Download Part A – Questions and Answers

UINT - I
ACCOUSTICS, ULTRASONICS AND CRYSTAL PHYSICS
PART A – QUESTIONS AND ANSWERS
1. Define reverberation time.
It is defined as the time taken by the intensity of sound to fall to onemillionth (10-6) of its initial intensity after the source of sound is cut off.
2. What are the characteristics of musical sound?
The characteristics of musical sound are
(i)
Pitch or Frequency
(ii)
Quality or Timbre
(iii)
Intensity or Loudness.
3. State Weber- Fechner law.
It states that the loudness of sound (L) is directly proportional to logarithm
of intensity
L  log10 I
L = k log10 I
where k is a constant, which depends on the quality of the sound, the
sensitivity of the ear and other factors.
4. Define absorption coefficient.
Absorption coefficient is defined as the ratio of the sound energy absorbed
by certain area of the surface to that of an open window of same area.
5. What is meant by loudness?
Loudness is the magnitude of sensation produced on the ear and varies
form one person to another person. Loudness is different form intensity of
sound.
6. What is reverberation?
The prolongation or persistence of sound inside a room or hall even after
the source of sound has stopped producing the sound is called
reverberation. This is due to multiple reflections form the walls, ceiling,
floor and other reflecting surfaces of the room.
7. Write Sabine’s for reverberation time.
0.165V
Reverberation time T =
seconds
 as
where V - volume of the hall in m3
a -absorption coefficients of surface areas of different materials
in O.W.U
s - surface areas of the different materials in m2
 as - Total absorption of sound in m2
8. What is meant by echelon effect?
The sound produced in front of regular structures like a set of railings or
staircase or any regular spacing of reflected surfaces may produce a
musical note dye to regular repetition echoes of the original sound to the
listener
This makes original sound to appear confused or unintelligible. Such an
effect is called echelon effect.
9. What are the different types of noises? How can they be controlled?
There are three types of noises
1. Inside noise
2. Airborne noise
3. Structure borne noise
Control of inside noise:
a. The machineries and typewriters may be placed over the sound
absorbing materials or pad.
b. Covering the walls, floors and ceilings with suitable sound
absorbing materials can reduce this type of noise.
Control of airborne noise
a. By allotting proper places for doors and windows.
b. By making perfect arrangement of shutting the doors and
windows.
c. Using heavy glasses in doors, windows and ventilators.
d. By making the hall air-conditioned, this noise maybe eliminated.
Control of structure borne noise
a. Introducing discontinuity in the path of the sound like using rubber
at junctions can control noise from water pipe.
b. Using double walls with an air space between them.
c. Covering the floors and ceilings with suitable sound absorbing
materials and anti vibration mounts.
10. What is pitch?
Pitch is the characteristic of sound, which distinguishes between a shrill
sound and a grave sound. Actually pitch of note is the sensation conveyed
to our brain by the sound waves falling on our ears.
The pitch depends directly on the frequency of the incident sound waves.
11. What is timbre?
Timbre of sound wave is that characteristic which enables us to
distinguish between musical notes emitted by different instruments or
voices even though they have the same pitch and loudness
12. Explain how intensity of sound is measured?
The intensity of a sound wave (I) at a point is defined as the amount of
sound energy (Q) flowing per unit area held normally at the point to the
direction of the propagation of sound wave.
The intensity of the sound wave
I = Q/tA
where Q is the sound energy, t is the time and A is the area of the sound
source normal to the propagation of sound.
Intensity is purely a measurable physical quantity. It is expressed in J
s-1 m-2
The power P = Q/t and
Intensity I = P/A
13. What are the factors affecting the acoustic quality of a building?
The following factors affect the acoustics buildings. They are
Optimum reverberation time
a. Loudness
b. Focusing
c. Echo
d. Echelon effect
e. Resonance
f. Noise
14. What are sound absorbing materials? Give examples.
Materials that absorb sound are called as sound absorbing materials.
Example: Carpets, open, window, hair felt, ordinary chair.
15. What is phon?
Phon is the unit of loudness. The interval of loudness corresponding to
one decibel on the intensity scale is called one phon.
16. What is sone?
Sone is the unit of loudness and it is defined as the loudness of a 1000Hz
tone of 40 dB intensity levels.
Sone is also equal to the loudness of any sound having a loudness level
of 40 phons.
17. What is Ultrasonic?
The sound waves having frequencies above the audible range i.e.,
frequencies above 20,000 Hz or 20 kHz are known as ultrasonic.
18. Distinguish between loudness and intensity of sound.
S. No.
Loudness
1.
It is the amount of
sensation produced in the
ear and hence it depends
upon the listener.
2.
3.
