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  4. The kinetic molecular theory attributes an average translational kinetic energy of =(3RT/2N) to each particle. What rms speed would a mist particle of mass 10-12 g have at room temperature (27°C) according to kinetic theory of gases?

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Q. The kinetic molecular theory attributes an average translational kinetic energy of $=\frac{3RT}{2N}$ to each particle. What rms speed would a mist particle of mass $10^{-12}\, g$ have at room temperature $(27^°C)$ according to kinetic theory of gases?

States of Matter

Solution:

K.E. per molecule $=\frac{3RT}{2N}$
$\Rightarrow \frac{1}{2}mu^{2}=\frac{3RT}{2N}$ or $u=\sqrt{\frac{3RT}{m\times N}}$
$=\sqrt{\frac{3\times8.314\times10^{7}\times300}{6.023\times10^{23}\times10^{-12}}}=0.35\,cm^{-1}$