Answer to Question #120761 in Molecular Physics | Thermodynamics for Abhishek

Question

What is Brownian motion ? Give at least three examples of such a motion. Using Einstein's theory, obtain an expression for the mean square displacement of a Brownian particle.

Answer 1

Answer: Brownian motion is a disordered, chaotic motion of a particle under the action of uneven impacts of molecules of matter on different sides in solutions. It is named after the botanist Robert Brown, who observed this phenomenon under a microscope in 1827. The theory of Brownian motion was formulated in 1905 by Albert Einstein.

Examples of Brownian motion: the motion of paint particles in water, the movement of dust in the sun; movement of a man lost in the woods.

Einstein formed a mathematical formula according to which the mean value of the square of the Brownian particle displacement (s2) for time $t$ is directly proportional to the temperature T and inversely proportional to the viscosity of the liquid $\eta$ , the particle size r and the Avogadro constant N_A: $s^2 = 2RTt/6 \pi\eta rN_A.$

R in the formula is a gas constant