1)/(4)] = (3 R)/(4)`
`implies R = (4)/(3 xx 122 xx 10^(-9)) m^(-1)`
The higest ferequency andsmallest wavelength for infrared region will be for transition of electron from`oo to 3^(rd)` orbit
`:. (1)/(lambda) = R ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
`implies (1)/(lambda) = (4)/(3 xx 122 xx 10^(-9)) ((1)/(3^(2)) - (1)/(oo))`
`lambda = (3 xx 122 xx 9 xx 10^(-9))/(4) = 823.5 nm`