Q: Find the ration of de-Broglie wavelength of molecules of hydrogen and helium which are at temperatures 27 °C and 127 °C respectively.

Sol: $\large \lambda = \frac{h}{m v}$

$\large \lambda = \frac{h}{\sqrt{3 m k T}}$

$\large \frac{\lambda_H}{\lambda_{He}} = \frac{\sqrt{m_{He} T_{He}}}{m_H T_H} = \sqrt{\frac{8}{3}}$