Fermi Definition and 384 Threads

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. C

    Fermi Estimate with atmospheric pressure

    1. There are many different definitions of the location of the top of the atmosphere – the near edge of outer space. • Until around 1600, it was believed that the Earth’s atmosphere extended throughout space (recall that the Earth was also considered to be the center of the Universe until...
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    Fermi level as a function of temperature

    Hello guys, very short question :), why does Fermi level go down with temperature? is there some physical explanation or discussion for this? apart from mathematics (well, some mathematics would be cool if necessary :)) Find attached some cool curve about this ;) Thanks guys :)
  3. P

    Orthonormal basis in fermi coordinates

    please help in this problem what are these basis and what are there there properties.how i can i put there values to solve my problems. ˆB = ( 1 2  + +)er er + ( 1 2  − +)e e + (× + !)er e + (× − !)e er . (4.13) where eµ are co-frame basis satisfying...
  4. D

    Stirling's approximation in Fermi Statistics derivation

    Hi People. I was looking at the derivation(s) of Fermi-Dirac Statistics by means of the "most probable distribution" (I know the correct way is to use ensembles, but my point is related to this derivation) and it usually employs Lagrange multipliers and Stirling's approximation on the...
  5. J

    Thermodynamics (Enrico Fermi): Thermodynamic vs. Dynamical State

    I'm reading Enrico Fermi's "Thermodynamics" book. In page 3 of his book, he says: It is evident from what we have said that the knowledge of the thermodynamical state alone is by no means sufficient for the determination of the dynamical state. What does he mean by dynamical state...
  6. C

    The Mystery of Anti-Matter at Fermi Lab

    at Fermi lab they create anti-matter or I guess they don’t create it but they synthesize it , where do they keep it so it doesn't react with regular matter and produce light.
  7. J

    What is the Fermi energy of metallic potassium at 0K?

    Homework Statement We must calculate the Fermi energy of metallic potassium at 0K. We have aleady found the number of atoms per m cubed, we are told that each atom contributes one electron to the free electron gas. Homework Equations Fermi energy = ((hbar^2)/2m)(((3Pi^2)N)/V)^3/2 The...
  8. W

    (Solid State) fraction of electrons within kT of fermi level

    Homework Statement Show that the fraction of electrons within kT of the fermi level is equal to 3kT/2Ef, if D(E) = E^1/2. Homework Equations f(E) = 1 / ( exp(E-Ef)/kT + 1 ) fermi distribution N = integral from 0 to inf of D(E)f(E)dE = total no. of electrons The Attempt at a...
  9. P

    Solid State in tight binding approximation, Brillouin zone, Fermi

    Hello, In few days, I have an examination, and I still have some dark zone in my head! If somebody could help me by giving me some advices/answers/way of reflexion/books to consult, it could be very great! Here is my questions: How to determine energy levels and wavefunction of the...
  10. U

    At 0k, why is fermi level halfway in bandgap?

    At 0k, why is fermi level halfway in bandgap?? Fermi Level is defined as the maximum energy an electron posesses at 0k, which appears to be midway in the bandgap. I learned that in the bandgap, there are no available states (i.e. no wavefunctions of electrons) hence, no electrons can possibly...
  11. F

    A question on Fermi free gas model

    When we are calculating the fermi energy, we say that each energy level is 2 fold degenerate and the fermions stack up into higher and higher energy level due to the Pauli Exclusion Principle. My question is: The Pauli Exclusion principle only says that we can't put different fermions into the...
  12. V

    Fermi Energy of 40P 50N Nucleus Sphere

    Homework Statement I am wondering about something: Calculate the Fermi energy for the neutrons confined to a nucleus with 40 protons and 50 neutrons which roughly forms a sphere of radius 4.6 10^(-15) m. Homework Equations the formula of the fermi Energy is EF=...
  13. V

    Calculating Fermi Energy for Neutrons Confined to a Nucleus

    I am wondering about something: Calculate the Fermi energy for the neutrons confined to a nucleus with 40 protons and 50 neutrons which roughly forms a sphere of radius 4.6 10^(-15) m. the formula of the fermi Energy is EF= ((h-bar)^2*(3*pi^2*n)^(2/3))/2m m:mass of electron, n = number...
  14. H

    Fermi Energy in 2D: Find Relation w/ 3D E=h(cut square)k(square)/2m

    relation of fermi energy in 3D is E=h(cut square)k(square)/2m, if i want a relation of fermi energy in 2D,what should i do?
  15. F

    When were Bose-Einstein and Fermi-Dirac statistics first defined?

