9716

Fermi-Dirac Distributions for Free Electrons in Metals

This Demonstration shows the variation in density of free electrons as a function of energy (in eV) for some representative metals at different temperatures . According to the Fermi–Dirac distribution, the number of free electrons per electron volt per cubic meter is given by , where is the Fermi energy of the metal and is the Boltzmann constant.
The dashed orange lines show the density of free electrons as a function of energy. The area under each curve equals the total number of free electrons per cubic meter of the metal.
The blue area shows where electrons have vacated energies in the neighborhood of . The red area shows the electrons that have acquired energies greater than as the temperature is increased.
For reference, the distribution of energy of free electrons at 0.001 °K is shown with bold purple lines.
  • Contributed by: Kallol Das (St. Aloysius College, Jabalpur, India)

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Fermi energy of elements and inadequacies inherent in the free electron model are taken from N. W. Ashcroft and N. D. Mermin, Solid State Physics, New York: Holt, Rinehart and Winston, 1976.
Details on the density of free electrons per electron volt are taken from C. Kittel, Introduction to Solid State Physics, 5th ed., New York: Wiley, 1983.
Additional information on the free electron model can be found on Wikipedia.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+