Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Question
Chapter 10, Problem 15P
(a)
To determine
The number of free electrons per unit volume.
(b)
To determine
The valence of aluminium.
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The Fermi energy of aluminum is 11.6 eV; its density and molar mass are 2.70 g/cm3 and 27.0 g/mol, respectively. From these data, determine the number of conduction electrons per atom.
For the free electrons in a solid, what is the value of the E/EF ratio knowing that the occupancy factor of the energy level E is equal to 0.05 at a temperature such that kT=EF/4? (NOTE: EF is the Fermi energy)
a) 3,65b) 4,20c) 0,26d) 1,74e) 0,04
Why is the following situation impossible? A hypothetical metal has the following properties: its Fermi energy is 5.48 eV, its density is 4.90 x 103 kg/m3, its molar mass is 100 g/mol, and it has one free electron per atom.
Chapter 10 Solutions
Modern Physics
Ch. 10 - Prob. 1QCh. 10 - Prob. 2QCh. 10 - Prob. 1PCh. 10 - Prob. 2PCh. 10 - Prob. 3PCh. 10 - Prob. 4PCh. 10 - Prob. 5PCh. 10 - Prob. 6PCh. 10 - Prob. 8PCh. 10 - The light from a heated atomic gas is shifted in...
Ch. 10 - Prob. 10PCh. 10 - To obtain a more clearly defined picture of the...Ch. 10 - Prob. 12PCh. 10 - Prob. 14PCh. 10 - Prob. 15PCh. 10 - Prob. 16PCh. 10 - Prob. 17PCh. 10 - Prob. 18PCh. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 26P
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- Why does the horizontal Line in the graph in Figure 9.12 suddenly stop at the Fermi energy? Figure 9.12 (a) Density of state for a free electron gas; (b) probability that a state is occupied at T = 0 K; (c) density if occupied states at T = 0 k.arrow_forwardTo 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_forwardIf the election number density (N/V) of a metal increases by a factor 8, what happens to the Fermi energy (EF)?arrow_forward
- Gold has an atomic mass of 197 u, a density of 19.3 x 10^3 kg/m^3, a Fermi energy of 5.54 eV, and a resistivity of 2.04 x 10^-8 ohms. Estimate the mean free path in atom spacings between collisions of the free electrons in gold under the assumption that each gold atom contributes one electron to the electron gas.arrow_forwardAt what temperature do 1.30% of the conduction electrons in lithium (a metal) have energies greater than the Fermi energy EF, which is 4.70 eV?arrow_forwardOn which of the following does the interval between adjacent energy levels in the highest occupied band of a metal depend: (a) the material of which the sample is made, (b) the size of the sample, (c) the position of the level in the band, (d) the temperature of the sample, (e) the Fermi energy of the metal?arrow_forward
- For a solid metal having a Fermi energy of 8.500 eV, what is the probability, at room temperature, that a state having an energy of 8.520 eV is occupied by an electron?arrow_forwardCalculate No(E), the density of occupied states, for copper atT = 1000 K for an energy E of (a) 4.00 eV, (b) 6.75 eV, (c) 7.00 eV,(d) 7.25 eV, and (e) 9.00 eV..The Fermi energy for copper is 7.00 eVarrow_forwardA certain material has a molar mass of 20.0 g/mol, a Fermi energy of 5.00 eV, and 2 valence electrons per atom.What is the density (g/cm3)?arrow_forward
- The occupancy probability at a certain energy E1 in the valence band of a metal is 0.60 when the temperature is 300 K. Is E1 above or below the Fermi energy?arrow_forwardSince the Fermi energy level of zinc is EF = 9.47 eV, what is the number of electrons per unit energy per unit volume at this energy level? Since the resistivity of zinc is 5.90 x 10^-8 ohm.m, calculate the average time interval between collisions of electrons.arrow_forwardConsider the silver in the metallic state with one free electron per atom. Calculate the Fermi energy. Given that density of silver is 10.5 g/cm3 and atomic weight is 108.arrow_forward
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