Question

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :

(1) \(\frac{1}{32}\)

(2) \(\frac{2 \sqrt{2}}{1}\)

(3) \(\frac{1}{4}\)

(4) \(\frac{1}{2 \sqrt{2}}\)

Answer 1

Correct option is :  (2)  \(\frac{2 \sqrt{2}}{1}\)

\(\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}_{\mathrm{w}}}}\)

\( \begin{aligned} \Rightarrow \frac{\mathrm{V}_{\mathrm{O}_{2}}}{\mathrm{~V}_{\mathrm{He}}} & =\sqrt{\frac{\mathrm{M}_{\mathrm{w}, \mathrm{He}}}{\mathrm{M}_{\mathrm{w}, \mathrm{O}_{2}}}} \end{aligned} \)

\(\begin{aligned}=\sqrt{\frac{4}{32}}=\frac{1}{2 \sqrt{2}} \end{aligned} \)

\( \begin{aligned} \frac{\mathrm{V}_{\mathrm{He}}}{\mathrm{V}_{\mathrm{O}_{2}}} & =\frac{2 \sqrt{2}}{1} \end{aligned} \)