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  4. The respective speeds of five molecules are 2, 1.5, 1.6, 1.6 and 1.2 km s-1, the most probable speed in km s-1 will be

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Q. The respective speeds of five molecules are 2, 1.5, 1.6, 1.6 and $1.2 \, km \, s^{-1}$, the most probable speed in $km\, s^{-1}$ will be

JIPMERJIPMER 2011Kinetic Theory

Solution:

$v_{mp} = 0.816 \, v_{rms} $
$= 0.816 \sqrt{\frac{v^{2}_{1}+v_{2}^{2}+v_{3}^{2}+v_{4}^{2}+v_{5}^{2}}{N}}$
$ =0.816 \sqrt{\frac{\left(2\right)^{2}+\left(1.5\right)^{2} +\left(1.6\right)^{2} +\left(1.6\right)^{2}+\left(1.2\right)^{2}}{5}}$
$= 1.31 \, Km \, s^{-1}$