JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
Consider a sample of oxygen behaving like an ideal gas. At \(300 \,K ,\) the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be : (Molecular weight of oxygen is \(32 \,g / mol\) \(\left. R =8.3 \,J K ^{-1} mol ^{-1}\right)\)
- A \(\sqrt{\frac{3}{8}}\)
- B \(\sqrt{\frac{8}{3}}\)
- C \(\sqrt{\frac{3 \pi}{8}}\)
- D \(\sqrt{\frac{8 \pi}{3}}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{\frac{3 \pi}{8}}\)
Step-by-step Solution
Detailed explanation
\(v _{vms }=\sqrt{\frac{3 RT }{ M }}\) \(v _{ avg }=\sqrt{\frac{8 RT }{\pi} \frac{ RT }{ M }}\) \(\frac{ v _{ rms }}{ v _{ avg }}=\sqrt{\frac{3 \pi}{8}}\)
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