Intensity
It is the amount of sound energy
flowing across unit area per
second. Hence it depends on
the source of sound and dies
not depend upon the listener.
It is not a purely physical 2. It is a pure physical quantity
quantity but it is subjective
in nature
Loudness is measured in Intensity is measured in Wm-2
sones.
19. Mention the properties of ultrasonics.
a. Ultrasonic waves have a high-energy content.
b. Just like ordinary sound waves, ultrasonic waves get reflected,
refracted and absorbed.
c. Ultrasonic waves can be transmitted over ling distances with no
appreciable loss of energy.
d. If an arrangement is made to form stationary waves of ultrasonic
waves in a liquid, it serves as a diffraction grating. It is called an
acoustic grating.
e. Ultrasonic waves produce intense heating effect when passed
though a substance.
20. What are the methods used to generate ultrasonic waves?
In general there are three methods of producing the ultrasonic waves.
a. Mechanical generators
b. Magnetostriction generator or oscillator.
c. Piezo - electric generator or oscillator.
21. Explain magnetostriction effect.
When a ferromagnetic rod like iron or nickel is placed in a magnetic field
parallel to its length, the rod experiences a small change in its length.
This is called magnetostriction effect.
22.What is piezoelectric effect?
When mechanical pressure is applied to one pair of opposite faces of a
quartz crystal, then the other pair of opposite faces develop equal and
opposite electrical charges on the crystal.
23. What is inverse piezoelectric effect?
The piezo electric effect is reversible.
If an electric field is applied to one pair of opposite faces of the quartz crystal,
alternative mechanical expansion of contraction is produced across the other
pair of opposite faces of the crystal.
This known as inverse piezo electric effect or electrostriction.
24. List the various modes of scanning in ultrasound imaging.
The various modes of scanning in ultrasound imaging are
a. A scan
b. B scan
c. TM scan
25. Mention four applications of ultrasonic?
a. Sonar is used in the location of shipwrecks and submarines on the
bottom of the sea.
b. It is used to fish- finding application and the detection of fish shoals.
c. Sonar is useful in all merchant and military ships.
d. It is used for seismic survey.
26. What is acoustical grating?
When ultrasonic waves travel through a transparent liquid, due to
alternating compression and rarefaction, longitudinal stationary waves are
formed.
If monochromatic light is passed though the liquid perpendicular to these
waves, the liquid behaves as a diffraction grating. Such a grating is
known as acoustic grating.
27. What is ultrasonic blood flow meter?
The ultrasonic blood flow meter is used to measure the velocity of blood
flow and it works under the principle of Doppler effect.
28. Define Lattice.
The periodic arrangement of atoms in a crystal.
29. Define miller indices
The set of integers used to describe a crystal plane.
30. Define primitive cell.
The smallest unit cell that can be repeated to form a lattice.
31. Define unit cell.
A small volume of a crystal that can be used to reproduce the entire
crystal.
32. Define space lattice.
A three dimensional representation of atoms.
33. Define atomic radius
Half the distance between two adjacent atoms in a structure.
34. Define coordination number.
Number of nearest atoms surrounding to a particular atom.
35. Define packing density.
Ratio between volume of atoms in a unit cell and the volume of the unit
cell.
36. Define Bravais lattices.
The fourteen possible way of arranging points in space lattice such that all
lattice points have exactly the same surroundings. These fourteen lattices
are called the Bravais lattices.
37. Define lattice planes.
Sets of parallel and equally spaced planes in a space lattice formed with
respect to the lattice points are called lattice planes.
38. Define lattice parameters.
The inter axial lengths a, b and c of a unit cell and the interfacial angles ,
 and  along three axes are called the lattice parameters.
PART B – QUESTIONS
1. State and explain Sabine’s formula for reverberation time of a hall. Derive
Sabine’s formula for reverberation time.
2. Derive an expression for the rate of growth of the intensity of sound in an
auditorium when a sound source is switched on. Obtain an expression for
the decay of sound when it is switched off. Hence arrive at a formula for
the reverberation time of the auditorium.
3. Explain piezoelectric effect. Draw the circuit diagram of a piezoelectric
oscillator and explain the production of ultrasonic waves using it. Explain
the application of ultrasonics in SONAR.
4. Explain the factors affecting the architectural acoustics of a building and
their remedy.
5. Draw the circuit diagram of a magnetostriction oscillator and explain the
construction, working and production of ultrasonic waves using it.
6. Explain with necessary block diagram the principle and working of
different ultrasound scanning methods.
7. Describe the structure of the crystal. Deduce the c/a ratio and hence the
packing factor of a hcp crystal.
8. Based on the lattice parameters, classify the different Bravais lattices of
standard crystal structures.
