# Brownian Motion Formula

## The Formula To Calculate Diffusion Constant

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

Where,

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.

#### Practise This Question

The circular wire of diameter 10cm is cut and placed along the circumference of a circle of diameter 1 metre. The angle subtended by the wire at the centre of the circle is equal to