Brownian Motion Formula

The Formula To Calculate Diffusion Constant

\(D=\frac{RT}{N_{a}6\pi \eta a} = \frac{k_{B}T}{6\pi \eta a}\)


R is the gas constant

NA = 6.06 X 1023/mol referred as Avogadro’s number

T is the temperature

η is the viscosity of the liquid

a is the radius of the Brownian particle

kB = R/NA is Boltzmans constant

Considering a large Brownian particle immersed in a fluid of much smaller particles (atoms). The radius of the Brownian particle is typically 10−9m < a < 5 × 10−7m.

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