9. Deduce an expression for the inter planar distance of a cubic lattice in
terms of Miller Indices and lattice constant.
10. Deduce the atomic radii in terms of lattice parameters and hence the
packing factors of sc, bcc and fcc crystals.
11. What are Miller indices? Sketch two successive (110) Planes. Show that
for a cubic lattice the distance between two planes (hkl) is given by
a
h2  k 2  l 2
UNIT II
WAVE OPTICS, LASERS AND FIBRE OPTICS
PART A – QUESTIONS AND ANSWERS
1. What are the applications of Michelson’s interferometer?
It is used to find
a. The wavelength of the given source of light.
b. The refractive index or thickness of a transparent material.
c. The resolution of wavelengths and
d. The standardization of one meter.
2. What is polarization of light?
The light, which has acquired the property of one sidedness, is called
polarization of light.
3. What are the different types of polarized light?
a. Plane
b. Circular and
c. Elliptically polarized light.
4. Define plane of vibration and plane of polarization.
a. The plane in which the vibrations take place (i.e, the plane
containing the direction of vibration and the direction of
propagation) is called the plane of vibration.
b. A plane perpendicular to the plane of vibration is called the
plane of polarization.
5. What are uniaxial and biaxial crystals? Give examples.
In uniaxial crystal there is one direction called the optic axis along
which the two refracted rays travel with the same velocity.
Example: calcite, tourmaline and quartz.
In biaxial crystals there are two optic axes
Example: topaz and aragonite.
6. Light waves can be polarized but sound waves cannot be polarized.
Why?
Light waves can be polarized because they are transverse in nature.
7. What are circularly and elliptically polarized light?
If the vibration of the light are along a circle or an ellipse lying in a
plane perpendicular to the direction of polarization, the light is said to
be circularly or elliptically polarized light.
8. What is plane-polarized light?
When the vibrations of the light are confined along a single direction
perpendicular to the direction of propagation, the light is known as
plane polarized light.
9. What is meant by double refraction?
The phenomenon of producing two refracted rays by a crystal is called
double refraction. It is also called birefringence.
10. What is a nicol prism?
It is an optical device made from a calcite crystal for producing and
analyzing plane polarized light.
11. What is a quarter wave plate?
A double refracting crystal plate having a thickness so as to produce a
path difference of /4 or a phase difference of /2, between the
ordinary and extraordinary rays is called a quarter wave plate.
12. What is a half wave plate?
A double refracting crystal plate having a thickness such as to produce
a path difference of /2 between the ordinary and extraordinary rays is
called a half wave plate.
13. What are uses of a half wave plate?
If plane polarized light is passed thorough a half wave plate, the
emergent light is also plane polarized but its direction of vibration is
inclined at angle 2 to that of the incident light, where  is the angle
between the incident vibration and the principal section of the plate.
Hence such a plate is used in polarimeters as half shade devices to
divide the field of view into two halves presented side by side.
14. What are uses of quarter wave plate?
The quarter wave plate is used for producing circularly and elliptically
polarized lights. In conjunction with a nicol prism, it is used for
analyzing all kinds of polarized light.
15. What is photo elastic effect?
When a transparent medium such as plastic or glass is mechanically
stressed, it exhibits temporary double refraction. This optical
phenomenon is known as the photo elastic effect.
16. Explain stress optic law.
The changes in the indices of refraction of a material when subjected
to stress are linearly proportional to the stresses.
1 - 0= c11 + c22
2 - 0 = c12 + c21
where 1, 2 are principle refractive indices of the material in the
stressed state associated with principal stresses 1and2
17. What are isoclinic fringes?
Isoclinic are loci points where one of the principle stress direction
coincides with the axis of the polarizer.
18. What are isochromatic fringes?
Isochromatic are the interference fringes each of which is the locus of
points of equal stress difference.
19. What are the essential parts of a photoelastic bench?
a. Polariscope
b. Compensator
c. Loading frame
d. Camera
e. Monochromatic lamp
20. Explain the principle used in photo elastic bench.
The photo elastic bench is based on the principle of photo elasticity.
When the transparent medium is strained, it becomes double refracting
and the medium is examined between crossed nicol prisms using
monochromatic light, interference fringes will be seen. This is made
use of for the testing and measurement of strains and stresses.
21. What is a polariser? Give examples.
The crystal, which produces polarized light, is called polariser.
Example: tourmaline crystal.
22. What is an analyzer? Give examples.
The crystal, which is used to analyses polarized light, is called an
analyzer.
Example: tourmaline crystal.
23. Explain the basic principle of fibre optic communication.
When light travels from a denser to a rarer medium, at a particular
angle of incidence called critical angle, the ray emerges along the
surface of separation. When the angle of incidence exceeds the critical
angle, the incident ray is reflected in the same medium and this
phenomenon is called total internal reflection.
