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

Answer

d

Explanation

K.E. of the particle at the given temp. `T` is given by `1/2mv^(2)=3/2kT`, where `k` is Boltzmann constant or `mv=1/(sqrt(3mkT))`
De-Broglie wavelength, `lambda=h/(mv)=h/(sqrt(3mkT))`
i.e. `lambda prop1/(sqrt(mT))`
`:. (lambda_(H))/(lambda_(He))=sqrt((m_(He)T_(He))/(m_(H)T_(H)))=sqrt((4m)/(2m)xx((273+127)K)/((273+27)K))=sqrt(8/3)`