What is Fermi: Definition and 383 Discussions

Enrico Fermi (Italian: [enˈriːko ˈfermi]; 29 September 1901 - 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and the "architect of the atomic bomb". He was one of very few physicists to excel in both theoretical physics and experimental physics. Fermi was awarded the 1938 Nobel Prize in Physics for his work on induced radioactivity by neutron bombardment and for the discovery of transuranium elements. With his colleagues, Fermi filed several patents related to the use of nuclear power, all of which were taken over by the US government. He made significant contributions to the development of statistical mechanics, quantum theory, and nuclear and particle physics.
Fermi's first major contribution involved the field of statistical mechanics. After Wolfgang Pauli formulated his exclusion principle in 1925, Fermi followed with a paper in which he applied the principle to an ideal gas, employing a statistical formulation now known as Fermi–Dirac statistics. Today, particles that obey the exclusion principle are called "fermions". Pauli later postulated the existence of an uncharged invisible particle emitted along with an electron during beta decay, to satisfy the law of conservation of energy. Fermi took up this idea, developing a model that incorporated the postulated particle, which he named the "neutrino". His theory, later referred to as Fermi's interaction and now called weak interaction, described one of the four fundamental interactions in nature. Through experiments inducing radioactivity with the recently discovered neutron, Fermi discovered that slow neutrons were more easily captured by atomic nuclei than fast ones, and he developed the Fermi age equation to describe this. After bombarding thorium and uranium with slow neutrons, he concluded that he had created new elements. Although he was awarded the Nobel Prize for this discovery, the new elements were later revealed to be nuclear fission products.
Fermi left Italy in 1938 to escape new Italian racial laws that affected his Jewish wife, Laura Capon. He emigrated to the United States, where he worked on the Manhattan Project during World War II. Fermi led the team that designed and built Chicago Pile-1, which went critical on 2 December 1942, demonstrating the first human-created, self-sustaining nuclear chain reaction. He was on hand when the X-10 Graphite Reactor at Oak Ridge, Tennessee, went critical in 1943, and when the B Reactor at the Hanford Site did so the next year. At Los Alamos, he headed F Division, part of which worked on Edward Teller's thermonuclear "Super" bomb. He was present at the Trinity test on 16 July 1945, where he used his Fermi method to estimate the bomb's yield.
After the war, Fermi served under J. Robert Oppenheimer on the General Advisory Committee, which advised the Atomic Energy Commission on nuclear matters. After the detonation of the first Soviet fission bomb in August 1949, he strongly opposed the development of a hydrogen bomb on both moral and technical grounds. He was among the scientists who testified on Oppenheimer's behalf at the 1954 hearing that resulted in the denial of Oppenheimer's security clearance. Fermi did important work in particle physics, especially related to pions and muons, and he speculated that cosmic rays arose when material was accelerated by magnetic fields in interstellar space. Many awards, concepts, and institutions are named after Fermi, including the Enrico Fermi Award, the Enrico Fermi Institute, the Fermi National Accelerator Laboratory (Fermilab), the Fermi Gamma-ray Space Telescope, and the synthetic element fermium, making him one of 16 scientists who have elements named after them. Fermi tutored or directly influenced no fewer than 8 young researchers who went on to win Nobel Prizes.

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  1. S

    Exploring 2D Fermi Surfaces and CDW Effects

    why cdw occurs at low dimensional solids with anisotropic fermi surfaces that have prominent nesting vectors?/ what it means : cdws are also common at the surface of solids??where they are more commonly called surface reconstruction or dimerization . PLZ tell me about two dimensional Fermi...
  2. P

    Frame of reference for Fermi Golden Rule

    Hi guys. I am currently studying Sub-atomic physics and it seems to me that there are different formulas that work in different frame of reference. In particular, I would like to ask: 1. Which frame should we use in applying Fermi's Golden Rule? (I've read somewhere that the matrix element...
  3. B

