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(C) The root mean square speed $(V_{rms})$ of a gas is given by the formula $V_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$

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$2v$

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(C) The root mean square speed $(V_{rms})$ of a gas is given by the formula $V_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass of the gas.Initially,for the diatomic gas,the speed is $v = \sqrt{\frac{3RT}{M}}$.When the temperature is doubled,the new temperature becomes $T' = 2T$. When the diatomic molecules dissociate into two atoms,the molar mass of the new species (atoms) becomes half of the original molar mass,so $M' = \frac{M}{2}$.The new root mean square speed $V'_{rms}$ is given by:$V'_{rms} = \sqrt{\frac{3RT'}{M'}} = \sqrt{\frac{3R(2T)}{M/2}} = \sqrt{4 \cdot \frac{3RT}{M}} = 2 \sqrt{\frac{3RT}{M}}$.Substituting the initial speed $v$,we get $V'_{rms} = 2v$.

The root mean square speed of the molecules of a diatomic gas is $v$. When the temperature is doubled,the molecules dissociate into two atoms. The new root mean square speed of the atom is

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