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

Explanation

Broglie wavelength is given by `lamda=(h)/(mv)`.
Root mean square velocity of a gas particle at the given temperature (T) is given as,
`(1)/(2)mv^(2)=(3)/(2)kT`
`v=sqrt((3kT)/(m))` Where k= Boltzmann's constant, `m=mass of the gas particle`, and `T=temperature of the gas in K`.
`mv=sqrt(3mkT)`
`lamda=(h)/(mv)=(h)/(sqrt(3mkT))`
`(lamda_H)/(lamda_(He))=sqrt((m_(he)t_(he))/(m_Ht_H))=sqrt(((4)(273+127))/((2)(273+27)))=sqrt((8)/(3))`