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

Question

The charge stored by the capacitor C in the given circuit in the steady state is _________ $\mu$C.

Answer 1

Root mean square speed ($V_{\text{rms}}$) is defined as:

\[ V_{\text{rms}} = \sqrt{\frac{3RT}{M_w}} \]

Here, $M_w$ represents the molar mass of the gas.

The ratio of root mean square speeds for helium ($V_{\text{He}}$) to oxygen ($V_{\text{O}_2}$) is calculated as:

\[ \frac{V_{\text{O}_2}}{V_{\text{He}}} = \sqrt{\frac{M_{w,\text{He}}}{M_{w,\text{O}_2}}} \]

Using the given values:

\[ \frac{V_{\text{O}_2}}{V_{\text{He}}} = \sqrt{\frac{4}{32}} = \frac{1}{2\sqrt{2}} \]

Consequently, the ratio $V_{\text{He}} / V_{\text{O}_2}$ is:

\[ \frac{V_{\text{He}}}{V_{\text{O}_2}} = \frac{2\sqrt{2}}{1} \]

The Correct Option is B