4.1 Brownian motion  (Page 3/5)

The subsequent observations of Theodor Svedberg and Felix Ehrenhaft on Brownian motion in colloids and onparticles of silver in air, respectively, helped to support Einstein’s theory, but much of the experimental work to actuallytest Einstein’s predictions was carried out by French physicist Jean Perrin, who eventually won the Nobel Prize in physics in 1926.Perrin’s published results of his empirical verification of Einstein’s model of Brownian motion are widely credited for finallysettling the century-long dispute about John Dalton’s theory for the existence of atoms.

Brownian motion and kinetic theory

The kinetic theory of matter states that all matter is made up of atoms and molecules, that these atoms andmolecules are in constant motion, and that collisions between these atoms and molecules are completely elastic.

The kinetic-molecular theory of heat involves the idea that heat as an entity is manifested simply in the form ofthese moving atoms and molecules. This theory is comprised of the following five postulates.

• Heat is a form of energy.
• Molecules carry two types of energy: potential and kinetic.
• Potential energy results from the electric force between molecules.
• Kinetic energy results from the motion of molecules.
• Energy converts continuously between potential energy and kinetic energy.

Einstein used the postulates of both theories to develop a model in order to provide an explanation of theproperties of Brownian motion.

Brownian motion is characterized by the constant and erratic movement of minute particles in a liquid or agas. The molecules that make up the fluid in which the particles are suspended, as a result of the inherently random nature of theirmotions, collide with the larger suspended particles at random, making them move, in turn, also randomly. Because of kinetics,molecules of water, given any length of time, would move at random so that a small particle such as Brown’s pollen would be subject toa random number of collisions of random strength and from random directions.

Described by Einstein as the “white noise” of random molecular movements due to heat, Brownian motion arises fromthe agitation of individual molecules by thermal energy. The collective impact of these molecules against the suspended particleyields enough momentum to create movement of the particle in spite of its sometimes exponentially larger size.

According to kinetic theory, the temperature at which there is no movement of individual atoms or molecules isabsolute zero (-273 K). As long as a body retains the ability to transfer further heat to another body – that is, at any temperatureabove absolute zero – Brownian motion is not only possible but also inevitable.

Brownian motion as a mathematical model

The Brownian motion curve is considered to be the simplest of all random motion curves. In Brownian motion, aparticle at time t and position p will make a random displacement r from its previous point with regard to time and position. Theresulting distribution of r is expected to be Gaussian (normal with a mean of zero and a standard deviation of one) and to beindependent in both its x and y coordinates.