Essential University Physics: Volume 2 (3rd Edition)
3rd Edition
ISBN: 9780321976420
Author: Richard Wolfson
Publisher: PEARSON
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Question
Chapter 37, Problem 51P
To determine
The Fermi temperature of silver.
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The 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.
Plot the Fermi function Vs. Energy at the temperature of 500 K, when EF = 2 eV
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.)
Chapter 37 Solutions
Essential University Physics: Volume 2 (3rd Edition)
Ch. 37.1 - Prob. 37.1GICh. 37.2 - If a scientist uses microwave technology to study...Ch. 37.3 - Prob. 37.3GICh. 37 - If you push two atoms together to form a molecule,...Ch. 37 - Prob. 2FTDCh. 37 - Prob. 3FTDCh. 37 - Does it make sense to distinguish individual NaCl...Ch. 37 - Prob. 5FTDCh. 37 - Prob. 6FTDCh. 37 - Radio astronomers have discovered many complex...
Ch. 37 - Prob. 8FTDCh. 37 - Prob. 9FTDCh. 37 - Prob. 10FTDCh. 37 - Prob. 11FTDCh. 37 - Prob. 12FTDCh. 37 - Prob. 13FTDCh. 37 - Prob. 14FTDCh. 37 - Prob. 15FTDCh. 37 - Prob. 16ECh. 37 - Prob. 17ECh. 37 - Prob. 18ECh. 37 - Prob. 19ECh. 37 - Prob. 20ECh. 37 - Prob. 21ECh. 37 - Prob. 22ECh. 37 - Prob. 23ECh. 37 - Prob. 24ECh. 37 - Prob. 25ECh. 37 - Prob. 26ECh. 37 - Prob. 27ECh. 37 - Prob. 28ECh. 37 - Prob. 29PCh. 37 - Prob. 30PCh. 37 - Prob. 31PCh. 37 - Prob. 32PCh. 37 - Prob. 33PCh. 37 - Prob. 34PCh. 37 - Prob. 35PCh. 37 - Prob. 36PCh. 37 - Prob. 37PCh. 37 - Prob. 38PCh. 37 - Prob. 39PCh. 37 - Prob. 40PCh. 37 - Prob. 41PCh. 37 - Prob. 42PCh. 37 - Prob. 43PCh. 37 - Prob. 44PCh. 37 - Prob. 45PCh. 37 - Prob. 46PCh. 37 - Prob. 47PCh. 37 - Prob. 48PCh. 37 - Prob. 49PCh. 37 - Prob. 50PCh. 37 - Prob. 51PCh. 37 - Prob. 52PCh. 37 - Prob. 53PCh. 37 - Prob. 54PCh. 37 - The critical field in a niobium-titanium...Ch. 37 - The transition from the ground state to the first...Ch. 37 - Prob. 57PCh. 37 - Prob. 58PCh. 37 - Youre troubled that Example 37.1 neglects the mass...Ch. 37 - Prob. 60PCh. 37 - The Madelung constant (Section 37.3) is...Ch. 37 - Prob. 62PCh. 37 - (a) Count the number of electron states N(E) with...Ch. 37 - Prob. 64PCh. 37 - Prob. 65PCh. 37 - Prob. 66PCh. 37 - Prob. 67PCh. 37 - Prob. 68PPCh. 37 - Prob. 69PPCh. 37 - Prob. 70PPCh. 37 - Prob. 71PP
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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_forwardQ3/ An experiment was conducted to find the relationship between the specific heat of potassium metal and the temperature, and it was found that this relationship takes the following formula at low temperatures 2.08 +2.57 T2 What is the value of each of: (1) the fermi temperature of potassium? (b) Debye temperature of potassium? Note that specific heat is measured in units of mj / mol / K.arrow_forwardWhat is the Fermi wavevector (kF) and the displacement of the Fermi sphere (delta kF) if a field of E = 1,000 V/cm is applied? The low temperature conductivity is 1x108 (Ω-cm)-1 and the Hall coefficient is -1x10-24 (in CGS units). Assume that the metal exhibits free electron characteristics. fasr in 30 minutesarrow_forward
- An atom’s nucleus is a collection of fermions— protons and neutrons. (a) In calculating the Fermi energy in a nucleus, the protons and neutrons must be considered separately. Why? (b) Find the Fermi energy of (i) the protons and (ii) the neutrons in a uranium nucleus, which has a radius of 7.4 x 10-15 m and contains 92 protons and 146 neutrons.arrow_forwardThe Boltzmann constant is k = 8.617 * 10-5 eV/K. For a metallic solid at room temperature (293 K), what is the probability that an electron state is occupied if its energy is 0.100 eV above the Fermi level?arrow_forwardSilicon atoms with a concentration of 7× 1010 cm3 are added to gallium arsenide GaAs at T = 400 K. Assume that the silicon atoms act as fully ionized dopant atoms and that 15% of the concentration added replaces gallium atoms to free electrons and 85% replaces arsenic to create holes. Use the following parameters for GaAs at T=300 K: N. = 4.7 x 1017cm-3 and N, = 7 × 1018cm-3. The bandgap is E, = 1.42 eV and it is constant over the temperature range. The hole concentration?arrow_forward
- Suppose we have an ideal fermion gas of identical particles in a "box" at T = 0 K. Which of the following statements are true? a. The multiplicity of the gas is =1 b. The multiplicity of the gas is =N! C. If the gas consists of electrons with densities that correspond to the typical densities of conduction electrons in metals, only a part of the electrons can contribute to the heat capacity of the system as the temperature rises. d. If the gas consists of electrons with densities corresponding the typical densities of conduction electrons in metals, all electrons can easily contribute to the heat capacity of the system as the temperature rises.arrow_forwardEach atom of gold (Au) contributes one free electron to the metal. Compute the Fermi energy for gold.arrow_forwardSilicon atoms with a concentration of 7× 1010 cm³ are added to gallium arsenide GaAs at T = 400 K. Assume that the silicon atoms act as fully ionized dopant atoms and that 15% of the concentration added replaces gallium atoms to free electrons and 85% replaces arsenic to create holes. Use the following parameters for GaAs at T = 300 K: N. = 4.7 × 1017 cm-³ and N, =7 × 1018cm-3. The bandgap is E, = 1.42 eV and it is constant over the temperature range. The electron concentration ?arrow_forward
- Silicon atoms with a concentration of 7x 1010 cm3 are added to gallium arsenide GaAs at T = 400 K. Assume that the silicon atoms act as fully ionized dopant atoms and that 15% of the concentration added replaces gallium atoms to free electrons and 85% replaces arsenic to create holes. Use the following parameters for GaAs at T = 300 K: N. = 4.7 x 1017 cm-3 and N, = 7 x 101cm-3. The bandgap is E, = 1.42 eV and it is constant over the temperature range. The donor concentration?arrow_forwardUsing 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.arrow_forwardSilver contains 5.8 * 1028 free electrons per cubic meter. At absolute zero, what is the Fermi energy (in J and eV) of silver?arrow_forward
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