24. What are the conditions to be satisfied for total internal reflection?
a. Light should travel from denser medium to rarer medium.
b. The angle of incidence () on core should be greater than the
critical angle (c).
i.e.  >c
c. The reflective index of the core(n1) should be greater than the
refractive index of the cladding(n2)
n1 >n2
25. Distinguish between step index and graded index fibres.
S. No.
Step index fibre
Graded index fibre
1.
The light rays propagate The light propagation is in
as meridinal rays and the form of skew rays and
pass through fibre axis.
does not cross the fibre
axis.
2.
It follows a zig-zag path of It follows a helical path of
light propagation.
light propagation.
3.
It has a low bandwidth.
4.
Distortion is more in Distortion is very less and
multimode step index is almost zero due to selffocusing effect.
fibre.
It has high bandwidth.
26. Define numerical aperture.
Numerical aperture determines the light gathering ability of the fibre. It
is measure of the amount of light that can be accepted by a fibre.
Numerical aperture can also be defined as the sine of the acceptance
angle (im). If n1 and n2 are the refractive indices of the core and
cladding respectively.
then, numerical aperture= sin im =
n12  n22
27. Define acceptance angle.
Accpetance angle is the maximum angle to the axis at which light may
enter into the fibre so that it can have total internal reflection inside the
fibre.
28. What is meant by fractional index change?
Fractional index change is the ratio of refractive index difference
between the core(n1) and the cladding(n2) to the refractive index of
core.
n  n2
i.e   1
n2
29. How will you classify optical fibres?
Optical fibre are classified into three major categories based on
a. Material
b. Number of modes
c. Refractive index profile.
a. Based on the material it can be classified into
i. Glass fibre
ii. Plastic fibre
b. Based on number of modes they classified as
i. Single mode fibre
ii. Multi mode fibre
c. Based on refractive indeed profile they can be classified as
i. Step index fibre
ii. Graded index fibre.
30. Differentiate between single mode and multimode fibre.
S. No.
1.
2.
Single mode fibre
Multimode fibre
Only one mode can be The fibre in this case
propagated
allows large number of
modes of light to
propagate through it.
It has a smaller core
diameter and difference
in refractive index of core
and cladding is small.
Here, since the core
diameter is large the
core
and
cladding
refractive
index
difference is also large.
31. Mention the applications of optical fibres in the engineering field.
a. It can be used for long distance communication in trunk lines.
b. A large number of telephone signals nearly 15,000 can be
passed through the Optical fibres in particular time without any
interference.
c. It is used in computer networks especially in LAN.
d. It is also used as optical sensors.
32. What are the types of sensors used in the fibre optics?
a. Intrinsic sensors.
b. Extrinsic sensors.
33. What is the characteristic of laser radiation?
Laser beam has
a. Directionality
b. Monochromaticity
c. High intensity and
d. Coherence.
34. What do you mean by coherence in laser light?
A coherent light is a pure sine wave and during its transmission it can
maintain constant phase difference between any two points in spare as
well as in a given time interval at any point along the transmission path.
35. What is meant by laser action? What are the conditions to achieve it?
Laser action means the amplification of light by stimulated emission of
radiation. For laser action there should be population inversion and
stimulated emission should take plane.
36. What is meant by threshold condition for laser oscillation?
There should be a minimum amount of population inversion from which
laser oscillation starts. This is called threshold condition for laser.
37. What is meant by population inversion?
In general the number of atoms in the ground state will be more than that
of a in the excited state. The establishment of a situation in which there
are more number of in the excited state than the ground state called
population inversion.
38. What are the different methods to achieve population inversion?
There are five methods by which the population inversion can be
achieved.
a. Optical pumping
b. Electrical discharge or direct electron oscillation
c. Inelastic atom – atom collision
d. Direct conversion
e. Chemical process
39. What is pumping?
In laser technology the process of creating population inversion in the
atomic stated is known as pumping actions. It is an essential
requirement for producing a laser beam.
40. What is meant by active medium in laser?
A medium in which the population inversion is achieved is called an active
medium.
41. What are the kinds of laser?
Depending on the type of active medium used, lasers are classified into
four types.
a. Solid state lasers
b. Gas lasers
c. Liquid lasers
d. Semiconductor lasers.
42. List any two uses of laser beams in engineering workshops.
a. Using high power lasers, we can weld or melt any material.
b. We can make small hole in the hard materials that cannot be
done by mechanical drilling.
c. Laser in used to test the quality of material.
43. Compare the characteristic of laser with ordinary thermal source of light.
S. No. Ordinary light
1.
Light emitted
monochromatic
2.
3.
