Question

For aluminum (units of eV) at T = 0 K, calculate the Fermi Energy of electrons....

For aluminum (units of eV) at T = 0 K, calculate the Fermi Energy of electrons. Assume that each aluminum atom gives up all of its outer-shell electrons to form the electron gas. b) Find the Fermi velocity of electrons in aluminum. c) How many times larger is the Fermi velocity compared to the velocity of electrons with kinetic energy equal to thermal energy at room temperature?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Silicon at 293 K has an energy gap Eg = 1.20 eV. (a) Calculate the probability...
Silicon at 293 K has an energy gap Eg = 1.20 eV. (a) Calculate the probability that an electron state is occupied at the bottom of the conduction band at a temperature of 293 K, i.e., at an energy 1.20 eV above the top of the valence band. (b) Doping silicon with aluminum adds acceptor levels in the gap, 0.067 eV above the top of the valence band of pure silicon, and changes the effective Fermi energy. See Fig. 41-...
2. Free Electron Gas a. Consider a free electron gas of valence 4s-electrons in potassium (atomic...
2. Free Electron Gas a. Consider a free electron gas of valence 4s-electrons in potassium (atomic mass M=39.1 and density 856 kg/m3). What is the energy (in electron volts, eV) of the highest filled level in the ground state (i.e., the Fermi energy at zero temperature)? b. Calculate the corresponding electron velocities. c. Calculate the density of states at the Fermi energy. How large is the number of electrons in so- called “soft zone” or “Fermi window” of about 4kBT...
The average energy per electron for the 3D electron gas at T=0 is 3*(E fermi) /...
The average energy per electron for the 3D electron gas at T=0 is 3*(E fermi) / 5, where E fermi is the Fermi energy. Now, calculate the average energy per unit volume for electron gas in 1, 2, and 3 dimensions at zero temperature. Your answer should be proportional to the Fermi energy, E fermi, and/or the electron concentration n = N / V (possibly to some power).
Q: (i) Neutron wavelength: Calculate the wavelength of thermal neutrons at (a) room temperature and (b)...
Q: (i) Neutron wavelength: Calculate the wavelength of thermal neutrons at (a) room temperature and (b) cooled to 4 K (liquid He temperature). How do these compare with 400 keV electrons and to typical Brehmmstrahlung radiation from an x-ray tube (ii) Thermal velocities, de Broglie wavelength: A thermal neutron has a kinetic energy of 3/2 kT, where T is room temperature, 300 K. i.e. these neutrons are in thermal equilibrium with their surroundings. (a) Calculate the thermal velocity of such...
A metal has a mass density ρ = 8.95 g/cm3 . Assuming the effective mass of...
A metal has a mass density ρ = 8.95 g/cm3 . Assuming the effective mass of electron in the metal m*=0.5m0. The electron rest mass m0 = 9.11×10-31 kg. The atomic mass is 63.5, Avogadro’s number is 6.022×1023 . The Boltzmann constant kB = 1.38×10-23 J/K = 8.62×10-5 eV/K. The reduced Planck constant ћ = 1.55×10-34 J·s. Calculate the following assuming the periodic boundary condition. (a) the concentration of the conduction electrons (assume that each Copper atom has one electron...
Show that a 3D gas of N free electrons at T = 0 K has kinetic...
Show that a 3D gas of N free electrons at T = 0 K has kinetic energy U0 = (3/5) NEF
A. Consider a hydrogen atom with one electron and quantized energy levels. The lowest energy level...
A. Consider a hydrogen atom with one electron and quantized energy levels. The lowest energy level (n = 1) is the ground state, with energy -13.6 eV. There are four states corresponding to the next lowest energy (n = 2), each with energy-3.4 eV. For the questions below, consider one of these four states, called one of the first excited states. 2. Assume that this hydrogen atom is present in a gas at room temperature (T ~ 300 K, kBT...
A) Given the following heat capacities of materials, which one, assuming equal mass and temperature changes,...
A) Given the following heat capacities of materials, which one, assuming equal mass and temperature changes, would be best able to store the smallest amount of thermal energy? Group of answer choices 100 J/(kg °C) 0.1 J/(kg °C) 1 J/(kg °C) 1000 J/(kg °C) B) Given the following heat capacities of materials, which one, assuming equal mass and temperature changes, would be best able to store the largest amount of thermal energy? k is the metric prefix for 1000 Group...
1. The shorter the wavelength of a photon, the more the photon behaves like a particle....
1. The shorter the wavelength of a photon, the more the photon behaves like a particle. Why? 2. In a H2 molecule there are two protons, and these have spin 1/2 ħ, that is, they are fermions. If we just look at the two protons, would you expect their spins to be parallel or anti parallel in the ground state of the H2 molecule? 3. Is there a type of viscosity that acts on holes in a semiconductor and gives...
Aluminum wires exposed to air form a layer of insulating Al2O3, through which electrons have to...
Aluminum wires exposed to air form a layer of insulating Al2O3, through which electrons have to tunnel to get through an interconnect. A simple model of electrons tunneling through an Al2O3 barrier of thickness L between two Al wires implies the following: for small fixed voltage V, the current I is Ce^(-2KL), where C and K are constants. In other words, the resistance R=V/I increases proportional to e^(2KL). Solving the Schrödinger equation gives K=sqrt(2mU/ 2 ) where m is the...