Created By : Naaz Fatima

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 19, 2023

Make use of our free Electrical Mobility Calculator to explore the Einstein-Smoluchowski relation. This Einstein relation connects the random motion of electrons in a wire. Provide the charge, temperature and electrical mobility values in the calculator to get the output i.e diffusion constant within no time.

Given
Diffusion Constant D
Temperature T
Charge q

### Steps to Calculate Diffusion Constant

Have a look at the detailed explanation on what are the simple steps to calculate the diffusion constant using the Einstein-Smoluchowski relation. Check out the instructions and follow them while solving the questions.

• Get temperature, the charge of carries, and electrical mobility values.
• Multiply the electrical mobility, temperature and Boltzmann constant.
• The Boltzmann constant value is 1.3806503 * 10-23 J/K.
• Divide the product by the charge to obtain the diffusion constant value.

### Einstein Relation Formula | Drift Velocity

Einstein-Smoluchowski relation also known as Einstein relation that connects diffusion constant with the electrical mobility.

The formula to calculate the diffusion constant as follows:

D = ╬╝ * kB * T / q

Where,

D is the diffusion constant

╬╝ is the electrical mobility

kB is the Boltzmann constant and kB = 1.3806503 x 10-23 J/K

T is the temperature

q is the charge of the carriers

Diffusion Constant:

When electrons are constant in a wire, then it is called thermal motion. If all electrons are in the smaller region of the wire, thermal motion quickly spreads throughout the whole wire. The diffusion constant means how quickly that happens. The unit is area/time.

Drift Velocity:

The change in voltage to wire results in the moving of electrons. The velocity of moving electrons is called the drift velocity. It depends on the voltage difference. The formula is ╬╝ = u / V.

Where,

u is the drift velocity

V is the voltage difference

Example

Question: If the electrical mobility in a wire is 3000 mm2/(Vs) and the room temperature is 20┬░C. The charge in electrons is 50e. Calcuate the diffusion constant?

Solution:

Given that

╬╝ = 3000 mm2/(Vs)

Temperature T = 20┬░C

The charge in electrons q = 50e

kB = 1.3806503 x 10-23 J/K

Einstein-Smoluchowski relation is D = ╬╝ * kB * T / q

D = (3000 x 1.3806503 x 10-23 x 20)/50

= 1.5157 mm2/s

Therefore, the diffusion constant is 1.5157 mm2/s.

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### Frequently Asked Questions on Electrical Mobility Calculator

1. What is the unit of mobility of charge?

Mobility is the motion of electrons or icons under the influence of an external electric field. The unit of mobility of charge is cm2/(V.s). The Si unit of mobility of charge is m2/(V.s).

2. What does Einstein's relationship mean?

Einstein-Smoluchowski relation connects the diffusion constant with the electrical mobility. Mobility is related to the species diffusion coefficient through an equation called the Einstein relation.

3. What is meant by drift velocity?

When an electron particle reaches the average velocity under the influence of an electric field is known as the drift velocity.

4. What is the formula of mobility?

Mobility is defined as the magnitude of drift velocity per unit electric field and its formula is ╬╝ = |Vd|/E.