PH-409 (2015)
Tutorial Sheet No. 4
* Problems shall be discussed in tutorial class
65. Calculate the Hall coefficient of Sodium on a free electron model, given that sodium has a bcc structure with lattice constant 4.28 66. In a Hall experiment on Silver, a current of 25 A passes through a long foil which is 0.1 mm thick (in the direction of 𝑩⃗⃗ ) and 3 cm wide. What is the Hall voltage for |𝐵⃗ |= 1.4 T, if the Hall coefficient is -0.84x10-10m3/C. Given the conductivity of Ag = 6.8x107mho/m, estimate the Hall angle and the mobility of electrons. What would be the values of the Hall voltage, Hall angle and the mobility if the width of the foil is doubled? 67.For Cu, the Hall coefficient is R = -0.55x10-10m3/C. If the relaxation time 2.1x10-14s and the conductivity = 6.0x107mho/m, calculate the mobility of the electron and the ratio of the average effective mass of the electron to the electron mass. 68*.In a Hall Effect experiment a hypothetical face centered cubic material is used. In this metal, there is one free electron per atom and all the assumptions of free electron theory are valid. A magnetic field of 2 Tesla is applied along the thin direction (0.1 mm thick), called +z direction. When a current of 20 A is used in +x direction, a Hall voltage of 25 μV is measured in +y direction. From the information given can you calculate the lattice constant of the metal and the Hall angle? Calculate these quantities if possible. If not, state which other information is needed to evaluate these quantities. 69.(a) Using the Fermi Dirac Statistics, find the probability that a state is occupied if its energy is higher than Fby 0.1 kT, 1.0 kT, 2.0 kT and 10.0 kT, where Fis the Fermi Energy. How good is the approximation of neglecting 1 in the denominator for an energy equal to 10 kT.(b) In the Fermi Dirac distribution substitute = F+. Compute for the probability of occupancy equal to 0.25 and 0.75. (c) Show that for a distribution system governed by F.D. distribution, the probability of occupation of a state with energy higher than Fby an amount E is equal to the probability that a state with energy lower than Fby E is unoccupied. 70.Show that the kinetic energy of a three dimensional gas of N free electrons at 0 K is (3/5)NF. 71. Using the data given and any other constants, evaluate the Fermi energy of the alkali metals.
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