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 utraviolet region will be for transition of electron from orbit 2 to orbit 1.
` therefore (1) / (lamda) = R ((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
`implies (1)/( 122 xx 10^(-9) m) = r[(1)/(I^2)-(1)/(2^2)]=R [1-1/4] = (3R)/(4)`
`implies R= (4)/( 3 xx 122 xx 10^(-9) )m^(-1)`
the highest frequency and smallest wavelength for infrared region will be for transtion of electron from `oo` to 3rd orbit .
` therefore (1) /( lamda) = R ((1)/( n_(1)^(2))-(1)/(n_(2)^(2)))implies (1)/( lamda) =(4)/( 3 xx 122 xx 10^(-9) ) ((1)/(3^2) -(1)/(oo))`
` therefore lamda = ( 3 xx 122 xx 9 xx 10^(-9))/( 4) = 823 .5 nm`