Enter the number of electrons per unit volume into the calculator to determine the Fermi Energy.
Fermi Energy Formula
The following equation is used to calculate the Fermi Energy.
Ef = (h^2/2me) * (3*pi^2*n)^2/3
- Where Ef is the Fermi Energy (Joules)
- n is the number of electrons per unit volume
- h is Planck’s Constant 6.62606957e-34
- me is the electron mass 9.10938188e-31
How to Calculate Fermi Energy?
The following two example problems outline the steps and information needed in order to calculate the Fermi Energy.
Example Problem #1:
- First, determine the number of electrons per unit volume. In this example, the number of electrons per unit volume is measured to be 9.
- Finally, calculate the Fermi Energy using the formula above:
Ef = (h^2/2me) * (3*pi^2*n)^2/3 =
Inserting the values from above and solving the equation with the imputed values gives:
Ef = (6.62606957e-34^2/(2*9.10938188e-31)) * (3*3.14159^2*9)^2/3 = 5.704e-33 joules
Example Problem #2:
Using the same process as example problem 1, we first define the needed variables outlined by the formula. In this case, the values are provide as:
number of electrons per unit volume = 3
Entering these values into the formula or calculator above gives us:
Ef = (h^2/2me) * (3*pi^2*n)^2/3 = 6.338e-34 (Joules)