    Calculating Fermi Level position in doped Silicon

    Estimate the Fermi level position EFn for a Si sample at room temperature that is doped with 1015 shallow donors cm-3. From coursework I've gatherred over the year I understand the equation needed is: EF=EC-kT ln(NC/n) n, being equal to the donor concentration EC is the conduction...
  4. A

    Fermi Vector in Ferromagnetic Material

    Homework Statement Consider an electron gas of density n_{0} in three dimensions that is completely ferromagnetic: all electron spins point in the same direction. Derive: a) The Fermi wave vector in terms of n_{0}. b) The parameter r as the radius in atomic unites that encloses one unit of...
  5. G

    Calculating Fermi Energy for Magnesium

    Homework Statement Calculate the Fermi energy for magnesium, assuming two free electrons per atom. Homework Equations {E_F} = \frac{{{\hbar ^2}}}{{2m}}{(3{\pi ^2}\rho )^{2/3}}, where \rho = q\frac{N}{V} and q is the number of free electrons. The Attempt at a Solution q = 2, so...
  6. jfizzix

    Chemical potential vs pressure and temperature; difficulty with Fermi gases

    For any system where the thermodynamic limit exists, we know that the internal energy U, the entropy σ, the total particle number N and the total volume V are all extensive. Because of this, we know that the Euler relation holds true U = -PV + \tauσ + \muN and that the chemical potential...
  7. T

    One loop Fermi Constant running

    Hi I am attempting to calculate the mass of the W boson according to one loop energies using the equation, Mw2=(πα/GF√2)/sin2θw(1-Δr) where (Δr)top=(3GFMt2)/8√2π2tan2θw using values:- α=α(MZ)=(127.916)-1 GF=1.16634×10-5 sin2θw=0.23116 =>...
  8. S

    What's the difference between a Luttinger surface and a Fermi surface?

    I'm trying to learn about Luttinger's sum rule, but I haven't taken QM yet, and the papers on the topic are very difficult to understand without it. However it seems qualitatively like the Luttinger surface is equivalent to the Fermi surface. If this is not the case, what's the difference? Does...
  9. S

    Regime of Fermi gas or liquid?

    Hi, I was wondering if anyone could clarify for me what the correct regime is for treating the electrons in a material as a Fermi gas. When is it that you must use Fermi liquid theory?
  10. B

    Calculate the ratio of the Fermi wavevector to the radius of the largest sphere

    Homework Statement Sodium is, to a good approximation, a monovalent free-electron metal which has the body-centred cubic structure. (a) Calculate the ratio of the Fermi wavevector to the radius of the largest sphere that can be inscribed in the first Brillouin zone. Remember that the...
  11. A

    What is the Fermi energy of Liquid He3 at absolute zero?

    Homework Statement The atom He^3 has spin 1/2 and is a fermion. The density of liquid He^3 is 0.081g/cm^3 near absolute zero. Calculate the Fermi energy \epsilon_F and the Fermi temperature T_F Homework Equations \epsilon_F = \frac{\hbar^2}{2m}(\frac{3 \pi^2 N}{V})^{2/3} T_F =...
  12. L

    Polarization of a Ideal Fermi Gas

    Homework Statement At T=0, what is the largest density that a gas can be completely spin polarized by a magnetic induction of 10 telsas Homework Equations μn= 10^-26 J/T mass= 5*10^-27 kg spin= 1/2 The Attempt at a Solution I am really not sure where to begin. The spin...
  13. O

    Flat band voltage, Fermi level

    Hi, I would like to get suggestions about the physical meaning of the (1) flat-band voltage and the (2) Fermi-level. Before being marked as newbie, I'd like to point out that I know how to calculate them and know that the (1) flat band voltage is the one which you apply, the energy band...
  14. alemsalem

    What are the natural generalizations (if any) to Bose and Fermi statistics?

