NEET-XII-Physics
24: Kinetic Theory of Gases
- #21Estimate the number of collisions per second suffered by a molecule in a sample of hydrogen at STP. The mean free path (average distance covered by a molecule between successive collisions) = 1.38 × 10-5 cm.Ans : Here,
`` \lambda =1.38\times {10}^{-8}\,\mathrm{\,m\,}``
`` ``
T = 273 K
M = `` 2\times {10}^{-3}\,\mathrm{\,kg\,}``
Average speed of the H molecules is given by
`` {v}_{avg}=\sqrt{\frac{8RT}{\,\mathrm{\,\pi M\,}}}``
`` =\sqrt{\frac{8\times 8.31\times 273}{3.14\times 2\times {10}^{-3}}}``
`` =1700m{s}^{-1}``
`` ``
`` ``
`` ``
The time between two collisions is given by
`` t=\frac{\lambda }{{v}_{avg}}``
`` \Rightarrow t=\frac{1.38\times {10}^{-8}}{1700}``
`` \Rightarrow t=8\times {10}^{-12}s``
`` \,\mathrm{\,Number\,}\,\mathrm{\,of\,}\,\mathrm{\,collisions\,}\,\mathrm{\,in\,}1\,\mathrm{\,s\,}=\frac{1}{8.11\times {10}^{-12}}=1.23\times {10}^{11}``
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