A) \[536.8\,m{{s}^{-1}}\]
B) \[839.2\,m{{s}^{-1}}\]
C) \[1245.5\,m{{s}^{-1}}\]
D) \[1255.3\,m{{s}^{-1}}\]
Correct Answer: D
Solution :
\[{{u}_{rms}}=\sqrt{\frac{3RT}{M({{N}_{2}})}}\] \[{{\overline{u}}_{avg}}=\sqrt{\frac{8RT}{\pi {{M}_{(He)}}}}\] Both are at same temperature \[\frac{\overline{u\,}(He)}{{{U}_{rms}}({{N}_{2}})}=\sqrt{\frac{8M({{N}_{2}})}{3\pi {{M}_{(He)}}}}\] \[=\sqrt{\frac{8\times 28\times {{10}^{-3}}}{3\pi \times 4\times {{10}^{-3}}}}=2.4375\] \[\overline{u\,}(He)=2.4375\times 515=1255.3\,m{{s}^{-1}}\]
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