Question

The ratio of de Brogile wave length of molcules of hydrogen and helium in two gas jars kept separately at temperatures of ${27}^{\circ }$ C and ${127}^{\circ }$ C respectively is

• A. $\frac{2}{\sqrt{3}}$
• B. $\frac{2}{5}$
• C. $\frac{\sqrt{3}}{8}$
• D. $\sqrt{\frac{8}{3}}$

Answer 1

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

K.E. of particle $\frac{1}{2}m{v}^2=\frac{3}{2}KT\Rightarrow p=\sqrt{3mKT}\therefore \lambda \alpha \frac{1}{\sqrt{mT}}\Rightarrow \frac{{\lambda }_H}{{\lambda }_{He}}=\sqrt{\frac{m_{He}{T}_{He}}{m_H{T}_H}}=\sqrt{\frac{4m}{m}\times \frac{400}{300}}=\sqrt{\frac{8}{3}}$