The Maxwell distribution function for differe | vedclass

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(D) The most probable speed $v_p$ of gas molecules is given by the formula $v_p = \sqrt{\frac{2RT}{M}}$,where $R$ is the universal gas constant,$T$ is

Vedclass · Accepted Answer

$A 	o O_2, B 	o Ne, C 	o He$

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(D) The most probable speed $v_p$ of gas molecules is given by the formula $v_p = \sqrt{\frac{2RT}{M}}$,where $R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass of the gas.From the formula,it is clear that $v_p \propto \frac{1}{\sqrt{M}}$.This means that the gas with the smaller molar mass will have a higher most probable speed.The molar masses of the given gases are: $M(O_2) = 32 	ext{ g/mol}$,$M(Ne) = 20 	ext{ g/mol}$,and $M(He) = 4 	ext{ g/mol}$.Comparing these,we have $M(O_2) > M(Ne) > M(He)$.Therefore,the order of their most probable speeds will be $v_p(O_2) Looking at the graph,the peak of the distribution shifts to the right as speed increases. Thus,the order of speeds corresponding to the peaks is $A Matching these,we get $A 	o O_2$,$B 	o Ne$,and $C 	o He$.

Column-$I$	Column-$II$
$(a)$ ${v_{rms}} = \sqrt {\frac{3P}{\rho}}$	$(i)$ For $1 \text{ mole ideal gas}$
$(b)$ ${v_{rms}} = \sqrt {\frac{3RT}{M_0}}$	$(ii)$ For one molecule of gas
$(c)$ ${v_{rms}} = \sqrt {\frac{3{k_B}T}{m}}$	$(iii)$ On the basis of kinetic theory

The Maxwell distribution function for different gases is shown in the figure. Which of the following is the correct matching?

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