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(B) The formula for the root mean square ($R.M.S.$) velocity of gas molecules is given by $C = \sqrt{\frac{3RT}{M}}$.From this relation, we can see th

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$100 \,m/s$

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(B) The formula for the root mean square ($R.M.S.$) velocity of gas molecules is given by $C = \sqrt{\frac{3RT}{M}}$.From this relation, we can see that $C \propto \sqrt{\frac{T}{M}}$.Let the initial velocity be $C = 200 \,m/s$ at temperature $T$ and molecular weight $M$.Given the new conditions: $T' = \frac{T}{2}$ and $M' = 2M$.The new $R.M.S.$ velocity $C'$ is given by the ratio:$\frac{C'}{C} = \sqrt{\frac{T'}{T} 	imes \frac{M}{M'}} = \sqrt{\frac{T/2}{T} 	imes \frac{M}{2M}} = \sqrt{\frac{1}{2} 	imes \frac{1}{2}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.Therefore, $C' = \frac{C}{2} = \frac{200}{2} = 100 \,m/s$.

The root mean square velocity of molecules of a gas is $200 \,m/s$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

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