4.
is
Laser light
not Light emitted is
monochromatic
highly
Light emitted does not It has high degree of
have high degree of coherence
coherence
Emits light in all direction
Emits light only in one
direction
Light in not intense and Laser light in much intense
bright
and bright
44. What is the use of nitrogen and helium laser?
In CO2 laser the nitrogen helps to increase the population of atoms in the
excited state of carbon dioxide, while helium helps to deport the atoms in
the ground state of CO2 and also helps in cooling the discharge tube.
45. Give some examples of direct and indirect band gap LED material?
Direct band gap LED materials
a. GaAs
b. GaAsP
Indirect band gap LED material
a. GaP doped with nitrogen
b. GaP doped with zinc
46. Define holography
Holography deals with construction of image by means of interference
techniques without using lenses. The amplitude and phase distribution is
recorded in 3D manner so as to get complete information of the object to
be photographed.
47. State some of application of lasers in engineering and industry.
a. Used for welding and cutting.
b. It is used to test the defects such as pores, cracks, flaws, holes,
etc, in the material.
c. High power lasers are useful to blast holes in hard steel and
diamond.
48. How is a LED different from a semiconductor laser?
S. No.
1.
LED
It requires low
density
LASER
current It requires high
density
2.
Power output is less
Power output is high
3.
Less intensity
Intensity in very high
4.
Minority carrier
takes place.
injection Stimulated
place
emission
current
takes
PART B – QUESTIONS
1. Explain the construction and working of Michelson’s interferometer and
hence explain how it is used to find the refractive index of a
transparent layer.
2. With necessary theory an experiment to measure the thickness of a
very thin foil using the principle of interference.
3. Explain the construction, types of fringes and application of
Michelson’s interferometer.
4. Explain with suitable mathematical derivations, the formation of plane,
circularly, and elliptically polarized lights.
5. Explain in detail the production and analysis of plane, circularly and
elliptically polarized lights.
6. Explain photo elasticity and discuss stress optic law. What are isoclinic
and isochromatic fringes?
7. Give the block diagram of a photo elastic bench and describe its
components.
8. Write a note on the arrangements of optical elements in plane and
circular polariscopes.
8. Describe the construction and working of the He-Ne laser and CO2
laser.
-
9. Describe the construction and working of the Nd - YAG laser. What are
its advantages over Ruby laser? Discuss briefly the industrial
applications of lasers.
10. Explain the propagation of light through optical fiber and applications of
optical fiber as wave-guide and sensor. Derive expressions for
acceptance angle and numerical aperture.
11. Give an account of sources, detectors and connectors and multiplexers
used in the optical communication system. What are the advantages of
optical fiber communication over conventional communication system?
12. a) What is meant by mode in an optical fibre? Arrive at an expression
for the numerical aperture.
b) Explain in detail the working of any one optical fibre sensor.
13. Write an essay on the working of fiber optic communication system.
UNIT III
CONDUCTING MATERIALS & QUANTUM PHYSICS
PART A – QUESTIONS & ANSWERS
1. Define electrical conductivity.
The electrical conductivity is defined as the quantity of electricity flowing
per unit area per unit time maintained at unit potential gradient.
ne 2 1 1

 m
m
where n – number of free electrons per unit volume
e – charge of the electron
 - relaxation time
m – mass of an electron
2. Define mobility of electrons.
When an electric field E is applied to metals, the electrons move in a
direction opposite to the field direction with the velocity v then mobility of
an electron is defined as the velocity acquired by the electron per unit
electric field.
v

E
3. Define drift velocity.
Drift velocity is defined as the average velocity acquired by the free
electron in a particular direction, due to the application of the electric field.
e E
vd  c
m
where e - charge of the electron
c – mean collision time
E – electric field applied
m – mass of the electron
4. Distinguish between relaxation time and collision time.
S. No.
1.
2.
Relaxation time
Collision time
Time taken by the free Average time taken by a free
electron to reach its electron
between
two
equilibrium position from its successive collisions.
disturbed position due to
the electric field applied.
 = 10-14 seconds
c =

c
seconds
5. What are the special features of classical free electron theory?
The classical free electron theory visualizes a metal as an array of atoms
(ions) permeated by a gas of free electrons. There is no mutual interaction
among the free electrons or between ions and electrons. The free
electrons can move freely in random directions under the constant
potential provided by the fixed ions of the lattice.
6. What are the failures or drawbacks of classical free electron theory?
a. Experimentally the electronic specific heat is about 0.01R.
b. The ratio between thermal conductivity and electrical conductivity is
not a constant at low temperatures.
c. The theoretical value of paramagnetic susceptibility is greater than
the experimental value.
d. The electrical conductivity of semiconductors, ferromagnetism,
photoelectric effect and black body radiation cannot be explained.
