WBUT Question Papers EE Physics – II
B Tech 4^{th} Sem 2012
Time Allotted : 3 Hours
The figures in the margin indicate fiill marks.
Candidates are required to give their answers in their own words
as far as practicable.
GROUP – A ( Multiple Choice Type Questions )
 Choose the correct alternatives for any ten of the following :
10 x 1 = 10
i) He^{3} and muon are
a) fermions
b) bosons
c) fermions & bosons respectively
d) bosons & fermions respectively.
ii) The degrees of freedom for a system of N particles with K constraint relations is given by
b) N – 3K
d) 3K – N.
iii) The coordination number for FCC structure is a) 6 b) 8
c) 12 d) 5.
iv) The dielectric constant of a conductor is a) 0 b) 1
c) – 1 d) infinity.
v) FermiDirac distribution approaches MaxwellBoltzmann distribution at
a) low temperature & high density
b) high temperature & low density t
c) low temperature & low density
d) high temperature & high density.
vi) If E j is the energy of the ground state of a onedimensional potential box of length I and E _{2} be the
energy of the ground state when the length of the box is halved, then
a) E _{2} = 2E j b) E_{2} = Ej
c) E_{2} = 4Ej d) E_{2} = 3E j .
%
vii) The reciprocal lattice of a body centered cubic ( bcc ) lattice is
r
a) bcc b) fee
c) sc d) hep.
viii) The wave function of a particle is ¥ = A cos ^{2}x for
71 K
2^{<x<}2




ix) The density of free electron states in a metal varies with energy E as
a) VE b) E^{2}
c) E^{0} d) g.
x) CurieWeiss law is obeyed by
a) paramagnetic materials
b) antiferromagnetic materials
c) ferromagnetic materials above the Curie temperature
d) ferromagnetic materials below the Curie temperature.
xi) The Miller indices of a plane parallel to XY plane is
a) (100) b) (010)
c) ( 001 ) d) ( 110 ) .
xii) If o and k be the electrical and thermal conductivities in a solid, then according to WidemannFranz law.
a) pp = const. b) ~ = const.
c) ^= const. d) okT = const.
( where T is the temperature )
xiii) The product of generalized force ( Q_{i} ) and generalized displacement ( 5 q_{J} ) must have the dimension of
a) force b) work
c) power d) length.
58 3 I Turn over
xiv) The spacing between the nth energy state and next energy state in a onedimensional potential box increases by
a) 2n 1 b) 2n + 1
c) n — 1 d) n + 1.
xv) In an ntype semiconductor, donor level
a) is nearer to conduction band
b) is at the middle between valence and conduction bands
c) is nearer to valence band
d) is not formed at all.
GROUP B ( Short Answer Type Questions )
Answer any three of the following. 3×5= 15
 a) Describe briefly microstate and macrostate with
suitable examples,
b) Show that the average energy of electrons at T = OK is given by  E _{F} ( where E _{F} is the Fermi energy ). 2 + 3
 a) What do you mean by cyclic coordinate ? Explain with
an example.
b) Show that if a given coordinate is cyclic in Lagrangian, it will also be cyclic in Hamiltonian. 2 + 3
 a) Define atomic polarizability. Establish a relation
 between polarization and atomic polarizability.
b) Calculate the induced dipole moment per unit volume of He gas if it is placed in an electric field of 6000 V cm ~ ^{1}. The atomic polarizability of He is 018 x 10 ” ^{40} Fm ^{2} and density of He is 2*6 x 10 ^{25} atoms per m ^{3} , 3 + 2
 a) Derive Curie s law of paramagnetism in the framework
of Langevin’s theory.
b) Are all orientations of the magnetic dipoles possible in quantum theory ? Explain. 4+1
 a) Explain what you mean by degeneracy of an eigenstate
with an example,
b) The eigenvalue equation for the momentum operator is f )(£)»• • Solve the above equation and hence show that for ¥ to be a physically admissible eigenstate, the eigenvalue \ must be real.
 Derive the Braggs law of Xray diffraction from Laue equation and deduce the vector form of Bragg s law of Xray diffraction in reciprocal space.
GROUP C ( Long Answer Type Questions )
Answer any three of the following. 3 x 15 = 45
 a) A free particle of mass m is confined within x = 0 and
i) Write down Schrodinger timeindependent equation for such a system.
ii) Solve the equation to find out the normalized eigenfunctions.
iii) Show that the eigenfunctions corresponding to two different eigenvalues are orthogonal.
b) If P and L be the momentum and angular momentum operators, find the values of [ L_{x} , x ] and [ L_{x} , y ].
c) Find the expectation value of x for the wave function
given by 4* ( x ) = Ae ~^{bx} . 3
 a) The energy wave vector dispersion relation for a one
dimensional crystal of lattice constant a is given by *
E ( k) = E_{q}– a2 p cos ka, where £_{fl} , a, p are
constants.
i) Find the value of k at which the velocity of an electron is a maximum.
ii) Find the difference between the top and the bottom of the energy band.
iii) Obtain the effective mass m* of the electron at the bottom and at the top of the band.
b) What do you mean by density of states ? Show that the density of states of free electrons vary with energy ( E ) as Ve~ .
c) In sodium metals, the free electron density is 25 x 10^{28} m ”^{3}. Calculate the Fermi energy and the dermi tefnperature.
 a) Define Hamiltonian of a dynamical system. When does
 it represent the total energy of the system ? Explain.
b) The Lagrangian of a particle of mass m in one dimension is given by
L = ^ m [ x^{2} – o) ^{2} x ^{2} ) e ^{bt}
Obtain the canonical momentum and equation of motion. Is the Hamiltonian constant of motion ? 3 + 3
c) Deduce D’Alembert s principle from the principle of virtual work. 4
 a) What do you mean by symmetric and antisymmetric
wave function ? How does FermiDirac ( FD ) statistics differ from BoseEinstein ( BE ) statistics ? 2
b) Explain graphically the Fermi distribution at zero and nonzero temperature. 3
c) Derive Planck’s radiation law from BE statistics. State clearly the assumptions made in the theory. 3 + 2
d) Compute the specific heat of a free electron gas using classical statistics. Using FD statistics, argue that the specific heat of electrons should vary linearly with temperature ( T).
 a) What is Larmor frequency ? 2
b) With the help of Weiss molecular field theory of ferromagnetism, derive the CurieWeiss law. 5
c) Draw the BH curve for a ferromagnetic material and
identify the retentivity and the coercive field on the
curve. What is the energy loss per cycle ?
d) Explain the reason behind the negative susceptibility of diamagnetic material. 2
e) Calculate the effective Bohr magneton for Gd ^{+3}. The electronic configuration for Gd ^{ }