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Question
The rms speed of oxygen molecules in a gas is v. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become
Options
v
\[v\sqrt{2}\]
2v
4v
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Solution
2v
\[\text { Given }: v = \sqrt{\frac{3RT}{32}}\]
\[\text { Let the new rms speed be v' } . \]
\[\text { Molecule dissociate }, M = 16\] \[v' = \sqrt{\frac{3R\left( 2T \right)}{16}}\]
\[ = \sqrt{\frac{3R\left( 4T \right)}{32}}\]
\[ = 2\sqrt{\frac{3RT}{32}} = 2v\]
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