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When the speed root mean square for oxygen molecule in a container at temperature of \left(1+\frac{2}{k}\right)^{\frac{1}{2}} \times v where k is any constant, v is average speed of molecules. Find the value of k. 

Option: 1

\frac{16}{5}


Option: 2

\frac{-16}{5}


Option: 3

\frac{16}{3\pi-8}


Option: 4

5


Answers (1)

best_answer

\begin{aligned} & \text { Vrms }=\sqrt{\frac{3 R T}{m}}, \quad \text { vavg }=\sqrt{\frac{8 R T}{\pi m}} \\ & \sqrt{\frac{3 R T}{m}}=\left(1+\frac{2}{k}\right)^{\frac{1}{2}} \sqrt{\frac{\theta R T}{\pi m}} \\ & \frac{3 R T}{m}=\left(1+\frac{2}{k}\right) \times \frac{8 R T}{\pi m} \\ & 3=\frac{\theta}{\pi}\left(1+\frac{2}{k}\right) \\ & \frac{3 \pi}{8}=1+\frac{2}{k} \\ & \frac{2}{k}=\frac{3 \pi}{8}-1=\frac{3 \pi-8}{8} \\ & k=\frac{8 \times 2}{3 \pi-8}=\frac{16}{3 \pi-8} \\ & \end{aligned}

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Divya Prakash Singh

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