7. State Wiedemann – Franz law. Give the value of Lorentz number and
state whether it holds good for all metals and at all temperatures.
Wiedemann – Franz law states that ‘the ratio between the thermal
conductivity K and the electrical conductivity  is directly proportional to
the absolute temperature T of the metal.
K
T

K
 LT

where L – Lorentz number = 2.44 x 10-8 WK-2 at T = 293 K.
This law holds well for all metals but not at low temperatures.
8. Define mean free path of an electron.
The average distance traveled between two successive collisions is called
mean free path.
  c c
where  - mean free path
c - root mean square velocity of the electron
 c - Collision time
9. What are the main stages of electron theory of solids?
a. Classical free electron theory or the Drude – Lorentz free electron
theory
A macroscopic theory according to which metals contain free
electrons and these free electrons, which are assumed to move in a
constant potential, are responsible for the electrical conduction in
the metal. This theory obeys the laws of classical mechanics.
b. Quantum free electron theory or Sommerfeld Quantum theory
A macroscopic theory according to which the electrons move in a
constant potential and they obey the laws of quantum mechanics.
c. Zone theory or Band theory of solids
According to the band theory of solids, the free electrons move in a
periodic potential provided by the periodicity of the crystal lattice.
Electrical conductivity is explained based on energy bands.
10. Define thermal conductivity.
The amount of heat flowing per unit time through the material having unit
area of cross section and maintaining unit temperature gradient.
dT
Q  K
dx
Q
K 
dT
dx
where K – coefficient of thermal conductivity of the material
Q – heat flux or heat flow density
dT
- temperature gradient
dx
11. What is the band theory of solids?
According to the band theory of solids, the free electrons move in a
periodic potential produced by the positive ion cores. The electrons are
treated as weakly perturbed by the periodic potential.
12. Distinguish between energy state, energy level and energy band.
Energy state – The energy state is described by the wave function and
four quantum numbers n, l, ml and ms.
Energy level – The energy of the electron in a shell or orbit is expressed in
terms of energy level. An energy level may contain one or more energy
states.
Energy band – The band is formed in crystals or solids. The closed
packing of an array of energy levels forms a band.
13. Write the Fermi Dirac distribution function.
The probability F(E) of an electron occupying a given energy level at
absolute temperature is called the Fermi Dirac distribution function.
1
F (E) 
1 e
 E  EF 
kT
where F(E) – Fermi function or Fermi factor or Fermi distribution function
E – energy of the level whose occupancy is being considered
EF – Fermi energy or Fermi level of the system
k – Boltzmann’s constant
T – absolute temperature
14. Define Fermi level and Fermi energy.
Fermi level – The energy level at any finite temperature above 0K in which
the probability of electron occupation is 0.5 or 50%. It is also the level of
maximum energy of the filled states at 0K.
Fermi Energy – The energy of a state at which the probability of electron
occupation is 0.5 at any temperature above 0K. It is the maximum energy
of filled states at 0K.
15. Draw the Fermi distribution curve for 0K and at any temperature TK or
how does the Fermi function vary with temperature?
Case (i)
At T = 0K and for E < EF
Then F(E) = 1
There is 100% chance that the electrons can occupy the energy levels
below the Fermi level.
At T = 0K and for E > EF
Then F(E) = 0
There is 0% chance for the electrons to occupy the energy levels above
the Fermi level.
Case (ii)
At T > 0K and for E = EF
Then F(E) = ½
There is 50% chance that the electrons can occupy the Fermi energy
level.
16. Define density of states. What is its use?
The number of energy states per unit volume in an energy interval is
defined as the density of states.
It is used to calculate the number of charge carriers per unit volume of the
solid.
17. Define band gap, valence band and conduction band.
Band Gap – The energy difference between the minimum energy of the
conduction band and the maximum energy of the valence band.
Valence band – The region of energy levels where the valence electrons
occupy their positions.
Conduction Band – The region of energy levels where the conduction
electrons or free electrons occupy their positions.
18. What is work function?
The minimum amount of external energy imparted to an electron to make
it leave the surface of the metal is known as the work function.
EW = EB – EF = eQ
PART B – QUESTIONS
1. Define density of states and derive an expression for free electrons.
Deduce the Fermi energy at 0K.
2. Obtain the Schroedinger’s wave equation for a particle in the box.
3. Explain Compton effect and derive an expression for the wavelength of
the scattered photon.
4. Derive an expression for the energy levels of a particle enclosed in
one-dimensional potential box of width ‘a’ and infinite height.
5. Derive Richardson – Dushman equation for electronic work function in
metals.
