Find the ratio of de Broglie wavelength of molecules of hydrogen and helium which are at temperatures `27^circ` and `127^circC`, respectively.

Options

A. `(1)/(2)`
B. `sqrt((3)/(8))`
C. `sqrt((8)/(3))`
D. `1`

Answer

C

Explanation

de - Broglie wavelength `lambda = (h)/(mv_(rms))` , `rms` velocity of a gas particle at the given temperature `(T)` is given as
`(1)/(2) mv_(rms)^(2) = (3)/(2) KT rArr v_(rms) =sqrt((3 kT)/(m)) rArr mv_(rms) = sqrt( 3 mkT)`
`:. Lambda = (h)/(mv_(rms)) = (h)/(sqrt(3 mkT))`
`rArr (lambda_(H))/(lambda_(He)) = sqrt((m_(He) T_(He))/(m_(H) T_(H))) = sqrt(( 4 ( 273 + 127))/(2(273 + 27))) = sqrt((8)/(3))`