A) 1 : 1
B) 2 : 3
C) 3 : 2
D) \[\sqrt{2}:\sqrt{3}\]
Correct Answer: D
Solution :
Root mean square velocity of gas molecules \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] or \[{{v}_{rms}}\propto \frac{1}{\sqrt{M}}\] or \[\frac{{{v}_{{{O}_{3}}}}}{{{v}_{{{O}_{2}}}}}=\sqrt{\frac{{{M}_{{{O}_{2}}}}}{{{M}_{{{O}_{3}}}}}}\] Here, \[{{M}_{{{O}_{2}}}}=32,\,\,{{M}_{{{O}_{3}}}}=48\] \[\therefore \] \[\frac{{{v}_{{{O}_{3}}}}}{{{v}_{{{O}_{2}}}}}=\sqrt{\frac{32}{48}}=\frac{\sqrt{2}}{\sqrt{3}}\] Note: Speed of sound in a gas is of the same order as rms speed of its molecules.
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