Created By : Vaibhavi Kumari

Reviewed By : Phani Ponnapalli

Last Updated : May 17, 2023

To learn more about the Einstein-Smoluchowski relationship, use our free Electrical Mobility Calculator. The random motion of electrons in a wire is connected by this Einstein relation. To calculate the diffusion constant, enter the charge, temperature, and electrical mobility values into the calculator.

Given
Diffusion Constant D
Temperature T
Charge q

### Diffusion Constant

The thermal velocity of electrons in a wire is constant. If we envision putting all of the electrons in a tiny area of a wire, the thermal motion quickly spreads them out across the entire wire. The diffusion constant D indicates how fast this occurs. The diffusion constant is measured in area/time.

The diffusion constant can be thought of in the following way. Assume that electrons occupy a specific area at some point in time. The diffusion constant is the area's rate of growth over time.

### Drift Velocity

Electric current is what we call it. There are two effects at work here. The electrons are accelerated in the electric field on one hand, but clash with each other. As a result, the electrons migrate at a specific speed, which is known as the drift velocity u.

To figure out how to calculate it, use the drift velocity calculator. The voltage differential V determines the drift velocity. Electrical mobility, which is defined as the ratio of the two, is a universal quantity. μ = u / V.

### Einstein Relationship Formula

The Einstein-Smoluchowski relationship, often known as the Einstein relation, is a relationship that links the diffusion constant to electric mobility.

The diffusion constant is calculated using the following formula D = μ * kB * T / q

• Where, D = diffusion constant
• μ = electrical mobility
• kB = Boltzmann constant and kB = 1.3806503 x 10^-23 J/K
• T = temperature
• q = charge of the carriers

### How to Calculate Diffusion Constant?

Take a look at the step-by-step procedures for calculating the diffusion constant using the Einstein-Smoluchowski relationship. Look over the directions and make sure you're following them when answering the questions.

• Step 1: Calculate temperature, carrying charge, and electrical mobility.
• Step 2: Multiply the electrical mobility, temperature, and Boltzmann constant by their respective values.
• Step 3: 1.3806503 * 10^-23 J/K is the Boltzmann constant.
• Step 4: To find the diffusion constant, divide the product by the charge.

### Electrical Mobility Examples

Question 1: If a wire's electrical mobility is 3500 mm^2/(Vs) and the ambient temperature is 15°C. Electrons have a charge of 40e. Do you know how to calculate the diffusion constant?

Solution:

Given:

μ = 3500 mm^2/(Vs)

Temperature T = 15°C

The charge in electrons q = 40e

kB = 1.3806503 x 10^-23 J/K

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

D = (3500 x 1.3806503 x 10^-23 x 15)/40

= 1.8121x 10^-20 mm^2/s

Hence, the diffusion constant is 1.8121x 10^-20 mm^2/s.

### FAQs on Electrical Mobility Calculator

1. What is drift velocity?

The drift velocity is the average velocity reached by an electron particle under the influence of an electric field.

2. What is the unit of charge mobility?

The migration of electrons or icons under the influence of an external electric field is known as mobility. The unit of charge mobility is cm^2/. (V.s). or m^2/ is the SI unit for charge mobility (V.s).

3. What is the significance of Einstein's relationship?

The diffusion constant and electrical mobility are linked by the Einstein-Smoluchowski relation. Through an equation known as the Einstein relation, mobility is linked to the species diffusion coefficient.

4. What is mobility in current electricity?

The value of the drift velocity per unit of electric field strength is formally defined as mobility; consequently, the quicker the particle moves at a given electric field strength, the greater the mobility.

5. What factors go into determining carrier mobility?

The Drude carrier drift velocity is commonly defined as μ ≡ v/E = σ/en, where E is the applied electrical field, which is considered to be modest, is conductivity, and n is carrier density.