Question

Find the ratio of de Broglie wavelength of molecules of hydrogen and helium which are at temperatures $27^{\circ }C$ and $327^{\circ }C$, respectively.

Answer 1

Answer: 2

Average K.E. per molecule of a gas at the given temperature $(T)$ is given as,
$\frac{1}{2}m{v}^2=\frac{3}{2}kT$
where, $m=$ molecular mass of the gas
$\therefore mv=\sqrt{3mkT}$
But, $\lambda =\frac{h}{mv}=\frac{h}{\sqrt{3mkT}}$
$\therefore \frac{{\lambda }_H}{{\lambda }_{He}}=\sqrt{\frac{m_{He}{T}_{He}}{m_H{T}_H}}$
$=\sqrt{\frac{(4)(273+327)}{(2)(273+27)}}=\sqrt{4}=2$