Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Question
Chapter 38, Problem 70P
To determine
The rms energy of a Fermi distribution and compare it with average and reason for their difference.
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Chapter 38 Solutions
Physics for Scientists and Engineers
Ch. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10P
Ch. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46PCh. 38 - Prob. 47PCh. 38 - Prob. 48PCh. 38 - Prob. 49PCh. 38 - Prob. 50PCh. 38 - Prob. 51PCh. 38 - Prob. 52PCh. 38 - Prob. 53PCh. 38 - Prob. 54PCh. 38 - Prob. 55PCh. 38 - Prob. 56PCh. 38 - Prob. 57PCh. 38 - Prob. 58PCh. 38 - Prob. 59PCh. 38 - Prob. 60PCh. 38 - Prob. 61PCh. 38 - Prob. 62PCh. 38 - Prob. 63PCh. 38 - Prob. 64PCh. 38 - Prob. 65PCh. 38 - Prob. 66PCh. 38 - Prob. 67PCh. 38 - Prob. 68PCh. 38 - Prob. 69PCh. 38 - Prob. 70PCh. 38 - Prob. 71PCh. 38 - Prob. 72PCh. 38 - Prob. 73PCh. 38 - Prob. 74PCh. 38 - Prob. 75PCh. 38 - Prob. 76P
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- Consider 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_forwardPlot the Fermi function Vs. Energy at the temperature of 500 K, when EF = 2 eVarrow_forwardAt T = 300 K, how far above the Fermi energy is a state forwhich the probability of occupation by a conduction electron is 0.10?arrow_forward
- If the temperature of a piece of a metal is increased, does the probability of occupancy 0.1 eV above the Fermi level increase, decrease, or remain the same?arrow_forwardIf the energy gap for an insulating material is 4.5 eV, what is the probability that an electron will be promoted to the conduction band when the temperature is 100 °C? You may assume that the Fermi energy is in the middle of the energy gap.arrow_forwardWhat is the probability that a state 0.0620 eV above the Fermi energy will be occupied at (a) T= 0 K and (b) T =320 K?arrow_forward
- For the free electrons in a solid, what is the value of the E/EF ratio knowing that the occupancy factor of the energy level E is equal to 0.05 at a temperature such that kT=EF/4? (NOTE: EF is the Fermi energy).arrow_forwardConsider the silver in the metallic state with one free electron per atom. Calculate the Fermi energy. Given that density of silver is 10.5 g/cm3 and atomic weight is 108.arrow_forwardConsider a n-type Si crystal at room temperature (300K) doped with 6 x1016 cm-3 arsenic impurity atoms and with certain number of shallowholes. Find out the equilibrium electron concentration, hole concentrationand Fermi level EF with respect to Ei, and the conduction band edge EC.For Si at 300K, the value of ni is 1.45 x 1010 cm-3 and k = 1.38 x 10-23 J/K,1eV = 1.60 x 10-19J. The band gap energy, Eg, of Si is 1.2eV.Solution:n @ Nd = 6 x 1016 cm-3.In equilibrium condition, hole concentration = 3.5 x 103 cm-3.EF – EI = 0.396eVEC – EF = 0.164eV.arrow_forward
- For a gas trapped in a two-dimensional harmonic oscillator, E = hf (nx+ny), sketch the positions of states in the n-plane and draw a couple of curves of constant energy. Calculate U/N at T = 0 and express it as a multiple of the Fermi energy. What is the density of states?arrow_forwardLet f (e) be the Fermi Dirac distribution function and U be the chemical potential. Obtain the expression for derivative of f (e) with respect to e at e=uarrow_forwardAssume that the total volume of a metal sample is the sumof the volume occupied by the metal ions making up the lattice andthe (separate) volume occupied by the conduction electrons. Thedensity and molar mass of sodium (a metal) are 971 kg/m3 and 23.0g/mol, respectively; assume the radius of the Na+ ion is 98.0 pm. (a)What percent of the volume of a sample of metallic sodium is occupiedby its conduction electrons? (b) Carry out the same calculationfor copper, which has density, molar mass, and ionic radius of8960 kg/m3, 63.5 g/mol, and 135 pm, respectively. (c) For which ofthese metals do you think the conduction electrons behave morelike a free-electron gas?arrow_forward
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