A) \[\sqrt{\frac{1}{8}}\]
B) \[\sqrt{\frac{32}{17}}\]
C) \[\sqrt{8}\]
D) \[\sqrt{\frac{2}{17}}\]
Correct Answer: A
Solution :
Density of mixture \[={{\rho }_{mix}}=\frac{{{V}_{{{O}_{2}}}}{{\rho }_{{{O}_{2}}}}+{{V}_{{{H}_{2}}}}{{\rho }_{{{H}_{2}}}}}{{{V}_{{{O}_{2}}}}+{{V}_{{{H}_{2}}}}}\] \[=\frac{V\left( {{\rho }_{{{O}_{2}}}}+{{\rho }_{{{H}_{2}}}} \right)}{2\,V}=\frac{{{\rho }_{{{O}_{2}}}}+{{\rho }_{{{H}_{2}}}}}{2}\](since\[{{V}_{{{O}_{2}}}}={{V}_{{{H}_{2}}}}=V\]) \[=\frac{{{\rho }_{{{H}_{2}}}}+16{{\rho }_{{{H}_{2}}}}}{2}=8.5{{\rho }_{{{H}_{2}}}}\]Þ \[v\propto \frac{1}{\sqrt{\rho }}\] Þ\[\frac{{{V}_{mix}}}{{{V}_{{{H}_{2}}}}}=\sqrt{\frac{{{\rho }_{{{H}_{2}}}}}{{{\rho }_{mxn}}}}=\sqrt{\frac{{{\rho }_{{{H}_{2}}}}}{8.5{{\rho }_{{{H}_{2}}}}}}\approx \sqrt{\frac{1}{8}}\]
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