    Hi everyone I need the historical articles that bose and fermi integrals were defined for the first time. Can anyone help me?
  16. O

    Degenerate Fermi temperature of 2 fermionic gases

    Homework Statement Consider 2 fermionic gases, each made of 10^6 atoms occupying 10^-3 m^3 volume: tritium, the nucleus containing one proton and two neutrons, and potassium, 19 protons and 21 neutrons. Which gas do you have to cool more in order for a Fermi surface to form? Find the ratio...
  17. P

    Fermi wave vector compared to 1st Brilloin zone.

    For a = 5Angstrom and n = 3 calculate kf and compare its magnitude with the dimension of the Brillouin zone, (all in 2D, square lattice). Relevant eqn: kf = (2*pi*n)^1/2 Here is my solution: kf = (2*pi* (3/a^2))^1/2 = ((6*pi)^1/2)/a =8.7x10^9 m^-1 1st BZ = (2*pi/a)*1/2...
  18. C

    Exploring Fermi Velocity and Its Relation to Fermi Energy

    Hi, Is this right: Fermi velocity is the velocity of electron-wave in a conductor. Why is it called Fermi velocity, i.e. what is its relation with Fermi energy, etc.. Thanks a lot. Cheers
  19. C

    Understanding Fermi Sphere: Deriving Fermi Energy

    Hi all, I'm studying on the current transfer at quantum level and I have a point that is not so much clear. While reading the Fermi sphere from the book "Current at the nanoscale", I could not understand the expression: The number of electrons in the conductor, N, is the ratio of the...
  20. N

    Fermi distribution of 3s electrons of sodium

    Homework Statement What fraction of the 3s-electrons of sodium is found within an energy k_b*T below the Fermi level? (Take room temperature at T= 300k) Fermi level for Na is 3.2 eV Homework Equations F(E) = 1 / {exp((E-E_f)/k_b*T) + 1} The Attempt at a Solution From what I can...
  21. MTd2

    Fermi (GLAST) almost kills all Lorentz violating theories.

    http://www.symmetrymagazine.org/breaking/2009/02/19/most-extreme-gamma-ray-blast-also-probes-quantum-gravity/Fermi%20Observations%20of%20High-Energy%20Gamma-Ray%20Emission%20from%20GRB http://www.nasa.gov/mission_pages/GLAST/news/high_grb.html...
  22. B

    Fermi velocity in a non-degenerate semiconductor

    Hi, Ok, so let's say we have a non-degenerate n-type semiconductor such that the Fermi-level/chemical potential is somewhere in the bandgap (probably needs to be low temperature). Typically in a metal you would say that the Fermi velocity is \hbar k_F/m_e. But since the Fermi-energy is below...
  23. C

    Fermi Energy in a 3D Box: What Happens in the 2D Limit?

    Homework Statement (I copy-pasted the question) Consider N non interacting electrons inside a 3D box similar to the one we saw in class, but this time it is not cubical, i.e. Lx = Ly \neq Lz. 1. Calculate the fermi energy as a function of N;Lx;Lz;me... 2. What happens if we take Lz --> 0...
  24. V

    Temperature effect on fermi level

    if fermi level is defined for 0K, then how does it vary in a semiconductor with temperature. also, why will the formation of holes affect the position of fermi level(by introducing acceptors). have i misunderstood something? please clear my doubt.
  25. M

    Fermi level rise up with raisng up the temperature

    Hi, Im just wondering, why the fermi level rise up with raisng up the temperature when donors are present in Extrinsic semiconductor? thanx
  26. B

    What is the SI unit for a Fermi in nuclear physics?

