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  4. If gas contains only three molecules that move with velocities of 100, 200, 500. What is the RMS velocity of the gas in m s-1?

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Q. If gas contains only three molecules that move with velocities of $100, 200, 500$. What is the $RMS$ velocity of the gas in $m \,s^{-1}$?

States of Matter

Solution:

$RMS$ velocity $=\sqrt{\frac{c^{2}_{1}+c^{2}_{2}+c^{2}_{3}+...}{n_{1}+n_{2}+n_{3}...}}$
$RMS$ velocity $=\sqrt{\frac{\left(100\right)^{2}+\left(200\right)^{2}+\left(500\right)^{2}}{3}}=\sqrt{10^{5}}$
$=100\sqrt{10}$