A) Ignored spin degeneracy in the first question.Otherwise it would have been multiplied by 2.
B) I assumed a specific dispersion relation between E and K.Plot is in arbitrary unit.
Hope it helps.
12. a) Using the fact that the allowed values of k in a one-dimensional lattice are given by k- n...
B3 (a) Assume that the T = 0 version of the Fermi-Dirac distribution, namely 1 f (E) exp [E E)/(kBT) +1 in the usual notation, with Ep the Fermi energy, applies for T> 0. Sketch, on the same axes, the distribution for T = 0 and for T> 0, marking the Fermi energy and indicating the thermal energy kBT 5 Marks (b) In the Sommerfeld model (free electron quantum gas), each electron occupies (n/L)3 of k-space volume. Remembering that we...
5.7 Consider the dispersion relation (4.4) for a one-dimensional monatomic lattice of N atoms. Show that the density of normal modes is given by 2N D(0) (02-22
4. A particle moves in a periodic one-dimensional potential, V(x a)-V(x); physically, this may represent the motion of non-interacting electrons in a crys- tal lattice. Let us call n), n - 0, +1, t2, particle located at site n, with (n'In) -Sn,Let H be the system Hamiltonian and U(a) the discrete translation operator: U(a)|n) - [n +1). In the tight- binding approximation, one neglects the overlap of electron states separated by a distance larger than a, so that where is...
4. (a) The energy states of Landau levels are given by where wc is the cyclotron frequency Using this and the 2D density of states given by where m is the carrier effective mass, deduce the degeneracy of a Landau Level Sketch these Landau levels on a graph of number n(E) verses energy (E), and indicate the position of the Fermi Energy for a filling factor of 8 4 (b) Sketch the band diagram for a heterojunction between p-type AlGaAs...
2. Microcanonical ensemble: One-dimensional chain. (24 pts.) Consider a one-dimensional chain consisting of N segments as illus- trated in Figure 1. Let the length of each segment be a when the long dimension of the segment is parallel to the chain and 0 when the long dimension is normal to the chain direction. Each segment has just two non-degenerate states: long dimension parallel to the chain or perpen- dicular to the chain. Now consider a macrostate of the chain in...
a) and b)
(a) The simplest quantum mechanical model for describing electrical conduction in a metal is the free electron gas in three dimensions. The density of states D(E) is given as: V 2m D(E)- 277 An estimate of the average electron energy can be obtained using the following expression: SEN(E)dE (E) - TH(E)DE where n(E)dE is the number of occupied electron states in an energy interval E to E + dE. Use a suitable expression for n(E) and introduce...
When monochromatic light of wavelength 500 nm is shown on a certain metal, el 1. are emitted with energy of 1.20 electron volts. a) How much energy was required to remove the electron from the metal? b What-is-the-de-Broghie wavelength ot the emitied oleetrons? het Flesti Soo 2. An electron is in box of length L, and is not allowed outside the box, so y 0 exc 0sxs L. The wavefunction for the electron is found to be Ψ(x)-Asin(kx). a) Use...
need help with I-K
I. The de Broglie wavelength for a baseball (100 g) traveling at 40 m/s is (a) 1.6x103 m (b) 3.3x10-34 m (c) 1.6x1024 nm (b) 3.3x1024 m Questions J and K refer to butadiene, C4Hs (4 carbon with 2 double bonds), a t electron system that can be studied using the particle-in-a-box model, and the allowed energies are given by n-4 n 3 n 1,2,3 En- n- 1 where L is the length of the box...
Q.3(a) Transfer function model of a plant is, G(s) The controller is Ge(s)-K, where K is a constant. Find the value of K such that steady-state error for unit ramp input is 0.1. Find the gain margin and the phase mar gin (6 marks) (b) What are the effects on gain margin, phase margin and steady-state error, if the gain K is increased? (3 marks (c) Can the closed loop be unstable if the controller of Q.3(a) is implemented digi...
Please Write the answer very clear By using PC.
2. How far below (or above) the Fermi energy can states be found which are 90% occupied by electrons at 300 K? Repeat this calculation for 99%, 10% and 1% Consider what would happen if instead of using periodic boundary conditions, the following the boundary conditions b. 40, y, z, t) 0, (L,y, z,t) 0, ?(z, 0, z, t)-0, y(z, L, z, t) 0, v(x,g, 0, t) 0, are retained for...