Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 10, Problem 17P
To determine
The Fermi energy and average energy for nucleons in Zn.
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- To obtain a more clearly defined picture of the FermiDirac distribution, consider a system of 20 FermiDirac particles sharing 94 units of energy. By drawing diagrams like Figure P10.11, show that there are nine different microstates. Using Equation 10.2, calculate and plot the average number of particles in each energy level from 0 to 14E. Locate the Fermi energy at 0 K on your plot from the fact that electrons at 0 K fill all the levels consecutively up to the Fermi energy. (At 0 K the system no longer has 94 units of energy, but has the minimum amount of 90E.) 1 Microstate8 others? One of the nine equally probable microstates for 20 FD particles with a total energy of 94E.arrow_forwardAssume a hydrogen atom is a sphere with diameter 0.100 nm and a hydrogen molecule consists of two such spheres in contact. (a) What fraction of the space in a tank of hydrogen gas at 08C and 1.00 atm is occupied by the hydrogen molecules themselves? (b) What fraction of the space within one hydrogen atom is occupied by its nucleus, of radius 1.20 fmarrow_forwardThe Fermi-Dirac statistic describes the probability of occupation of an energy state E, as a function of temperature and of the parameter Ef, the Fermi energy.a) What is the physical interpretation for the result obtained when E = Ef?b) Under which conditions of temperature and position of the Fermi level, Ef, can the Fermi-Dirac statistic be written as a simple exponential? Justify your answer.arrow_forward
- Consider a free Fermi gas in two dimensions, confined to a squarearea A = L2. Find the Fermi energy (in terms of N and A), and show that the average energy of the particles is €F /2.arrow_forwardIn the canonical ensemble, we control the variables T, p, and N, and the fundamental function is the Gibbs free energy (G). But if we control T, p, and μ, then we will have a different fundamental function, Z (This is the case for cells that often regulate their temperature, pressure, and chemical potentials to maintain equilibrium). Which of the below options should the Z function equal? H - TS - μN H + TS + μN H + TS - μN G + μN F - pV - μN -H + TS + μNarrow_forwardIn a fully degenerate gas, all the particles have energies lower than the Fermi energy. Using the provided equation for the Fermi energy (EF), and assuming a white dwarf star has a temperature T = 107 K and a mass M = 1Msun, evaluate numerically the ratio Eth/EF, where Eth is the characteristic thermal energy of an electron in a gas of temperature T, to prove that the electrons inside a white dwarf are indeed degenerate. (Hint: Estimate the characteristic density (ne) based on the given conditions inside a white dwarf)arrow_forward
- calculate the fermi temperature for element X. where its fermi energy is 4.69 evarrow_forwardWhat is the number of occupied states in the energy range of 0.0300 eV that is centered at a height of 6.10 eV in the valenceband if the sample volume is 5.00 * 10-8 m3, the Fermi level is 5.00 eV, and the temperature is 1500 K?arrow_forwardThe 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.arrow_forward
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