What will be the effect on the root mean squa | vedclass

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(B) The root mean square velocity $(V_{rms})$ of a gas is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$.Given that the temperature is doubled

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The velocity of atomic oxygen doubles

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(B) The root mean square velocity $(V_{rms})$ of a gas is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$.Given that the temperature is doubled,$T' = 2T$.When oxygen molecules $(O_2)$ dissociate into atomic oxygen $(O)$,the molar mass is halved,so $M' = M/2$.Substituting these into the proportionality $V_{rms} \propto \sqrt{\frac{T}{M}}$,we get:$\frac{(V_{rms})_{atomic}}{(V_{rms})_{molecular}} = \sqrt{\frac{T'}{M'} \cdot \frac{M}{T}} = \sqrt{\frac{2T}{M/2} \cdot \frac{M}{T}} = \sqrt{4} = 2$.Therefore,the velocity of atomic oxygen becomes $2$ times the initial velocity of the oxygen molecules.

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

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