A Brownian particle is observed to diffuse 100 μm in 60 s, on average. (Diffusion distance mean

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A Brownian particle is observed to diffuse 100 μm in 60 s,...

A Brownian particle is observed to diffuse $100 \mu \mathrm{m}$ in $60 \mathrm{~s}$, on average. (Diffusion distance means magnitude of the net displacement.) A second particle with twice the diameter and ten times the mass of the first is observed. How far, on average, will the second particle diffuse in $60 \mathrm{~s}$ at the same temperature?

Key Concepts

Mean Square Displacement

Mean square displacement (MSD) is a statistical measure that represents the average squared distance a particle travels over time during diffusion. The MSD is directly proportional to time and serves as a link between the microscopic diffusion coefficient and the macroscopic observable displacement, making it essential in analyzing diffusion processes.

Brownian Motion

Brownian motion describes the random, stochastic movement of particles suspended in a fluid, resulting from collisions with the fluid's molecules. This phenomenon is a classical illustration of thermal motion at the microscopic scale and forms the basis for many diffusion processes observed in physics and chemistry.

Diffusion Coefficient

The diffusion coefficient quantifies how quickly a particle spreads out in a medium due to random motion. It is a central parameter in diffusion theory, linking the microscopic behavior of particles to macroscopic transport phenomena, and depends on properties such as temperature, the viscosity of the medium, and the size of the diffusing particle.

Stokes-Einstein Relation

The Stokes-Einstein relation connects the diffusion coefficient of a spherical particle in a fluid to the temperature, the fluid's viscosity, and the particle's radius. This relation shows that an increase in particle size (or radius) leads to a lower diffusion coefficient, providing a quantitative framework for understanding how physical attributes influence the rate of diffusion.

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