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

Variables:

  • 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:

  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.
  2. 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)