    What are the "natural" generalizations (if any) to Bose and Fermi statistics? fermions: 1 particle per state Bosons: unlimited number of particles per state do people consider things in between like states with a capacity n? are there other generalizations of these statistics? Thanks!
  15. S

    Fermi level de-pinning & Schottky barrier

    Hello. I was womdering does anyone know any good resources of information on Fermi level de-pinning & Schottky barriers? I have been hunting around online, with not much luck. I thought someone here might be able to suggest some things. Thanks. Seán
  16. H

    Density of states, fermi energy

    Homework Statement Consider an electron gas with a density of states given by D(e) = ae2. Here a is a constant. The Fermi energy is eF. a) We first consider the system at zero temperature. Compute the total number of electrons N and the groundstate energy E. Show that the average energy per...
  17. U

    Fermi Temperature and Black-body radiation

    My understanding is that the Fermi temperature is a measure of the energy of a system at its lowest energy state. This suggests that at the Fermi temperature is a minimum temperature where the system can't radiate away any more energy. If this were a physical temperature it seems the system...
  18. C

    Band structure and fermi surface of copper

    Hi I've been searching on the web for this two topics, band structure and fermi surface, both of copper. I can't find any of them from a free source, I am doing just a report of my class of introduction to solid state and I just have found this two things in articles that must be bought. If...
  19. L

    Question: # of particles within an energy range below Fermi Energy.

    Homework Statement Here's what the question says. "Consider a cube of gold 1 mm on an edge. calculate the approximate number of conduction electrons in this cube whose energies lie in the range from 4.000 to 4.025 at 300k. Assume Ef(300K) = Ef(0)." Homework Equations Well, I know...
  20. L

    Fermi Level - clarification needed

    Fermi Level -- clarification needed Homework Statement Revered Members, Can i know what is meant by fermi level? I googled this, but i could not understand. One site says Fermi level as top of collection of electron energy levels at absolute zero. Homework Equations The Attempt...
  21. L

    F.E.G. fermi sphere radius problem

    Homework Statement Calculate the electron concentrations (# electrons/atom) needed for the fermi sphere to contact the zone faces (first bril. zone edges) in BCC and FCC structures. Homework Equations kf = (3*pi^2*n)^(1/3) where n is # electrons per atom. For cubic structures...
  22. itaischles

    Fermi energy (in semiconducors) vs. chemical potential

    Hi all, In the solid state physics course I took a year ago we used the chemical potential μ which appeared inside the fermi-dirac distribution function to describe the energy that above it no electrons resides and below it they all reside as the temperature reaches 0 kelvin. Now, when I...
  23. U

    What would Fermi say now about his 'paradox'?

    When Fermi was asked if he believed in the existence of E.T.s he replied "where are they?" and I think the idea was that if there were E.T.s they should have colonized the galaxy by now. What I am curious about is ... given the fact that the ability to detect earth-like worlds with signatures of...
  24. M

    Fermi Energy level with respect to band gap energy

    Homework Statement Calculate Efi with respect to the center of the bandgap in silicon for t= 200, 400, 600 kelvin. Homework Equations ni = Nc e^-((Ec- Ef)/(kt)) k = boltzman constant t= temperature in kelvin Ec = energy level of the conduction band ef= fermi energy level ni=...
  25. S

    Work function, Fermi levels and the MOS capacitor

    Hello. I am doing an electronics degree, and we were told in our solid state devices class that "work function is the energy required to release an electron from the influence of the material to vacuum. When the system is brought together to form the MOS capacitor, the Fermi levels must...
  26. A

    What is the relationship between Fermi energy and temperature?

