A) \[\sqrt{8}\]
B) \[\sqrt{2/17}\]
C) \[\sqrt{1/8}\]
D) \[\sqrt{32/17}\]
Correct Answer: B
Solution :
Let one mole of each gas has same volume as V. When they are mixed, then density of mixture is. \[{{\rho }_{mixture}}=\frac{mass\text{ }of\,C>2+mass\text{ }of\,{{H}_{2}}}{volume\text{ }of\,{{O}_{2}}+volume\text{ }of\text{ }{{H}_{2}}}\] \[=\frac{32+2}{V+V}\] \[=\frac{34}{2\,V}=\frac{17}{V}\] also, \[{{\rho }_{{{H}_{2}}}}=\frac{2}{V}\] Now, velocity \[\upsilon ={{\left( \frac{\gamma P}{\rho } \right)}^{\frac{1}{2}}}\]or \[\upsilon \propto \frac{1}{\sqrt{\rho }}\] \[\frac{{{\upsilon }_{mixture}}}{{{\upsilon }_{{{H}_{2}}}}}=\sqrt{\left( \frac{{{\rho }_{{{H}_{2}}}}}{{{\rho }_{mixture}}} \right)}\] \[=\sqrt{\left( \frac{2/V}{17/V} \right)}\] \[=\sqrt{\left( \frac{2}{17} \right)}\]
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