Lab lesson 10 (IP10)!

This lab lesson talked about brownian motion.

The random movement of microscopic particles suspended in a liquid or gas, caused by collisions with molecules of the surrounding medium. Also called Brownian movement.

The first part of Einstein's argument was to determine how far a Brownian particle will travel in a given time interval. Classical mechanics is unable to determine this distance on account of the enormous number of bombardments a Brownian particle will undergo, roughly of the order of 10²¹ collisions per second.Thus, Einstein was led to consider the collective motion of Brownian particles where if ρ(x,t) is the density of Brownian particles at point x at time t then it will satisfy the diffusion equation,

where D is the diffusion coefficient. Assuming all the particles were located at the origin at the initial time t = 0, the diffusion equation has the solution,

This expression allowed Einstein to calculate the moments directly. The first moment is seen to vanish meaning that the Brownian particle is equally likely to move to the left as it is to move to the right. The second moment is, however, non-vanishing and is given by

Applications of Brownian Motion



Brownian motion is a sophisticated random number generator, based on a process discovered in plants(R. Brown; 1827) This continuous random motion of solid microscopic particles when suspended in a fluid medium is due to the consequence of continuous bombardment by atoms and molecules. It has a wide range of applications, including modeling noise in images, generating fractals, growth of crystals and stock market simulation.

Reflection

This Laboratory Lesson proved the existence of atoms and how atoms constantly move in random directions, this helps us to know more about how atoms move. Before this laboratory lesson, I thought of atoms as just stationary tiny particles of matter and after this lab lesson I realised that atoms were actually moving and not just stationary. They are even moving in a solid just that the inter-molecular forces in a solid are too strong and that this actually causes the atoms not to move as rapidly and quickly as they would do in a gas or in a liquid.

Summary

• Brownian Motion can be used other than for proving the existenc of atoms, it can also be used to formulate random numbers and stimulate a stock market
• Brownian Motion proves the existence of atoms