    Hey everyone, So unfortunately I haven't taken Stat Mech yet (and my GRE is in a week), but through casual reading and forums I've gathered what the concept of fermi temperature and energy is...or thought I did. From what I understand, below the fermi energy (the fermi energy within an atom...
  27. R

    Fermi level in semiconductors

    1. Fermi level is also defined as highest energy level at which electron can exist at 0K then it should be top of valence band but why is it in between conduction band and valence band ( in forbidden gap)? It should be in conduction band or valence band. How to explain this? 2. If density of...
  28. P

    Fermi level in extrinsic semiconductors

    Fermi level in an extrinsic semiconductor(after attaining thermal equilibrium) is said to be invariant (constant ) , and the proof uses the fact 'no current must flow thorough any cross-section'..But I don't think its true, charge will be transported due to diffusion and this is countered by...
  29. A

    Do particles in a system at absolute zero still have kinetic energy?

    Is it weird that at absolute zero in a metal, electrons at the fermi level still move around at the fermi velocity. Is the notion that everything stops at absolute zero incorrect? Thank you
  30. S

    Fermi level, band structure of solids, and effect on electrical conduction

    how is the relationship between fermi level and band structure of solids can effect electrical conduction properties of a material?
  31. M

    Fermi Golden Rule: Conservation of Energy

    A way to write Fermi golden rule is W_{fi} = \sum{\frac{d P_{fi}}{dt}} = \frac{2 \pi}{\hbar} \sum_{f} |V_{fi}|^2 \delta(\varepsilon_f - \varepsilon_i) where "i" is the initial unperturbed state and "f" is the final state of an ensemble of final states (i sum over them). But because of...
  32. Z

    Fermi LAT Sensitivity: Estimating Spectral Flux in Jy

    I'm trying to figure out the sensitivity of the Fermi LAT, in units of spectral flux---e.g. Jansky, or a limiting magnitude which could easily be converted. I've only found sensitivity in traditional high-energy terms, e.g: 4\times10^{-6} \textrm{ photons/s/cm}^2 for photons above 100 MeV, with...
  33. S

    Solving Fermi Nuclear Model Homework: A & B

    Homework Statement This question is about the Fermi nuclear model (see Das & Ferbel page 56 or http://www.e12.physik.tu-muenchen.de/stud/vorlesungen/fabbietti/WS2007/Lecture3.pdf" ). Let the nucleon mass be m, the number of nucleons be A and the number of protons be Z. Assume a hypothetical...
  34. J

    Fermi and Gamow-Teller beta decays

    Am I right in thinking Fermi type beta decay is helicity suppressed, due to the necessity of having a right handed electron? This was implied but not explicitly stated in my lectures. And is this why Gamow-Teller type beta decay is the generally favoured mode?
  35. J

    About the energy bands, fermi levels in PN junctions?

    I'm having a bit of trouble understanding what's going on with the energy diagram of a PN junction. For your normal undoped semiconductor at zero bias, if you're plotting the energy as a function of distance along the material then you've just got the two horizontal lines where the upper one...
  36. K

    Fermi Electron Gas in 2D Crystal Planes

    Homework Statement Imagine non-interacting electrons confined to a two-dimensional plane between atomic layers within a crystal. Discuss the properties of the resulting fermi electron gas. Homework Equations None The Attempt at a Solution I don't really have any idea how to go...
  37. F

    Solving Confusion: Ashcroft & Electrochemical/Chemical Potential

    Hello. There is no agreement on the meaning of terms electrochemical potential and chemical potential (see for example http://web.mit.edu/6.730/www/ST04/Lectures/Lecture26.pdf"). While proper definitions would call chemical potential to \mu\equiv\left(\frac{\partial U}{\partial...
  38. T

    Fermi Energy Matching in Semiconductors

    I have taken several courses in semiconductors at the undergraduate level. Both the pure physics part (k vectors) and the more engineering parts (silicon processing, band diagrams) etc. So for all the junctions (Schottky, Ohmic, p-n) - I have never managed to imagine the idea of the Fermi...
  39. R

    Fermi energy (density of electron)

    To find the Fermi energy I need to find the electron density of the material and that I can do by finding the density of atoms in the material in some instances this same density. From what I gather it's not always that way Sometimes you have to multiply a certain number For example...
  40. J

    What is the equation for the bulk modulus of a Fermi gas?

