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Brownian motion

Brownian Motion is the random movement of particles suspended in a fluid (liquid or gas), resulting from collisions with the molecules of the fluid. This phenomenon was first observed by botanist Robert Brown in 1827 while studying pollen grains in water. The motion of these particles, though seemingly random, can provide valuable insights into the properties of the particles and the fluid in which they are suspended.

Brownian motion has two key aspects:

  • its random nature and
  • its microscopic origin.

The motion is erratic and unpredictable because it results from countless collisions with molecules that are themselves moving randomly. This randomness is a fundamental characteristic of thermal motion at the molecular level. On a microscopic scale, the constant, thermal-driven impacts of fluid molecules on suspended particles cause the particles to exhibit Brownian motion.

Zero net movement

\[ \left\langle x^2 \right\rangle = \frac{\sum x_i^2}{n} \]