Match the following (where U_{rms} = root mea | vedclass

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Question

(A) The formulas for molecular speeds are: $U_{mp} = \sqrt{\frac{2RT}{M}}$,$U_{av} = \sqrt{\frac{8RT}{\pi M}}$,$U_{rms} = \sqrt{\frac{3RT}{M}}$. $(a)$

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$ (a)-(iii), (b)-(ii), (c)-(i) $

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(A) The formulas for molecular speeds are: $U_{mp} = \sqrt{\frac{2RT}{M}}$,$U_{av} = \sqrt{\frac{8RT}{\pi M}}$,$U_{rms} = \sqrt{\frac{3RT}{M}}$. $(a)$ Ratio $U_{rms} / U_{av} = \sqrt{\frac{3RT}{M}} / \sqrt{\frac{8RT}{\pi M}} = \sqrt{\frac{3\pi}{8}} \approx \sqrt{1.178} \approx 1.086 \approx 1.08$. $(b)$ Ratio $U_{av} / U_{mp} = \sqrt{\frac{8RT}{\pi M}} / \sqrt{\frac{2RT}{M}} = \sqrt{\frac{4}{\pi}} \approx \sqrt{1.273} \approx 1.128 \approx 1.13$. $(c)$ Ratio $U_{rms} / U_{mp} = \sqrt{\frac{3RT}{M}} / \sqrt{\frac{2RT}{M}} = \sqrt{1.5} \approx 1.224 \approx 1.22$. Thus,the correct matching is $(a)-(iii), (b)-(ii), (c)-(i)$.

List-$I$	List-$II$
$(a)$ $U_{rms} / U_{av}$	$(i)$ $1.22$
$(b)$ $U_{av} / U_{mp}$	$(ii)$ $1.13$
$(c)$ $U_{rms} / U_{mp}$	$(iii)$ $1.08$

Match the following (where $U_{rms}$ = root mean square speed,$U_{av}$ = average speed,$U_{mp}$ = most probable speed)
List-$I$ List-$II$
$(a)$ $U_{rms} / U_{av}$ $(i)$ $1.22$
$(b)$ $U_{av} / U_{mp}$ $(ii)$ $1.13$
$(c)$ $U_{rms} / U_{mp}$ $(iii)$ $1.08$

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Match the following (where $U_{rms}$ = root mean square speed,$U_{av}$ = average speed,$U_{mp}$ = most probable speed) List-$I$List-$II$$(a)$ $U_{rms} / U_{av}$$(i)$ $1.22$$(b)$ $U_{av} / U_{mp}$$(ii)$ $1.13$$(c)$ $U_{rms} / U_{mp}$$(iii)$ $1.08$