Question

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

Answer 1

The translational kinetic energy of a molecule at a temperature T is `E=3/2kT`.
So, `lambda=h/sqrt(3mkT)` as `lambda=h/sqrt(2mE)`
`lambda_(H_2)/lambda_(He)=sqrt((m_"He"T_"He")/(m_(H_2)T_(H_2)))`
`lambda_(H_2)/lambda_"He"=sqrt(8/3)`