A) \[12.42\times {{10}^{-21}}J,\,\,968\,\,m/s\]
B) \[6.21\times {{10}^{-21}}J,\,968\,m/s\]
C) \[8.78\times {{10}^{-21}}J,\,684\,\,m/s\]
D) \[12.42\times {{10}^{-21}}J,\,\,684\,\,m/s\]
Correct Answer: D
Solution :
As \[KE=\frac{3}{2}\,kT\] and \[{{V}_{rms}}=\sqrt{\frac{3RT}{M}}\] \[\therefore \] \[K{{E}_{2}}=2K{{E}_{1}}=2\times 6.21\times {{10}^{-21}}\] \[=12.42\times {{10}^{-21}}J\] \[\frac{{{V}_{rms,\,\,2}}\,}{{{V}_{rms,\,\,1}}}=\sqrt{\frac{{{T}_{2}}}{{{T}_{1}}}}=\sqrt{2}\] \[\therefore \] \[{{V}_{rms,\,\,2}}=\sqrt{2}\times {{V}_{rms,\,\,1}}\] \[=684\,\,m/s\]
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