Answered: h² (3n2/3 2m 87 E,(0) = (42.23) e…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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(a) State what the Fermi energy depends on according to the free-electron theory of metals and how the Fermi energy depends on that quantity. (b) Show that Equation 42.23 can be expressed as E_F = (3.65 x 10^-19)n_e ^2/3, where E_F is in electron volts when n_e is in electrons per cubic meter. (c) According to Table 42.1, by what factor does the free-electron concentration in copper exceed that in potassium? (d) Which of these metals has the larger Fermi energy? (e) By what factor is the Fermi energy larger? (f) Explain whether this behavior is predicted by Equation 42.23.

TABLE 42.1 Calculated Values of the Fermi Energy for Metals
at 300 K Based on the Free-Electron Theory
Metal
Electron Concentration (m-3)
Fermi Energy (eV)
Li
4.70 X 1028
4.72
Na
2.65 X 1028
3.23
1.40 X 1028
8.46 × 1028
K
2.12
Cu
7.05
Ag
Au
5.85 X 1028
5.48
5.90 X 1028
5.53

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