Calculate the ratio of de-Broglie wavelength of molecules of hydrogen and oxygen kept in two separate jars at `27^(@)C` and `127^(@)C` respectively.

Options

A. `(2)/(sqrt(3))`
B. `2 : 3`
C. `(sqrt(3))/(4)`
D. `sqrt((8)/(3))`

Explanation

`de-`Broglie wavelength, `lambda=(h)/(mv)`
where the speed (r.m.s) of a gas particle at the given temperature `(T)` is given as
`(1)/(2)mv^(2)=(3)/(2)KT`
`rArr v=(h)/(mv)=(h)/(qBr)` where `K=`Boltzmann's constant and `m=` mass of the gas particle and `T=` temperature of the gas in `K`
`rArrmv=sqrt(3 m KT)rArrlambda=(h)/(mv)=(h)/(sqrt(3mKT))`
`:.(lambda_(H))/(lambda_(He))=sqrt((m_(He)T_(He))/(m_(H)T_(H)))=sqrt(((4"amu")(273+127)^(@)K)/((2"amu")(273+27)^(@)K))=sqrt((8)/(3))`