The single particle energy eigenstates of a hypothetical system are nondegenerate and have energies given by...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The single particle energy eigenstates of a hypothetical system are nondegenerate and have energies given by a = o: where & = 6.25 x 10-21 eV. The index a runs over the positive integers. The system contains N = 1020 fermions and is at temperature T = 300 K. [20 points] a. Show that the difference between energy levels is small enough so that the total energy can be calculated by integrating the density of energy states over the range of populated energies, and write an expression for D (E). b. Show that the Fermi energy &F = Neo and calculate the Fermi temperature. How does T compare to the Fermi temperature? c. Provide good estimates of the total energy U and the heat capacity, expressing your answers in terms of N, o, k, and T. The single particle energy eigenstates of a hypothetical system are nondegenerate and have energies given by a = o: where & = 6.25 x 10-21 eV. The index a runs over the positive integers. The system contains N = 1020 fermions and is at temperature T = 300 K. [20 points] a. Show that the difference between energy levels is small enough so that the total energy can be calculated by integrating the density of energy states over the range of populated energies, and write an expression for D (E). b. Show that the Fermi energy &F = Neo and calculate the Fermi temperature. How does T compare to the Fermi temperature? c. Provide good estimates of the total energy U and the heat capacity, expressing your answers in terms of N, o, k, and T.
Expert Answer:
Answer rating: 100% (QA)
a To show that the difference between energy levels is small enough to calculate the total energy by integrating the density of energy states we can consider the density of energy states DE The densit... View the full answer
Related Book For
Introduction To Quantum Mechanics
ISBN: 9781107189638
3rd Edition
Authors: David J. Griffiths, Darrell F. Schroeter
Posted Date:
Students also viewed these chemical engineering questions
-
Step 1: Using the reference table below, state which category you are interested in and explain which tool from that categom feel is the best to use in the workplace. Step 2: Describe how the...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Jerome Neeson is a shareholder in Gourmet Chefs Inc., a company that owns and operates a test kitchen in a large metropolitan area. The company is involved in a number of businesses, including...
-
1. In your own words, explain how to subtract like fractions. 2. Mike Cannon jogged 3/8 of a mile from home and then rested. Then he continued jogging farther from home for another 3/8 of a mile...
-
Every differential equation is either separable or linear. Determine whether each of the following statements is true or false, and explain why.
-
Two small, irregularly shaped conducting objects, one carrying charge \(+q\) and one carrying charge \(-q\), are placed on an \(x\) axis at \(x=-4.0 \mathrm{~m}\) and \(x=+4.0 \mathrm{~m}\),...
-
Nature's Own makes three types of wood flooring: Oak, Hickory, and Cherry. The company's tax rate is 40 percent. The following costs are expected for 2011: Per-square-yard expected selling prices are...
-
You are planning a 30-day vacation in Malaysia in one year's time. The present charge for a luxury suite plus meals is RM760.00 per day and the RM is presently trading at RM 3.8000/$. Hence the $...
-
The effects of a tariff on imported kumquats can be divided into the following categories: tariff revenues received by the treasury ($8 million); increased use of resources to produce more kumquats...
-
What are important factors needed to absorb tidal load- a into the grid supply? Draw a load duration curve in support of your answer.
-
Denise and Richard Deleon want to buy a house for $375,000. They can make a down payment of $100,000 from a combination of their RSPs ($25000 each under the Home Buyers program) and wedding gifts...
-
1. Materials purchased on account were $256,500, and wages for factory workers were $110,840. 2. Materials requisitioned and factory labour used by each job were as follows: Job Number A1 A2 A3 A4...
-
(a) Compare 'free cash flow to the firm' and 'free cash flow to equity' as inputs to discounted cash flow models. In your answer, you should (i) (ii) (iii) describe each model (including its inputs);...
-
Section B (40 marks) Attempt all questions. Question 1 (15 marks) The economy of Melvis Pink in the early 1970's, was a simple closed economy rich in oil reserves and not much of anything else. The...
-
How is water engineering related to civil and environmental engineering?
-
2. What coefficients would balance the following equation? _C2H6 +_02_002 +_H20 A 102H6 + 502 - 2002 + 3H20 B. 202H6 + 502 - 4C02 + 6H20 C. 202H6 + 702 4CO2 + 6H20 O D. 202H6 + 1002 - 4CO2 + 6H20 3....
-
Find the APR in each of the following cases: NUMBER OF TIMES COMPOUNDED Semiannually Monthly Weekly Infinite EAR APR 10.4% 8.9 11.6 15.4
-
Coherent states of the harmonic oscillator. Among the stationary states of the harmonic oscillator (Equation 2.68) only n = 0 hits the uncertainty limit ( x p = /2); in general, x p = (2n + 1) /2,...
-
Given the following two matrices: compute: (a) A+B, (b) AB, (c) [A,B] (d) A, (e) A*, (f) A+, (g) det(B) (h) B -1 . Check that BB -1 = 1. Does A have an inverse? A = - 1 2 2i 1 0 3 2 - 2i 2 B 0 0-i 1...
-
Make a plot of E vs. q for the band structure in Section 5.3.2. Use = 1 (in units where m = = a = 1). In Mathematica, ContourPlot will graph E(q) as defined implicitly by Equation 5.71. On other...
-
Why is it important to test a theory? Why not simply accept a theory if it sounds right?
-
What is the intuition behind the geometric growth in interest?
-
You have $100,000 to donate to your college. You want to endow a perpetual scholarship that makes its first payment in 1 year. If the colleges discount rate is 4%, how large will the annual...
Study smarter with the SolutionInn App