A) \[v\]
B) \[\sqrt{2}v\]
C) \[2v\]
D) \[4v\]
Correct Answer: C
Solution :
As the rms speed is given by \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\Rightarrow {{v}_{rms}}\propto \sqrt{\frac{T}{M}}\] When temperature is doubled and molecules dissociates into atoms, then \[\frac{{{v}_{rm{{s}_{1}}}}}{{{v}_{rm{{s}_{2}}}}}=\frac{\sqrt{\frac{T}{M}}}{\sqrt{\frac{2T}{M/2}}}=\frac{\sqrt{\frac{T}{M}}}{\sqrt{\frac{4T}{M}}}=\frac{\sqrt{T}}{\sqrt{4T}}=\frac{1}{2}\] If \[{{v}_{rm{{s}_{1}}}}\]then \[{{v}_{rm{{s}_{2}}}}\]will be \[2v.\]
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