Question

The ratio of de Broglie wavelength of molecules of hydrogen and helium in two gas jars kept separately at temperatures of ${27}^{\circ }C$ and ${127}^{\circ }C$ respectively is:

• A. $2/\sqrt{3}$
• B. $2/3$
• C. $\sqrt{3}/4$
• D. $\sqrt{8/3}$

Answer 1

The correct option is D $\sqrt{8/3}$

De - Broglie wavelength $\lambda =\frac{h}{mV}$

We know, $\frac{1}{2}{mV}^2=\frac{3}{2}{K}^T$

$V=\sqrt{\frac{3K^T}{m}}$

$mV=\sqrt{3m{K}^T}$

$\lambda =\frac{h}{mV}=\frac{h}{\sqrt{3m{K}^T}}$

$\frac{{\lambda }_H}{{\lambda }_{He}}=\sqrt{\frac{mHe{T}_{He}}{m_H{T}_H}}$

$=\sqrt{\frac{\left(14amu\right){(273+127)}^{0}K}{\left(2amu\right){(273+27)}^{0}K}}=\sqrt{\frac{8}{3}}$ (correct option).