PHY/VI/12 Student's Copy
2 0 1 8
6th Semester
PHYSICS
TWELFTH PAPER
Solid-State Physics—II
Revised
Full Marks 55
Time 2½ hours
PART A—OBJECTIVE
Marks 20
The figures in the margin indicate full marks for the questions
SECTION—A
Marks 5
Tick the correct answer in the brackets provided 1×5=5
1. For a solid with diatomic linear chain of atoms, acoustical branch
disappears
if mass of the heavier atom tends to zero
if mass of the lighter atom tends to zero
if mass of the heavier atom tends to infinity
if mass of the lighter atom tends to infinity
2. The permanent magnetic moment in ferromagnetic material arises due to
partially filled electronic shells
completely filled electronic shells
innermost electronic shells
empty electronic shells
/495 1 Contd.
3. The electronic polarizability ae of a monatomic gas atom is
4pe0R 4 0
pe R2
4 0
pe R3 4 0
pe R4
where the symbols have their usual meanings.
4. The energy of the lowest state in a one-dimensional potential box of length
a is
zero 2h2 /ma2
h2 /8ma2
5. A superconducting material when placed in a magnetic field will
attract the magnetic field toward its centre
repel all the magnetic lines of forces passing through it
not influence the magnetic field
reflect all the magnetic lines of forces
SECTION—B
Marks 15
Write short answers of the following questions 3×5=15
1. Determine the phase velocity and group velocity of wave motion along a
one-dimensional monatomic lattice. What happens to the group velocity
when ka ±p
2. How does internal field (Weiss field) arise in ferromagnetic crystals?
3. Write a short note on anomalous dispersion.
4. What is the concept of effective mass of an electron?
5. What is Meissner effect? Deduce that a superconductor is a perfect
diamagnetic.
PART B—DESCRIPTIVE
Marks 35
The figures in the margin indicate full marks for the questions
1. Derive the expressions for phase and group velocity of a wave. What do
they signify physically?
PHY/VI/12 2 Contd.
OR
What is dispersion relation in the vibration of lattice? Give some important
facts about the vibration of a diatomic lattice. What is the difference
between the two branches of the dispersion relation?
2. What is the origin of magnetic moment in an atom? Discuss the origin of
magnetic property in diamagnetic, paramagnetic and ferromagnetic
materials. How does the susceptibility vary with temperature in these three
types of magnetic materials?
OR
Discuss the quantum theory of paramagnetism and hence deduce the
expression for susceptibility. What difference is observed in the result in
comparison to the expression obtained from Classical Langevin theory?

3. What are polar and non-polar dielectrics? Discuss Classical theory of
electronic polarizability.
OR
Derive Clausius-Mossotti equation. 7
4. State and prove Bloch theorem. 7
OR
Explain how an energy gap originates in the energy bands of a solid. Show
from graph that materials can be classified into conductors,
insulators and semiconductors.
5. What is superconductivity? Explain the term critical magnetic field in a
superconductor. How does superconducting energy gap vary with
temperature?
OR
Discuss BCS theory to give an account for zero resistivity at T TC of the
superconductors. 7