Prove equation Ef (Fermi energy). The lowest-energy state of N free electrons is therefore obtained by filling
Fantastic news! We've Found the answer you've been seeking!
Question:
Prove equation Ef (Fermi energy).
Transcribed Image Text:
The lowest-energy state of N free electrons is therefore obtained by filling the N states of lowest energy. • Thus all states are filled up to an energy EF, known as The Fermi energy, obtained by integrating the density of states between 0 and E, The result should equal N. Remember that V -(2m)/² E"2 272h 3/2 g(E)= EF EF N = [ g(E)dE = [ V (2m) 3/2 E/2 dE = V (2mE,)1 3/2 3 2n h Solving for Er (Fermi energy); 2/3 h? ( 37²N E = 2m V • The occupied states are inside the Fermi sphere in k-space as shown below; the radius is Fermi wave number kr. 2/3 h ( 3n N EF F EF 2m 2m. From these two equations, Fermi Surface E = EF kF can be found as, 1/3 KF k F V • The surface of the Fermi sphere represents the boundary between occupied & unoccupied k states at T = 0 for the free electron gas. • Typical values may be obtained by using monovalent potassium metal (K) as an example; for potassium, the atomic density & hence the The lowest-energy state of N free electrons is therefore obtained by filling the N states of lowest energy. • Thus all states are filled up to an energy EF, known as The Fermi energy, obtained by integrating the density of states between 0 and E, The result should equal N. Remember that V -(2m)/² E"2 272h 3/2 g(E)= EF EF N = [ g(E)dE = [ V (2m) 3/2 E/2 dE = V (2mE,)1 3/2 3 2n h Solving for Er (Fermi energy); 2/3 h? ( 37²N E = 2m V • The occupied states are inside the Fermi sphere in k-space as shown below; the radius is Fermi wave number kr. 2/3 h ( 3n N EF F EF 2m 2m. From these two equations, Fermi Surface E = EF kF can be found as, 1/3 KF k F V • The surface of the Fermi sphere represents the boundary between occupied & unoccupied k states at T = 0 for the free electron gas. • Typical values may be obtained by using monovalent potassium metal (K) as an example; for potassium, the atomic density & hence the
Expert Answer:
Related Book For
Physics
ISBN: 978-0077339685
2nd edition
Authors: Alan Giambattista, Betty Richardson, Robert Richardson
Posted Date:
Students also viewed these physics questions
-
Doping changes the Fermi energy of a semiconductor. Consider silicon, with a gap of 1.11 eV between the top of the valence band and the bottom of the conduction band. At 300 K the Fermi level of the...
-
Cohesive energy of free electron Fermi gas, we define the dimensionless length r 1 , as r 0 /a H , where r 0 is the radius of a sphere that contains one electron, and a H is the bohr radius h 2 /e 2...
-
Calculate the Fermi energy for (a) Al, (b) K, and (c) Sn using the number densities given in Table27-1. Free-Electron Number Densities and Fermi Energies at T 0 for Selected Elements NIV,...
-
Why would an organization use outplacement strategies before downsizing? Outplacing employees helps former employees develop new skill sets. Outplacement strategies are a means of eliminating problem...
-
A horizontal magnetic field of 1.0 x 10-4T is at an angle of 30o to the direction of the current in a straight, horizontal wire 75 cm long. If the wire carries a current of 15 A, (a) What is the...
-
A magnetic field directed into the page changes with time according to B = (0.030 0t + 2 1.40)T, where t is in seconds. The field has a circular cross section of radius R = 2.50 cm (Fig. P31.32)....
-
In an experiment to determine whether there is a systematic difference between the weights obtained with two different scales, 10 rock specimens were weighed, in grams, on each scale. The following...
-
Clover Dairy Products Corp. buys one input, full-cream milk, and refines it in a churning process. From each gallon of milk Clover produces three cups of butter and nine cups of buttermilk. During...
-
Rooney Co acquired 7 0 % of 1 0 0 , 0 0 0 $ 1 equity share capital of Marek Co , its only subsidiary on 1 January 2 0 X 6 for $ 2 5 2 , 0 0 0 when the retained earnings of Marek was $ 2 5 0 , 0 0 0 ....
-
In receiving terminals of petrochemical plants, some of the liquid natural gas (LNG) storage Tanks are designed to be in ground, to avoid receiving radiation from the sun and also being protected...
-
1. Differentiate Traditional and Behavioral Finance in terms of the advantages and disadvantages they provide. If you are to choose from the two theories which between the two is best fit for a...
-
Your parents' marginal tax rate on interest income is 41.3%. Your parents' marginal tax rate on dividend income is 19.1%. Your parents have a taxable investment account. They opened the account 33...
-
A paint production facility makes batches of white (W), yellow (Y), red (R), and black (B) paints. The facility must be cleaned between successive batches. The cleanup times are given below. You want...
-
Smith-Kline Company maintains inventory records at selling prices as well as at cost. For 2024, the records indicate the following data: ($ in 000s) Cost Retail Beginning inventory $ 90 $ 150...
-
Ne-Jupiter Enterprises anticipates that its dividend at the end of the year will be $2.00 a share. The dividend is expected to grow at a constant rate of 7 percent a year. The risk-free rate is 4...
-
Main Line Restaurant Group (MLRG) is a company that owns and operates a national chain of Italian-themed restaurants. Each of its restaurants is equipped with a series of hoods that ventilate smoke...
-
A 1200 kg car traveling north at 10 m/s is rear-ended by a 2000 kg truck traveling at 28 m/s. What is the total momentum before and after the collision? before collision after collision kg.m/s kg.m/s
-
Refrigerant R-12 at 30C, 0.75 MPa enters a steady flow device and exits at 30C, 100 kPa. Assume the process is isothermal and reversible. Find the change in availability of the refrigerant.
-
A flat conducting sheet of area A has a charge q on each surface. (a) What is the electric field inside the sheet? (b) Use Gauss's law to show that the electric field just outside the sheet is E =...
-
A hollow conducting sphere of radius R carries a negative charge q. (a) Write expressions for the electric field E inside (r < R) and outside (r > R) the sphere. Also indicate the direction of the...
-
The half-life of I-131 is 8.0 days. A sample containing I-131 has an activity of 6.4 108 Bq. How many days later will the sample have an activity of 2.5 106 Bq?
-
While you're waiting for the ribs to cook, you muse about the propane tank of your barbecue. You're curious about the volume of propane versus the actual tank size. Find the liquid propane volume...
-
Derive the following conversion factors: (a) Convert a volume flow rate in cubic inches per minute to cubic millimeters per minute. (b) Convert a volume flow rate in cubic meters per second to...
-
Express the following in \(\mathrm{BG}\) units: (a) \(50 \mathrm{~m}^{2}\) (b) \(250 \mathrm{cc}\) (c) \(100 \mathrm{~kW}\) (d) \(5 \mathrm{~kg} / \mathrm{m}^{2}\)
Study smarter with the SolutionInn App