6. Explain relaxation time and mean free path. Derive Wiedemann –
Franz law relating to electrical and thermal conductivity of metals.
7. Obtain an expression for the electrical conductivity of a metal. Write a
note on electrical conductivity at high frequencies.
8. Discuss the essential features of the electron energy band structure of
solids.
9. Derive Schroedinger’s
equations.
time
dependent
and
time
independent
10. How is the electrical conductivity of a metal affected by temperature
and alloying.
11. What are the basic postulates of quantum theory of radiations? Derive
Planck’s law of radiation.
UNIT IV
SEMICONDUCTING AND SUPERCONDUCTING MATERIALS
PART A – QUESTIONS AND ANSWERS
1. What is a semiconductor? Give examples.
A material whose resistivity or conductivity lies in between a conductor
and an insulator is known as a semiconducting material. Resistivity is
of the order of 10-4 to 0.5 ohm metre. Semiconductors have a nearly
conduction band and an almost filled valence band with a very small
energy band gap (= 1eV).
Examples: Germanium (Ge), Silicon (Si), Gallium (Ga), Arsenic (As)
2. State the properties of a semiconductor.
a. Resistivity lies between 10-4 to 0.5 ohm metre.
b. At 0K they behave as insulators.
c. Conductivity of a semiconductor increases due to both
temperature and impurities.
d. Semiconductors have negative temperature coefficient of
resistance.
e. Holes and electrons are charge carriers in semiconductors.
3. Compare elemental and compound semiconductors. (or) What are the
differences between direct and indirect band gap semiconductors?
S. No. Elemental or Indirect band gap Compound or Direct band gap
Semiconductor
Semiconductor
1.
Single element semiconductors. They are made of compounds.
Eg. Ge, Si, etc.
Eg. GaAs, GaP, CdS, etc.
2.
Electron - hole recombination Electron - hole recombination takes
takes place through traps, which place directly with each other.
are present in the band gap.
3.
Heat is produced
recombination.
4.
Lifetime of charge carriers is Lifetime of charge carriers is less
more
due
to
indirect due to direct recombination.
recombination.
5.
Current amplification is more.
6.
Used in the manufacture of Used in the manufacture of LEDs,
diodes and transistors.
Laser diodes, ICs, etc.
due
to Photons
are
recombination.
emitted
during
Current amplification is less.
4. Draw the energy band diagram of a semiconductor.
E
Empty
Conduction Band
Small
Gap Eg
Filled
Band
Energy
Valence
5. What is an extrinsic semiconductor?
A semiconducting material in which the charge carriers originate from
impurity atoms, added to the material is known as an extrinsic
semiconductor or impure semiconductor. This semiconductor is
obtained by doping a tetravalent semiconductor with a trivalent or a
pentavalent impurity.
Examples: Ge or Si doped with As, Sb, P, Al, B, etc.
6. What is an intrinsic semiconductor?
A semiconductor in an extremely pure form (without the addition of
impurities) is known as an intrinsic semiconductor. Electrical
conductivity is entirely due to thermal excitation.
Examples: Ge and Si.
7. Distinguish between intrinsic and extrinsic semiconductors.
S. No. Intrinsic Semiconductor
Extrinsic Semiconductor
1.
Pure semiconductors are called Semiconductors
doped
with
intrinsic semiconductors.
impurity
are
called
extrinsic
semiconductors.
2.
Charge carriers are produced Charge carriers are produced due
due to thermal agitation.
to impurities as well as thermal
agitation.
3.
They
have
conductivity.
low
electrical They
have
conductivity.
high
electrical
4.
They
have
temperature.
low
operating They
have
temperature.
high
operating
5.
At 0K, Fermi level lies exactly At 0K, Fermi level lies closer to
between conduction and valence conduction band in the n type
bands.
semiconductor and closer to the
valence band in the p type
semiconductor.
Examples: Ge and Si.
Examples: Ge or Si doped with As,
Sb, P, Al, B, etc.
8. Compare n type and p type semiconductors.
S. No. n - type Semiconductor
1.
n – type semiconductor is
obtained by doping an intrinsic
semiconductor with pentavalent
impurity.
p - type Semiconductor
p – type semiconductor is obtained
by
doping
an
intrinsic
semiconductor
with
trivalent
impurity.
2.
Electrons are majority carriers Holes are majority carriers and
and holes are minority carriers.
electrons are minority carriers.
3.
Donor energy levels lie close to Acceptor energy levels lie close to
the conduction band.
the valence band.
4.
When temperature is increased
these semiconductors can easily
donate an electron from the
donor energy level to the
conduction band.
When temperature is increased
these semiconductors can easily
accept an electron from the valence
band to the acceptor energy level
9. Write the expression for the concentration of holes in the valence band
and the concentration of electrons in the conduction band of an
intrinsic semiconductor.
