A) 10 seconds : He
B) 20 seconds : \[{{O}_{2}}\]
C) 25 seconds : CO
D) 55 seconds : \[C{{O}_{2}}\]
Correct Answer: B
Solution :
\[r\propto \frac{1}{\sqrt{M}}\] \[\because \,\,r=\frac{Volume\,\,effused}{time\,\,taken}=\frac{V}{t}\] \[\frac{V}{t}\propto \frac{1}{\sqrt{M}}\] \for same volumes (V constant) \[t\propto \sqrt{M}\,\therefore \frac{{{t}_{1}}}{{{t}_{2}}}=\sqrt{\frac{{{M}_{1}}}{{{M}_{2}}}}\] \[{{t}_{He}}={{t}_{{{H}_{2}}}}\sqrt{\frac{{{M}_{He}}}{{{M}_{{{H}_{2}}}}}}=5\sqrt[{}]{\frac{4}{2}}=5\sqrt{2}s.\] \[{{t}_{{{O}_{2}}}}=t\]\[=5\sqrt[{}]{\frac{32}{2}}=20s\] \[{{t}_{CO}}=\]\[5\sqrt[{}]{\frac{28}{2}}=5\sqrt{14}s\] ; \[{{t}_{C{{O}_{2}}}}=\]\[5\sqrt[{}]{\frac{44}{2}}=5\sqrt{22}s\]
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