BSc Physics SEM V 2016 17 2016-17 Physics Paper II Solid State Physics Question Paper - Mumbai University | munotes

(2 > Hours ) [Total Marks : 75
N.B.(1) All questions are compulsory
(2) Figures to the right indicate full marks
(3) Neat diagrams should be drawn wherever necessary
(4) Use of calculators /log tables is allowed
(5) Symbols have their usual meaning unless otherwise stated
List of Constants:
Charge of an electron e = 1.6021x10-19 Coulomb
Mass of an electron me = 9.109x10-31 kg :
Permeability of free space pio = 10-7 Henry/m
Attempt any ONE: | 10
i) Give the outline of classical theory of metallic conduction and hence
Derive an expression for density of energy states in metals at an
Based on Fermi-Dirac statistics, state the nature of the Fermi
distribution function. State and explain how it will vary with
ii) Compute the average kinetic energy of a gas molecule at
Express the result in eV. if the gas is hydrogen, what is the order of
magnitude of the velocity of the molecules at
Given: Mass of hydrogen atom =1.008 x 1.67 x
Attempt any ONE:
i) Using E-k curve derive an expression for the effective mass of
electron. Explain with relevant graphs the variation in effective mass
of electron with wave vector k
ii) State the salient features of superconductivity. Explain how the
superconducting transition temperature varies with magnetic field
i) Discuss the conclusions of Kronig — Penny model with the scattering
power of potential as : a) P 0 and
il) Calculate the critical current density which can flow through a long
thin superconducting wire of aluminium of diameter 10-3 m. The
critical magnetic field for Aluminium is 7.9 x 10? Amp/m
A Attempt any ONE: 10
What is diamagnetism? Derive an expression for the Larmor
Frequency of precession of angular momentum vector about the
direction of applied field and hence obtain an expression for the
diamagnetic susceptibility for a spherical charge distribution in an
ti) Discuss the quantum theory of Paramagnetism. Derive an expression
for paramagnetic susceptibility at ordinary and normal
Attempt any ONE: 05
i) Write a note on Antiferromagnetism
2 it) The magnetic field strength in silicon is 1000 A/m. If the magnetic
field susceptibility is -0.3 x10-5, calculate the magnetization and flux
density in silicon
Obtain an expression for concentration of electrons in an intrinsic
semiconductor. Assuming the expression for concentration of holes
for an intrinsic semiconductor, prove that its Fermi energy lies exactly
halfway between the top of the band and bottom of the
conduction band for m*h = m*e
ii) ‘Derive an expression for the total current in a p-n junction diode as a
function of an applied voltage
Discuss the temperature dependence of saturation current for Ge and
An electric field of 100V/m is applied to the sample of n-type
semiconductor whose hall coefficient is found to be
Determine the current density in the sample assuming the mobility of
the electron is 0.36m2/Vs
Attempt any ONE: 04
The Fermi temperature of copper is 8.18 x 104 K. Calculate the
Fermi velocity of electrons in copper
The Fermi energy of silver is 5.51 eV. Calculate a) The average
energy of the free electrons of silver at 0 K. b) Speed of the electrons
with this energy
> i) The magnetic field intensity in the tin material is zero at a
temperature of 3.69 K and 2.387 x 10*A/m at zero kelvin. Calculate
the temperature of the superconductor state if the field intensity
it) Consider a two dimensional square lattice of sides 0.25 nm. At what
electron momentum values do the sides of the first Brillouin zone
comes? Calculate the energy of the free electron with this
i) A paramagnetic substance has 1028 The magnetic
moment of each atom is 1.8x10-23 Amp m2.Calculate the
ii) A magnetic material made of steel has a magnetic moment of 2.5
Am? and-a mass of 6.6 x1 kg. If the density of steel is 7.9 x 103
kg/m3, find the magnetization of the material
D Attempt any ONE: 03
‘In an n-type semiconductor, the Fermi level lies 0.4 eV below the
conduction band. If the concentration of donor atoms is doubled, find
the new position of the Fermi level. Assume KT= 0.003 eV
In an intrinsic semiconductor, the effective mass of the electron is
and that of the hole is 0.4 mo where is the rest mass ofthe
electron. Calculate the intrinsic concentration of charge carriers at