2016 Feb

Brownian Motion: Tumult of the Tiny World

February 10, 2016

Brownian Motion1

In the year 1827 Robert Brown, a Scottish botanist, observed pollen grains suspended in water using a microscope and his discovery startled him. He observed that tiny particles ejected from the pollen grains moved randomly in a jittery motion. This is back in those days when motion is often associated with life. To verify if this phenomenon is caused by ‘living’ nature of the pollen grains he repeated the experiment with inorganic materials only to observe the same behavior. The question is what caused the tiny material to move around and how did it get energy adequate for its motion.

Albert Einstein, in the year 1905, explained Brownian motion using the concept of atoms and molecules. He stated that the random motion observed by Brown is because of the constant bombardment of pollen by the molecules of water. Molecules in liquids are not bound tightly like they are in solids. The relatively free liquid molecules move across the volume of the liquid and this motion is dependent on factors like temperature, pressure and nature of the liquid. Generally this motion of molecules is high at higher temperatures. This motion is the same reason why (soluble) ink spreads across the volume of water.

We have learnt about Brownian motion during our Physics tuition classes, but to have a better understanding, let’s imagine this scenario: a giant football whose diameter is of the order of 25 meters is left in a crowded place and people in the crowd are moving randomly. Whenever a person hits this football a tiny motion should be observed in it. But due to the size of the crowd and their random motion the chances of force applied by one being cancelled by other are high. Whenever the resultant force on the giant football is not zero, it experiences motion and the direction of the motion and its magnitude are also random due to the random motion of the crowd. The same applies to motion of pollen in water, where pollen can be compared with the giant football and the crowd with molecules of water.

Brownian motion is a stochastic process i.e. the motion is probabilistic and the direction of displacement and the magnitude of displacement can be described by random variables with each of the possible outcomes having certain probability. Brownian motion is so random that the mathematical models used to predict the path of particle undergoing it can also be used in stock market predictions.

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