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

Options

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

Answer

B

Explanation

The skallest , frequency end large wavwlength in ullraviolet region will be for transtion of from orbit `2` to orbit`1`
`:. (1)/(lambda) = R ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
`rArr (1)/(122 xx 10^(-9)m) = R[(1)/(1^(2)) - (1)/(2^(2))] = R [(1 - (1)/(4)] = (3R)/(4)`
E = (4)/(3 xx 122 xx 10^&(-9)) m^(-1)`
The highest frequency and smaller wavelength for infrared reguion will be for transtionfrom `oo` ti 3rd orbit
`:. (1)/(lambda) = R((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
`rArr (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`