The root mean-square (rms) speed of oxygen mo | vedclass

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(C) The $rms$ speed 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 tem

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$2\upsilon$

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(C) The $rms$ speed 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.For oxygen molecules $(O_2)$ at temperature $T$,the molar mass is $M$. Thus,$v_{rms} = \sqrt{\frac{3RT}{M}} = \upsilon$.When the temperature is doubled $(T' = 2T)$ and the oxygen dissociates into atomic oxygen $(O)$,the molar mass becomes $M' = M/2$.The new $rms$ speed is: $v'_{rms} = \sqrt{\frac{3R(2T)}{M/2}} = \sqrt{4 \cdot \frac{3RT}{M}} = 2 \sqrt{\frac{3RT}{M}} = 2\upsilon$.

The root mean-square $(rms)$ speed of oxygen molecules $(O_2)$ at a certain absolute temperature is $\upsilon$. If the temperature is doubled and the oxygen gas dissociates into atomic oxygen,the $rms$ speed would be

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