Question

The ratio of average speed of an oxygen molecule to the RMS speed of nitrogen molecule at the same temperature is:

• A. ${\left(\frac{3\pi }{7}\right)}^{1/2}$
• B. ${\left(\frac{7}{3\pi }\right)}^{1/2}$
• C. ${\left(\frac{3}{7\pi }\right)}^{1/2}$
• D. ${\left(\frac{7\pi }{3}\right)}^{1/2}$

Answer 1

Answer: (B)

${\left(\frac{7}{3\pi }\right)}^{1/2}$

Answer:-

$V_{(av.)}{O}_2=\sqrt{\frac{8RT}{\pi \times 32}}$

$V_{\left(RMS\right)}{N}_2=\sqrt{\frac{3RT}{28}}$

$\frac{V_{(av.)}{O}_2}{V_{\left(RMS\right)}{N}_2}=\sqrt{\frac{8\times 28}{\pi \times 32\times 3}}=\sqrt{\frac{7}{3\pi }}={\left(\frac{7}{3\pi }\right)}^{\frac{1}{2}}$