Find the average energy of an electron in a metal using a quantum mechanics and classical mechanics assuming the temperature be 1000 K and the Fermi energy be 7.5 eV.
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Find the average energy of an electron in a metal using a quantum mechanics and classical mechanics assuming the temperature be 1000 K and the Fermi energy be 7.5 eV. |
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- The Fermi energy of sodium is 3.23 eV. (a) Find the average energy Eav of the electrons at absolute zero. (b) What is the speed of an electron that has energy Eav ? (c) At what Kelvin temperature T is kT equal to EF ? (This is called the Fermi temperature for the metal. It is approximately the temperature at which molecules in a classical ideal gas would have the same kinetic energy as the fastest-moving electron in the metal.)Each atom of gold (Au) contributes one free electron to the metal. Compute the Fermi energy for gold.Using the Fermi function, estimate the temperature at which there is a 1% probability that an electron in a solid will have an energy of 0.5 eV above the Fermi energy.
- At low temperatures, copper has a free-electron concentration n = 8.45 *1028 m-3. Using the free-electron model, find the Fermi energy for solid copper, and find the speed of an electron with a kinetic energy equal to the Fermi energy.The Fermi energy of copper is 7.0 eV. Verify that the corresponding Fermi speed is 1600 km/s.The probability that a state at Ec+kT is occupied by an electron is equal to the probability that a state at Ey-kT is empty. Determine the position of the Fermi energy level as a function of Ec and Ey.
- The Fermi energy level for a particular material at T = 300 K is 5.50 eV. The electrons in this material follow the Fermi-Dirac distribution function. a) Find the probability of an energy level at 5.50 eV being occupied by an electron. b) Repeat part (a) if the temperature is increased to T = 600 K. (Assume that EF is a constant.). c) Calculate the energy level where probability of finding an electron at room temperature is 70%. d) Calculate the temperature at which there is a 7 percent probability that a state 0.4 eV below the Fermi level will be empty of an electron.If the Fermi energy of a metal is E, = 4.6 eV, and the mean free time of an electron is 3*10^-14what is the average free path in the metal?Silver contains 5.8 * 1028 free electrons per cubic meter. At absolute zero, what is the Fermi energy (in J and eV) of silver?
- Compute the Fermi speed for (a) Ca (EF = 4.69 eV) and (b) Be (EF = 14.3 eV).The Fermi energy of copper at 300 K is 7.05 eV. (a) What is the average energy of a conduction electron in copper at 300 K? (b) At what temperature would the average translational energy of a molecule in an ideal gas be equal to the energy calculated in part (a)?The fermi energy is the highest energy of an electron at 0K. At what temperature can we expect a 50% probability that the electron is silver have an energy that is 1% above the fermi energy of 5.5eV?