    I've been reading an article that refers to the distance of a fermi. What is this in SI units? A google search isn't proving fruitful. Cheers!
  27. A

    Spin Exchange in Fermi Sea - Evaluating S_x \cdot S_{x+1}

    I've found the simplest hopping Hamiltonian for fermions (diagonal in momentum space) has a so-called Fermi sea ground state. H = -2 t \sum_k \cos(k) f^+_k f_k (t is some parameter in units of energy). How do I evaluate the expected value of the spin exchange operator S_x \cdot...
  28. V

    Question about Spectral Density at the Fermi level

    Hi everybody, I have the following homework assignment: 1. Derive the expression of density of state D(E) in free electron system. D(E) = \frac{m\sqrt{2m}}{{\hbar}^3\pi^2}V\sqrt{E}, (1) where m and V are electron mass and volume of the system, respectively. 2...
  29. N

    What Does It Mean When the Fermi Level is in the Band Gap?

    hello to everyone. It is normally said that in semiconductors the Fermi level is half way between the valence and the conduction band. I have the following question on that: what does it mean that the Fermi level is in the band gap? It should mean that the maximum energy of an electron in the...
  30. I

    What's so special about Cu, Ag, and Au? fermi level? band gap?

    i know this is a simple question, but i have been looking for a while (maybe 15 min) and i cannot find what is so special about Cu, Ag, and Au? i know there is something special about these 3 metals. something that none of the other metals have. i remember it having to do with fermi velocity /...
  31. S

    About Fermi energy and Fermi temperature

    In classical statistical mechanics, temperature of a system is the measure of its average kinetic energy. In quantum statistical mechanics, Fermi energy corresponds to last filled level at absolute zero and corresponding temperature is the Fermi temperature. Is the Fermi temperature also take...
  32. B

    Fermi Dirac- missing something from Ashcroft derivation

    [SOLVED] Fermi Dirac- missing something from Ashcroft derivation Homework Statement Deriving Fermi Dirac function following ashcroft all good up to equation 2.43 but then it does the folowing at 2.44 and I can't see how you reach 2.44. Homework Equations as (2.43) f_{i}^{N}= 1-...
  33. A

    Calculating Fermi Level in Doped Silicon at Room Temperature and 0K

    Homework Statement (a)If a silicon crystal is doped with 10^15 cm−3 phosphorus atoms, find out the electron concentrations and hole concentrations in the silicon at room temperature. Find out the Fermi level. (b)Repeat at temperature = 0K Homework Equations n*p=ni^2...
  34. E

    Why Is the Radius of a Fermi Sphere Given by \( k_F = (3 \pi^2 n)^{1/3} \)?

    [SOLVED] radius of the fermi sphere Homework Statement On page 249 of ISSP, Kittel says that the radius of a free electron Fermi sphere is k_F = \left(3 \pi^2 n \right)^{1/3} where n is the concentration of electrons. I don't know why that is true. EDIT: never mind; they derive that on...
  35. E

    Solving Quasi Fermi Levels: EHP Generation & Conductivity Change

    Can someone please help with this problem. I've been looking at it for a week! I can't figure out what equation to use. A si sample with 10^15/cm^3 donors is uniformly optically excited at room temperature such that 10^19 EHPs (Electron Hole Pairs) are generated per second. Find the...
  36. E

    Solve Quasi Fermi Levels: Separation of Fn-Fp

    Can someone please help with this problem. I've been looking at it for a week! I can figure out what equation to use. A si sample with 10^15/cm^3 donors is uniformly optically excited at room temperature such that 10^19 EHPs (Electron Hole Pairs) are generated per second. Find the...
  37. I

    Chemical Potential in a Degenerate Fermi Gas

    in a Fermi gas, we know that when the temperature is much less than the Fermi energy, it becomes a degenerate gas. does this mean the chemical potential of the system be very large?
  38. R

