Answer to Question #88787 in Molecular Physics | Thermodynamics for Shivam Nishad

Question

What is Brownian motion ? Give two examples of Brownian motion. Discuss Perrin's experiment to determine Avogadro's number.

Answer 1

Brownian motion - thermal chaotic motion of molecules. An example of a Brownian motion can be the following: if you spray perfume in one place of the room, then after a while, you can smell it at the other end of the room. Or if paint particles are dissolved in water, they will also move. In his experience, Perrin used the law of the distribution of particles in height, exploring the Brownian motion. Thanks to the mathematical operation below, he derived the Avogadro number from the law of the distribution of particles at heights h1 and h2.

$$n = n' \times e^{\frac{-mgh}{kT}}$$

$$n = n' \times e^{\frac{-(m-m1)gh}{kT}}$$ $$m1=\frac{4}{3}\times pi \times r^3 \times p1$$

$$n1=n' \times e^{\frac{-(m-m1)gh1}{kT}}$$

$$n2=n' \times e^{\frac{-(m-m1)gh2}{kT}}$$

$$\frac{n1}{n2} = e^{\frac{-g(h1-h2) \times (m-m1)}{kT}}$$

$$ln(\frac{n1}{n2}) = \frac{g(h2-h1) \times \frac{4}{3} \times pi \times r^3 \times (p-p1)}{kT}$$

$$k = \frac{g(h2-h1) \times \frac{4}{3} \times pi \times r^3 \times (p-p1)}{ln(n1/n2) \times T}$$

$$k \times Na = R, R = 8.31$$

Na = 6.02*10^23

p and p1 - density

The conclusion of Avogadro constant was given here through the density distribution of particles at heights h1 and h2.