An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Question
Chapter 7.3, Problem 33P
(a)
To determine
The reason why in the first approximation model, the chemical potential must always lie precisely in the middle of the gap.
(b)
To determine
The expression for the number of
(c)
To determine
The number of conduction electrons in the cubic centimeter of Silicon at room temperature and the comparison between conduction electrons of Silicon and of Copper.
(d)
To determine
The reason why semiconductor conducts electricity better at higher temperature.
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Students have asked these similar questions
.Consider a free electron moving in a pure 2D semiconductor. Assume that m and E are
the mass and energy of electrons, respectively.
(a) Show that the density of states is a constant (not dependent on energy).
(b)Derive the Fermi energy at temperature T=0K.
(c) What is the optical transition selection rule in the electron intersubbands?
Using the appropriate distribution function, f(E) for electrons in metals, show that the
probability of occupation of electrons at Fermi energy. Er for temperatures above 0 K is 0.5. If
the temperature is raised to 100 K, will the probability of occupation at E, increase or remain
the same? Use the distribution function to prove your answer.
Metallic lithium has a bcc crystal structure. Each unit cell is a cube of side length a = 0.35 nm. (a) For a bcc lattice, what is the number of atoms per unit volume? Give your answer in terms of a. (Hint: How many atoms are there per unit cell?) (b) Use the result of part (a) to calculate the zero-temperature Fermi energy EF0 for metallic lithium. Assume there is one free electron per atom.
Chapter 7 Solutions
An Introduction to Thermal Physics
Ch. 7.1 - Prob. 1PCh. 7.1 - Prob. 3PCh. 7.1 - Prob. 4PCh. 7.1 - Show that when a system is in thermal and...Ch. 7.1 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 11PCh. 7.2 - Prob. 12PCh. 7.2 - Prob. 13P
Ch. 7.2 - Prob. 14PCh. 7.2 - Prob. 15PCh. 7.2 - Prob. 16PCh. 7.2 - Prob. 17PCh. 7.2 - Prob. 18PCh. 7.3 - Prob. 19PCh. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - Prob. 22PCh. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 29PCh. 7.3 - Prob. 32PCh. 7.3 - Prob. 33PCh. 7.3 - Prob. 34PCh. 7.4 - Prob. 37PCh. 7.4 - Prob. 38PCh. 7.4 - Prob. 39PCh. 7.4 - Prob. 40PCh. 7.4 - Prob. 41PCh. 7.4 - Prob. 42PCh. 7.4 - Prob. 43PCh. 7.4 - Prob. 44PCh. 7.4 - Prob. 45PCh. 7.4 - Prob. 46PCh. 7.4 - Prob. 47PCh. 7.4 - Prob. 48PCh. 7.4 - Prob. 49PCh. 7.4 - Prob. 50PCh. 7.4 - Prob. 51PCh. 7.4 - Prob. 52PCh. 7.4 - Prob. 53PCh. 7.4 - Prob. 54PCh. 7.4 - Prob. 55PCh. 7.4 - Prob. 56PCh. 7.5 - Prob. 57PCh. 7.5 - Prob. 58PCh. 7.5 - Prob. 59PCh. 7.5 - Prob. 60PCh. 7.5 - The heat capacity of liquid 4He below 0.6 K is...Ch. 7.5 - Prob. 62PCh. 7.5 - Prob. 63PCh. 7.5 - Prob. 64PCh. 7.6 - Prob. 65PCh. 7.6 - Prob. 66PCh. 7.6 - Prob. 67PCh. 7.6 - Prob. 68PCh. 7.6 - If you have a computer system that can do...Ch. 7.6 - Prob. 70PCh. 7.6 - Prob. 71PCh. 7.6 - Prob. 72PCh. 7.6 - Prob. 73PCh. 7.6 - Prob. 75P
Knowledge Booster
Similar questions
- 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_forwardConsider a copper wire that is carrying, say, a few amperes of current. Is the drift speed vd of the conduction electrons that form that current about equal to, much greater than, or much less than the Fermi speed vF for copper (the speed associated with the Fermi energy for copper)?arrow_forward(a) What is the heat capacity Cv of a three-dimensional cubic lattice of atoms at room temperature? Assume each atom to be bound to its equilibrium position by Hooke's law forces. (b) Assuming that a metal can be represented by such a lattice of atoms plus freely moving electrons, compare the specific heat due to the electrons with that due to the lattice, at room temperature. The room temperature is 300 K°arrow_forward
- A typical value for the Fermi energy is 1.00 eV. At 298 K, calculate the energy above the Fermi energy at which the probability has fallen to 0.25; express your answer in eV.arrow_forwardThe Fermi energy for gold is 5.51 eV at T = 293 K. (a) Find the average energy of a conduction electron at that temperature. (b) Compute the temperature at which the average kinetic energy of an ideal gas molecule would equal the average energy you found in (a). (c) Comment on the relative temperatures in (a) and (b).arrow_forwardIf the electrons are distributed in a "quantum-wire" geometry, that is, an ideal- ized one-dimensional space with a given "line" carrier density ne (1/cm), (a) derive a one-dimensional density of states and plot it versus the energy E. (b) Find the relation between ne and the Fermi level at a given temperature T. (c) Repeat (b) for T = 0.arrow_forward
- = 1.663. (a) Show that the c/a ratio for an ideal hexagonal close pack (HPC) structure is (a) Sodium transforms from BCC (lattice constant = 4.23Å) to HCP at about T = 23K. Assuming that the density remains fixed, and the c/a ratio of the HCP stacking is ideal, calculate the lattice parameters (i.e., a and c) of the HCP lattice. J M K Ja N d M K A K c/2arrow_forwardLet's look at a copper crystal, where each copper atom donates one conduction electron to the crystal. a) Use the free electron model to determine the prediction for copper fermi energy EF, fermi temperature TF and degeneration pressure Pdeg (at temperature T = 0 K). b) Further calculate the contribution of the degeneration pressure to the isothermal compression coefficient of copper. B = -V др (SP) T c) Finally, determine the model prediction for the electronic molar specific heat capacity Cy . The empirical form for this is Cy = yT and the experimentally determined value for copper is Y = 0.695 mJ mol-¹ k-². = Compare this numerical value with your resultarrow_forwardFor free electrons in a solid with Fermi energy EF and temperature T, find the energy for which the probability that a state at that energy is occupied is 0.90.arrow_forward
- Consider a one-dimensional chain of alternating singlyionized positive and negative ions. Show that the potential energy associated with one of the ions and its interactions with the rest of this hypothetical crystal is U(r) = -ake(e2)/(r)where the Madelung constant is a = 2 ln 2 and r is the distance between ions. Suggestion: Use the series expansion for ln (1 + x).arrow_forwardASAParrow_forwardConsider a three-dimensional infinite-well modeled as a cube of dimensions L x L x L. The length L is such that the ground state energy of one electron confined to this box is 0.50eV. (a) Write down the four lowest energy states and evaluate their corresponding degeneracy. (b) If 15 (total) electrons are placed in the box, find the Fermi energy of the system. (c) What is the total energy of the 15-electron system? (d) How much energy would be required to lift an electron from Fermi energy of part (b) to the first excited state? Need full detailed answers and explanations to understand the concept.arrow_forward
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