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.
Electrical Mobility Calculator: Learn about the Einstein relation with the help of our handy Electrical Mobility Calculator tool. Get to know about the diffusion constant, drift velocity, mobility and many more in the following sections. Find the solved examples, formulas, and detailed steps to calculate diffusion constant on this page.
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.
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 = μ * kB * T / q
D is the diffusion constant
μ 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
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.
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 μ = u / V.
u is the drift velocity
V is the voltage difference
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?
μ = 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 = μ * 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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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 μ = |Vd|/E.