A) \[\sqrt{\frac{3}{2}}\]
B) \[\sqrt{\pi /4}\]
C) \[\sqrt{2/3}\]
D) \[3\pi /8\]
Correct Answer: D
Solution :
[d] Root means square velocity of molecule in left part \[{{V}_{rms}}=\sqrt{\frac{3KT}{{{m}_{L}}}}\] Mean or average speed of molecule in right part \[{{V}_{av}}=\sqrt{\frac{8\,KT}{\pi \,{{m}_{R}}}}\] According to problem \[\sqrt{\frac{3KT}{{{m}_{L}}}}=\sqrt{\frac{8\,KT}{\pi \,{{m}_{R}}}}\] \[\Rightarrow \frac{3}{{{m}_{L}}}=\frac{8}{\pi {{m}_{R}}}\] \[\Rightarrow \frac{{{m}_{L}}}{{{m}_{R}}}=\frac{3\pi }{8}\]
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