Fermi energy and fermi dirac distribution law, Physics

Q. Define Fermi energy. Write down the expression for Fermi Dirac distribution law. Deduce an expression for Fermi energy of a system of free particles.

Sol. The Fermi Energy : it is important to determine how the electrons may distribute themselves in a band among the energies from zero to E. The number of energy levels in the energy rage dE available to a free particle enclosed in a box of volume V is given by each level can accommodate two electrons (one with spin up and one with spin down). Therefore if we refer to a unit volume, the total number of electrons per unit volume with energy between E and E + dE, is. The quality is shown in fig. for a given band the curve should stop at E. The number of electrons per unit volume that can be accommodated up to an energy E is given by

If the metal is in its ground state (which takes place at absolute zero), all electrons occupy the lowest probable energy levels in accordance with the exclusion principle. If the total number of electrons per unit volume is less than the total number of energy levels available in the band, the electrons will then occupy all energy states up to a maximum energy designated by E, and called the Fermi energy. If we put E = EF in equation (3), we must have n = n0. Therefore for the Fermi energy we obtain the value.

Thus the energy distribution of electrons in the metal, ground state corresponds to the shaded area in fig. when the Fermi energy is equal to the bandwidths the band is completely occupied. When a band is not completely filled, a small amount of energy is sufficient to excite the uppermost electrons to nearby energy levels.

Posted Date: 8/1/2012 7:47:12 AM | Location : United States







Related Discussions:- Fermi energy and fermi dirac distribution law, Assignment Help, Ask Question on Fermi energy and fermi dirac distribution law, Get Answer, Expert's Help, Fermi energy and fermi dirac distribution law Discussions

Write discussion on Fermi energy and fermi dirac distribution law
Your posts are moderated
Related Questions
Difference between Fission and Fusion Fission                                                                                         Fusion 1. Heavy metal is divided int

Explain full wave bridge circuits showing the waves

Copper losses: These losses occur because of ohmic resistance of the transformer windings. If I1 and I2 are primary and secondary currents correspondingly and R1and R2 are the res

how to write a program from this using c language

What is the universal law of universal gravitation? Statement that any particle of matter in the universe attracts any other with a force varying directly as the product of the


Q. How does the laser printer works? Answer:- When a text or else image is entered into the CPU it produces a series of varying voltages. This manages a LED (light emittin

How Far Will It Skid? Most drivers' education classes teach future drivers in which the stopping distance of a skidding car is in a straight line proportional to the square of

In an amusement park ride called The Roundup, passengers stand inside a 19.0 -diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane.

What instrument is used to measure volume? Liquid volume is calculated with beakers, measuring cups, spoons, graduated cylinders, and the like. For regular objects, solid volum