Expression for the concentration of holes in the valence band of an
intrinsic semiconductor
3
 2mh * kT  2  EV  EF kT
p  2
 e
2
h


Expression for the concentration of electrons in the conduction band
of an intrinsic semiconductor
3
 2me * kT  2  EF  EC kT
n  2
 e
2
h


10. What is meant by Hall effect, Hall voltage and Hall coefficient?
Hall Effect – When a current carrying conductor is placed in a
transverse magnetic field, an electric field is produced inside the
conductor in a direction normal to both the current and the magnetic
field.
Hall Voltage – the generated voltage is the Hall voltage.
Hall Coefficient – Hall field per unit current density per unit magnetic
induction is called Hall coefficient.
11.
PART B – QUESTIONS
1. Discuss the following properties of superconductors
a. Meissner effect
b. Isotope effect
c. Quantum interference leading to SQUID
2. Derive expressions for electron and hole concentrations for an intrinsic
semiconductor.
3. Discuss the theory of Hall effect and explain an experimental
procedure for the study of it.
4. Derive the relation for carrier concentration in n-type semiconductor.
Explain the generation and diffusion of charge carriers in
semiconductors.
5. Explain the BCS theory of superconducting materials. Distinguish
between Type I and Type II superconductors. Describe high T C
superconductors.
6. Discuss the properties and applications of superconductors.
7. Discuss the variation of Fermi level with carrier concentration and
temperature in n-type semiconductor.
8. Derive an expression for the density of holes in the valence band and
also explain how does the Fermi level vary with the concentration of
impurities in the p-type semiconductor.
9. Discuss carrier concentration, the variation of Fermi level with
temperature in the case of p-type and n-type semiconductors for high
and low doping levels.
10. Show that for a p-type semiconductor the Hall coefficient RH is given by
1
. Discuss the applications of Hall effect.
pe
UNIT V
DIELECTRICS, NEW MATERIALS AND NDT
PART A – QUESTIONS AND ANSWERS
1. Distinguish between radiography and fluoroscopy.
S. No.
1
Radiography
Image is developed
photographic films
Fluoroscopy
on Image is developed on
fluorescent screen.
2
High resolution and high Fair resolution and low
contrast
contrast
3
Immediate image cannot be Immediate image can be
obtained
viewed
through
the
monitor
4
X-ray energy is converted X-ray energy is converted
into chemical energy
into visible light
5
Expensive
Inexpensive
6
Time consumption is high
Time consumption is low
2. What is NDT method?
NDT method is a method of testing the application without impairing or
changing its usefulness for future service. It is used to examine the
material and to detect the flaws present in the material without
damaging it.
3. Give the importance of NDT method
By using NDT testing, the location, dimension flaws and material
structure are determined. Due to the determination of factors in the
earlier stage, we can increase.
a. The quality of the product.
b. Productivity and profits
c. The serviceability
4. Give any four techniques of testing a material by NDT.
a. Liquid penetrant method
b. Ultrasonic inspection
c. Radiography methods
d. Thermography
5. What is the principle of ultrasonic flaw detector?
Whenever there is a change in medium, the ultrasonic waves will be
reflected. From the intensity of the reflected echoes the flaws are
detached.
PART B – QUESTIONS
1. Discuss the internal or local field theory of dielectrics and deduce the
Claussius – Mossotti equation.
2. What are shape memory alloys? Discuss their properties and
applications.
3. Describe pulse echo and through transmission method to identify the
flaw in a metal. Describe the different stages of liquid penetrant
method.
4. Write a short not on x-ray radiography technique for the determination
of depth of the flaw. Also compare its merits and demerits with that of γ
– ray spectrography.
5. a) Draw the block diagram of an ultrasonic flaw detector and explain
the function of its various components.
b) Explain the tube shift method of finding the depth of flaw in a
material using x-rays.
6. Discuss the principle of radiography in NDT. Hence describe the x-ray
radiographic method of NDT.
7. Explain the theory of dielectric loss mechanism and discuss the
different dielectric breakdown methods.
8. Explain ionic, electronic, space charge and orientational polarizations.
9. What are metallic glasses? How will you prepare metallic glasses by
melt spinning method? Mention any four applications.
10. Discuss any two methods (other than liquid penetrant method) of NDT,
pointing out their limitations.
11. What is the basic principle of radiographic inspection? Explain their
inspection techniques. What are its limitations?
12. Discuss different polarizations mechanisms and explain their frequency
and temperature dependence.
13. Obtain an expression for the frequency dependence of the electronic
polarisability and show that the imaginary part of the polarisability gives
rise to absorption of energy by the system from the field.