# Brownian Motion Formula

## Brownian Motion Formula

The random movement of particles inside a fluid is referred to as Brownian Motion Formula. Brownian Motion Formula is a particle’s erratic zigzagging motion that is often seen with a high-powered ultramicroscope. Brownian Motion Formula may be understood as the chaotic or erratic motion of particles inside a fluid, brought on by repeated collisions with other quickly moving molecules. Generally speaking, smaller particles, less viscous liquids, and greater temperatures are shown to have increased random movement of a particle. These particles interact with one another when they move. The random movement of tiny particles floating in fluids is explained by the Brownian Motion Formula.

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## The Formula To Calculate Diffusion Constant

The diffusion constant is a quantity that is used to compute the Brownian Motion Formula. The ratio of the product of the gas constant and temperature to the product of six pi times the Avogadro number, fluid viscosity, and particle radius yields the formula for it. It is represented by the letter D. Since it is the ratio of two identical numbers, it has no dimensional formula and is a unitless quantity.

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### Brownian Motion Formula

In chemistry, Brownian Motion Formula is a random movement. The tiny particles floating in fluids are another way to see it. Additionally, it is also referred to as the “Brownian Motion Formula” since it is the consequence of collisions between the particle and other fast-moving particles in the fluid.

One particle’s course will be altered when two particles meet. A second collision also makes the particle move randomly, leading to the term “zigzagging.” During this process, the particles trade momentum and energy.

Under a high-power microscope, a particle can be seen to move randomly in a zigzag pattern, which is what is known as the Brownian Motion Formula in biology. Robert Brown called this motion, which is akin to how pollen grains travel in water, the Brownian Motion Formula.

Albert Einstein further confirmed the Brownian Motion Formula of pollen in his work by stating that the pollen was transported by water molecules. With this revelation, atomic and molecular existence has been enhanced.

It is crucial to appreciate the Brownian Motion Formula, which forms the foundation of contemporary atomic theory. The Brownian Motion Formula model of particles is also the foundation of the kinetic theory of gases. Many academic fields, including physics, arithmetic, economics, chemistry, and more, utilize the mathematical models that explain the Brownian Motion Formula.

## Sample Problems

Example 1:If a Brownian particle has a radius of 2 m, a fluid viscosity of 0.056 Pas, and a temperature of 300 K, determine the particle’s diffusion constant.

Solution:

We’ve got

T = 300

r = 2

η = 0.056

Using the existing formula,

D = kBT/6πrη

= (1.381 × 10-23 × 300) / (6 × 3.14 × 2 × 0.056)

= 1.96 × 10-21

Example 2: If a Brownian particle has a radius of 3 m, a fluid viscosity of 0.068 Pas, and a temperature of 250 K, determine the particle’s diffusion constant.

Solution:

We’ve got

T = 250

r = 3

η = 0.068

Using the existing formula,

D = kBT/6πrη

= (1.381 × 10-23 × 250) / (6 × 3.14 × 3 × 0.068)

= 8.98 × 10-22

Example 3: If a Brownian particle’s diffusion constant is 7.5 10-22, its radius is 2.5 m, and the fluid’s viscosity is 0.087 Pa s, determine the environment’s temperature.

Solution:

We’ve got

D = 7.5 × 10-22

r = 2.5

η = 0.087

Using the existing formula,

D = kBT/6πrη

=> T = 6πDrη/kB

= (6 × 3.14 × 7.5 × 10-22 × 2.5 × 0.087) / (1.381 × 10-23)

= 22.25 × 10

= 222.5 K

Example 4: If a Brownian particle’s diffusion constant is 6.8 10-22, its radius is 4 m, and the fluid’s viscosity is 0.062 Pa s, determine the environment’s temperature.

Solution:

We’ve got

D = 6.8 × 10-22

r = 4

η = 0.062

Using the existing formula,

D = kBT/6πrη

=> T = 6πDrη/kB

= (6 × 3.14 × 6.8 × 10-22 × 4 × 0.062) / (1.381 × 10-23)

= 23 × 10

= 230 K