Answer to Question #158278 in Molecular Physics | Thermodynamics for Akshat Kotnala

Question

 The mean speed of the molecules of an ideal gas is 2.0 x 10^3 m/s.

The radius of a gas molecule is 1.5 x 10^ -10 m

Calculate the (i) collision frequency, and 

(ii) mean free path. It is given that n= 4 x 10^24 per m^3

Answer 1

1)

$\nu=4\pi r^2 n v=4\cdot 3.14 \cdot 1.5^2\cdot 10^{-20}\cdot 4\cdot 10^{24}\cdot 2\cdot 10^3=2.26\cdot 10^9 ~Hz.$

2)

$\lambda=\frac{1}{4\pi r^2 n}=\frac{1}{4\cdot 3.14 \cdot 1.5^2\cdot 10^{-20}\cdot 4\cdot 10^{24}}=0.88\cdot 10^{-6} ~m.$