    Homework Statement It is just a line of equation from my Stat Mech textbook, that says B = -V(dp)/(dV) = (10U)/(9V) = (2nEf)/3 where B is the bulk modulus, V is the volume, p is the pressure, U is the energy, n is the number per unit volume and Ef is the fermi energy. Homework...
  41. H

    Equilibrium fermi level and carrier concentration

    Problem statement: Determine electron and hole concentrations in Si at room temperature given that the Fermi level is 0.20eV above the valence band energy. So my thoughts on this problem: First we draw the band diagram, and it's clear that this is P type. Then, p0 = Nv * exp((Ef - Ev)/KT)...
  42. M

    Quick Fermi Energy QuestionFree electrons?

    Quick Fermi Energy Question..Free electrons?? A quick question on the Fermi energy. From a 3D cubic well, one can derive an expression for the Fermi energy of a solid: Ef = h^2/2m . (3.pi^2.N/V)^2/3 Now, I have come across an expression where N/V, electrons per volume, is replaced by...
  43. B

    Fermi Energy of Non-Interacting Identical Li Atoms in a 3D Harmonic Potential Well

    Homework Statement The degeneracy of the nth level above the ground state for a three dimensional harmonic oscillator is (n+1)(n+2)/2 where n takes values n=0,1,2,... A gas of N non-interacting identical lithium atoms (mass 6amu) each having spin1/2 is confined in a 3d harmonic potential...
  44. M

    Find Fermi Level Pos. of Si w/ 6x1015 Donors & 2x1015 Acceptors @ 300K

    Si is doped with 6 x 1015 cm-3 donors and 2 x 1015 cm-3 acceptors. Find the position of the Fermi level with respect to Ei at 300 K. i know the equations are (for n-type) EF = kT ln(ND/ni) + Ei (for p-type) EF = kT ln(ni/NA) + Ei however, since the problem gives me both donors and...
  45. H

    Finding total energy as a function of the Fermi Energy

    Homework Statement "The numerator of this fraction: \overline{E}=\frac{\int \! E N(E)D(E)dE}{\int \! N(E)D(E)dE} (N(E) is the number of particles in an energy state, D(E) is the density of states) is the total (as opposed to the average particle) energy, which we'll call U_{total} here...
  46. S

    Fermi Gas in Pathria | Magnetic Field & Maxwell Boltzman Statistics

    Hi again! another question! I statistical mechnics by Pathria, it has all about the fermi gas in a magnetic field in chapter8 I have another question what if the electron was in some boundaries? what would change then about magnetization of grand partition function? For example for an...
  47. M

    Fermi's Golden Rule: Explained

    For a perturbation that is constant within a given time, we can use Fermi's Golden Rule. In developing Fermi's Golden Rule, 2 approximations are made: (1) The energy interval E (continuum) to which discrete states are scattered is small enough such that the density of states is constant...
  48. T

    Fermi level and Fermi wavevector

    Note: I already asked this question ion the introductory physics forums but have had no replies. The question I'm being asked is: If the Fermi level of copper is 7eV calculate the magnitude of the Fermi wavevector?The formula I'm pretty sure it goes with is Kf=(3pi^2ne)^2/3 The reason I'm...
  49. C

    Fermi estimate of the week: Riemann hypothesis

    For those not familiar with the term Fermi estimate/problem/question see here: http://www.vendian.org/envelope/dir0/fermi_questions.html http://en.wikipedia.org/wiki/Fermi_problem My question: Between the time that Riemann posed his famous question (in 1859) and now, how many hours have...
  50. N

    Integrating over the Fermi sphere

    Homework Statement Hi I have the following integral over wavevectors inside the Fermi circle (we are in 2D) \int {dk_x \int {dk_y \sin ^2 \left( {k_x x} \right)} } Ok, so I know that kx2+ky2=kf2, so ky2=kf2-kx2 - this takes care of ky. But what about kx? What should this run from in order...
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