Question

In two vessels of the same volume, atomic hydrogen and helium with pressure 1 atm and 2 atm are filled. If temperature of both the same is the same, then the average speed of hydrogen atom $v_H$ will be related to helium $v_{He}$ as

• A. $v_H$ $=\sqrt{2}$ $v_{He}$
• B. $v_H$ $=$ $v_{He}$
• C. $v_H$ $=$ 2$v_{He}$
• D. $v_H$ $=$ $\frac{v_{He}}{2}$

Answer 1

The correct option is C $v_H$ $=$ 2$v_{He}$

By Maxwell's speed distribution, $<v>\alpha \sqrt{\frac{RT}{M}}$. Since the temperature of two gases is same, hence

$<v>\alpha \sqrt{\frac{1}{M}}$

Also, $M_{He}=4M_H$

Hence, $<v_H>=2<v_{He}>$

Answer is option C.