Ex/MET/T/326/81/2009
BACHELOR OF METALLURGICAL ENGG. EXAMINATION, 2009
(3rd Year, 2nd Semester)
PHYSICS OF METAL
Time : Three hours Full Marks : 100
Answer any five questions.
1. a) State and explain different symmetry elements. 10
b) Explain why five fold rotational symmetry is absent
incrystals. 10
2. a) Explain the interpretation of wave function Y. 4
b) Let Y be the wave function and G be the dynamicalvariable.
Give the expression for the expectation value ofdynamical variable.
State and explain the condition thesystem must satisfy so that the
measurement of the
dynamical variable would yeild definite result. 2+4
c) The wave function of a free particle in a rigid box oflength
L is given by,
n
2Sin
L Lhpc
Y =
Find the average value of momentum. Comment on theresult
obtained. Why zero energy of particle is excluded.Explain.
6+2+2
3. a) Define free electrons. Define Fermi energy. Find the
[ TURN OVER ]
( 2 ) ( 3 )
expression for Fermi energy of free electrons using
periodic boundary condition. 2+2+10
b) Find the average energy of free electrons at T = 0K.6
4. a) Explain why the classically predicted electronic heat
capacity of metal is higher than what is found
experimantally. 6
b) Show that the electronic heat capacity of metal (Cel) is
given by,
Where the symbols have got usual meaning. 14
5. a) Draw and justify the first Brillouis zone for a simple
cubic
solid. Find the number of quantum states in the zone for
the above solid containing N number of atoms. 7+3
b) Derive an effective mass of electron in solids. Effective
mass near the zone boundary is negative. Explain.8+2
6. a) Show that a loop of area A carrying a current I is
equivalent to a magnetic dipole moment, given by,
Where n is unit vector normal to the plane of loop. 10
b) An electron of mass m and charge e rotates in a circle
of redius r. The magnetic dipole moment mm is given
by,
Where Ma
is the angular momentum.
Hence define Bohr magneton. 8+2
7. What is Curie-Weiss law. Differentiate betweenferromagnetic
and paramagnetic Curie temperature.Extend the theory on
paramagnetic spin system toexplain (i) Curie-Weiss law and (ii)
spontaneousmagnetization. 2+2+16
8. a) Explain the motion of electrons in Fermi Sphere underthe
application of electric field. Hence explain thatelectrons lying
near the Fermi energy takes part in the
conduction process. 12
b) Explain the basis and classification of magnetic materials.
8
2e l
F
1 TC N k
2 T= p
nm
m = I A
Mam 2m
m = - l
