Question

At a certain temperature, the r.m.s. velocity for$O_{2}$is 400 m/sec. At the same temperature, the r.m.s. velocity for $H_{2}$ molecules will be

• A. 100 m/sec
• B. 25 m/sec
• C. 1600 m/sec
• D. 6400 m/sec

Answer 1

Answer: (C)

1600 m/sec

Answer 2

$v_{rms} = \sqrt{\frac{3RT}{M}} = v_{rms} \propto \frac{1}{\sqrt{M}}$ $\lbrack\because T = \text{constant}\rbrack$

$\Rightarrow \frac{(v_{rms})_{O_{2}}}{(v_{rms})_{H_{2}}} = \sqrt{\frac{M_{H_{2}}}{Mo_{2}}} \Rightarrow \frac{400}{(v_{rms})_{H_{2}}} = \sqrt{\frac{2}{32}} = \frac{1}{4}$

$\Rightarrow (v_{rms})_{H_{2}} = 1600m/s.$