Indian Institute of Technology Kharagpur (IIT-K) 2008 M.Sc Physics -2 - Question Paper
DEPARTMENT OF PHYSICS AND METEOROLOGY INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR End Autumn Semester Examination 2008 Number of Students: 140 Date of Examination: //2008
Subject Number: PH20003 Subject: Physics II
Time: 3 hours Full Marks: 50
Instructions: Question A1 is compulsory. Answer NINE other questions of your choice from Group A and Group B or Group C. Use a separate answer script for Group A.
Physical constants and some conversions: me = 9.1x101 kg, h = 1.054x1 O'34 Js, jVa = 6.022xl023 atoms/mole, k% = 1.38x1 O'23 J/K, e = 1.6xl0'19 C, 1 eV = 1.6xl0*19 J, 300 K = 0.0258 eV, s0= 8.85xl0'12 F/m
GROUP A (for all)
(Al)consider the 1D potential well: V > go for x < 0; V - -VQ for 0 < x < b\ V - 0 for x > b. (a) Draw a figure representing this well, (b) Consider a particle of mass m. What should this particles energy E be for it to be bound inside the well, i.e., E should be negative or positive, less or more than V? (c) Show that its bound energy levels are given by a cot {ba) = -/?, where a = 2m(V0-\E\)ih2 and p = 2m\E\/h2
A2. (a) In a Rutherford experiment, an a particle of energy 10 MeV is scattered from a gold nucleus (Z = 79).
Find the distance of closest approach for a head-on collision between these two particles, (b) Let E denote the energy eigenvalues of a ID system and the corresponding energy eigenfunctions. Suppose that the normalized wave
function of the system at t = 0 is given by y/(x,t = 0) = ~=eiaj/{x) + ~e'a2if/2{x) + eiayy/x), where the a, are
o O
constants. Write down the wavefunction \u(x, t) at time t = t0. .
h 3 1
rA3\Plancks radiative energy density spectrum for thermal light isp{co) = 3hak - . (a) Show that in
%7$IC 1
terms of wavelength it becomes p(X) - -5--T,-. (b) For the following data, calculate the radiative power
X 6 H 1
incident per unit area of the Earths atmosphere facing the Sun: T (temperature of the Suns surface) = 5800 K., Rs (Suns average radius) = 6.96xl05 km, Rs.e (mean Sun to Earth distance) = 1.50x10s km, S, (total radiative energy density of a body at temperature T) = (7i2b47*V(15c3/23).
GROUP B (for EC, EE, IE, PH)
Bl. (a) Derive the distribution function for indistinguishable particles governed by the Pauli Exclusion Principle.
(b) Compare the occupation index as a function of energy at different temperatures with those of classical particles and particles having integral spin.
B2. Consider the motion of electrons in a periodic potential in a one-dimensional solid, (a) Plot the energies of the electrons in first three Brillouin zones in both extended and reduced zone schemes, (b) Find out the number of possible wavefunctions in any band for a finite crystal of length L. (c) Plot the velocity of the carriers in the first Brillouin zone.
B3. (a) Calculate the packing fraction of a diamond lattice, (b) The ionization energy of potassium is 4.34 eV and the electron affinity of chlorine is 3.61 eV. What must the separation be between a K+ and Cl* ion if their total energy is to be zero? The Madelung constant for the KC1 structure is 1.748 and the equilibrium distance between ions of opposite sign is 3.14A. Compute the cohesive energy of KC1 crystal.
B4. (a) Show that the Fermi level EF has the property that the probability that an electron state AE above EF is occupied is the same as the probability that a state AE below EF is empty, (b) Show that the density of states for electron in a two dimensional quantum well is independent of energy.
B5. Consider the population of electrons in a bulk metal, (a) What is the available number of states in the energy ranges between 0 and 1 eV? (b) Compare this with the density of states near the Fermi level, by considering a spherical Fermi surface for the metal, showing a resistivity of 2.0 pO-cm with electrons having Fermi velocity 108cm/s and scattering relaxation time 3x1 O'14 s.
B6. (a) How the critical magnetic field strength of a superconductor vary as a function of temperature. Plot the characteristics for a Type-II superconductor, (b) A sample of Copper 0.1 mm thick, 5.0 cm long with resistivity 2pO-cm carries a current of 1.0 amp along the length of the sample. A magnetic field of 2.0 Tesla results in a Hall voltage
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