    Fermi level pinning in doped semiconductors

    I am reading 'Mesoscopic electronics in Solid State Nanostructures', second edition, by Thomas Heinzel. And I find it a bit too difficult from time to time. Especielly on the concept of Fermi level pinning in doped semiconductors. Does anyone know where to find a good explanation for this...
  39. P

    Fermi energy level in terms of Na and Nd the concentration of dopant?

    fermi level?? is there any relation ( equation) that give the fermi energy level in terms of Na and Nd the concentration of dopant??
  40. E

    My thoughts Emergent physics: Fermi point scenario G.E. Volovik

    My thoughts "Emergent physics: Fermi point scenario G.E. Volovik" http://arxiv.org/abs/0801.0724 Emergent physics: Fermi point scenario G.E. Volovik What if Volovik is correct that the true TOE is some sort of Fermi point scenario? 1 string theory is dead, and SM particles are not...
  41. T

    Distribution of electrons below the Fermi energy

    I feel dumb that I can't figure this out. I'm sure its something simple that I'm just not seeing, but its really frustrating. Homework Statement How many electrons (in percent of the total number of electrons per mole) lie KbT (ev) below the Fermi energy? Take Ef=5eV and T=300K...
  42. S

    Fermi levels in p-n junction under voltage

    I understand that for a semiconductor p-n junction under zero voltage, the Fermi level is constant throughout the junction because that is the condition for a system in thermodynamic equilibrium. I also understand that p-n junction under applied voltage (forward or reverse) is not a system in...
  43. T

    Fermi function for Superconductors?

    I don't really understand why the Fermi-Function is often used to describe superconductors. According to the BCS theory Cooper pairs should be Bosons with Spin 0. Wouldn't it make more sense to use the Bose-Einstein-Function? Thanks Tanja
  44. Z

    Further plausible (?) elaboration on Fermi Paradox

    Relating to Fermi Paradox, how far away from Earth might the oxygen signature of our atmosphere be spectographically detectable? The flip side is how far away might an exo-terrestrial planet's atmospheric oxygen signature be detectable? For example,Gliese 581 c,d are larger (5-7x earth)...
  45. J

    How Do Fermi and Bose Statistics Explain Particle Behavior in Quantum Mechanics?

    Suppose we have particles of kind B, that consist of two fermions of kind F. Now the particles B satisfy the Bose statistics. But what precisely does this mean? If we have four F particles, the system is described by a wave function \psi(x_1,x_2,x_3,x_4) Suppose the particles 1 and 2...
  46. L

    Understanding Quasi Fermi Levels & Calculating QFL Equation

    Hello all! My professor talked about the quasi fermi levels in my Photonics class. While he did make a good effort, I still am not able to understand the concept. I do plan on going to him on Tuesday to get a clearer idea. But I was wondering if any of you folks could give a general...
  47. P

    Fermi Question - quantum tunnelling of a person

    Homework Statement The probability of a person quantum mechanically tunnelling through a wall Homework Equations The Attempt at a Solution I'm not too sure how to approach this problem, I calculated the de Broglie wavelength of the person (mass = 60kg, velocity = 30 m/s; These values are...
  48. J

    Fermi statistics in experiments

    In what kind of experiments does the fermi statistics show? What kind of experiments have been carried out to verify that electrons obey fermi statistics? This fermi statistics stuff has been quite theoretical only in texts I have encountered so far.
  49. M

    Calculating Electron-Electron Self Energy in Fermi Liquid Systems

    Ahoy, I'm trying to do a calculation of the electron-electron self energy of a Fermi Liquid, which is supposed to exhibit a dependence on the square of the temperature of the system. I've read through the first six chapters of "Green's Functions for Solid State Physicists" by Doniach and...
  50. P

    Boundary Conditions for Fermi Gas

    Hi I am new to solid state. I just read about fermi gas in a cube. For some reason the author used periodic boundary conditions? Why didn't they choose finite well potential where the height of the well is related to the work function?
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