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(C) The root mean square (rms) speed of an $O_2$ molecule is given by $u = \sqrt{\frac{3RT}{M}}$,where $T$ is the temperature and $M$ is the molar mas

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$2u$

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(C) The root mean square (rms) speed of an $O_2$ molecule is given by $u = \sqrt{\frac{3RT}{M}}$,where $T$ is the temperature and $M$ is the molar mass of $O_2$.When the temperature is doubled $(T' = 2T)$ and the molecule dissociates into two atoms,the molar mass of the oxygen atom becomes $M' = \frac{M}{2}$.The new rms speed $u'$ is given by $u' = \sqrt{\frac{3RT'}{M'}} = \sqrt{\frac{3R(2T)}{M/2}}$.Simplifying this,we get $u' = \sqrt{4 \cdot \frac{3RT}{M}} = 2 \sqrt{\frac{3RT}{M}}$.Since $u = \sqrt{\frac{3RT}{M}}$,we have $u' = 2u$.

The speed of an oxygen molecule in a gas is $u$. If the temperature is doubled and the molecule dissociates into two atoms,the speed will be:

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