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d) Atomic radius (r) The atomic radius is defined as half the distance between neighboring
Unit -1:Crystal Structures,Crystal Defects & Principles of Quantum Mechanics atoms in a crystal of pure element.

Part-A (SAQ-2Marks) 4) What are properties of matter Waves.

I.B.Tech (CSE/EEE/IT & ECE) 1) Define a) Space Lattice b) Basis c) Co-ordination number d) Packing factor e) Miller De-Broglie proposed the concept of matter waves, according to which a material particle of
Indices. called de-
Engineering Physics Syllabus a) Space lattice: is defined as an infinite array of points in three dimensions in which every Broglie wavelength.
point has surroundings identical to that of every other point in the array.
UNIT-I b) Basis: Group of atoms or molecules identical in composition. Co-ordination number =8
1. Crystal Structures: Lattice points, Space lattice, Basis, Bravais lattice, unit cell and lattice parameters, Lattice + basis = crystal structure
Seven Crystal Systems with 14 Bravais lattices , Atomic Radius, Co-ordination Number and Packing c) Co-ordination number: The no of equidistant neighbors that an atom has in the given Nearest neighbor distance =
Factor of SC, BCC, FCC, Miller Indices, Inter planer spacing of Cubic crystal system.
Wavelength is associated with moving particle and independent of charge of the particles.
structure .Greater the co-ordination no, the atoms are said to be closely packed. Greater the mass, velocity of the particle, lesser will be the wavelength. Lattice constant = a=
2. Defects in Crystals: Classification of defects, Point Defects: Vacancies, Substitution, Interstitial, For Simple Cubic: 6, BCC: 8, FCC: 12
Concentration of Vacancies, Frenkel and Schottky Defects, Edge and Screw Dislocations (Qualitative Number of atoms per unit cell = v= 1
d) Packing factor (PF): It is the ratio of volume occupied by the atoms or molecule in unit Part- B (Descriptive- 10marks) 3
3. Principles of Quantum Mechanics: Waves and Particles, de Broglie Hypothesis, Matter Waves, cell to the total volume of the unit cell.
Davisson and Volume of unit cell =V= a3=
Atomic Packing Factor (APF) = 1) Calculate the Packing factor of SC, BCC, FCC (or) Show that FCC is the closest
Independent Wave Equation-Physical Significance of the wave Function-Particle in One Dimensional
Potential Box. For Simple Cubic: 52%, BCC: 68%, FCC: 74% packing of all the three cubic structures. Atomic Packing Factor is = 0.68 = 68%
UNIT II e) Miller Indices: are the reciprocals of intercepts made by the planes on the crystallographic
1. Electron Theory of Metals: axis when reduced to smallest integers. Simple cubic: There are 8 atoms at 8 corners of the cube. The corner atoms touch with each Ex: - Li, Na, K, and Cr.
Relaxation time and Drift velocity, Failures of Classical free electron theory, Quantum free electron other. If we take a corner atom as a reference, this atom is surrounded by 6 equidistant nearest Face centered structure (FCC)
theory, Fermi-Dirac distribution, Fermi energy, Failures of Quantum free electron theory. neighbors.
2. Band Theory of Solids: Electron in a periodic potential, Bloch Theorem, Kronig-Penny 2) Describe seven crystal systems with lattice parameters and Bravais Lattice points. In FCC there are 8 atoms at 8 corners of the unit cell and 6 atoms at 6 faces. Considering the
Model(Qualitative Treatment), origin of Energy Band Formation in Solids, Classification of Materials atoms at the face center as origin, it can be observed that this face is common to 2 unit cells
into Conductors, Semi Conductors & Insulators, Effective mass of an Electron. S:No Name of the Primitives Interfacial angles Bravais Lattice and there are 12 points surrounding it situated at a distance equal to half the face diagonal of
3. Semiconductor Physics: Intrinsic Semiconductors and Carrier Concentration, Extrinsic Semiconductors crystal systems points the unit cell.
and Carrier Concentration, Fermi Level in Intrinsic and Extrinsic Semiconductors, Hall Effect and 1 Cubic a= b= c o
3(P,I,F)
Applications. o
UNIT III 2 Tetragonal 2(P,I)
o
1. Dielectric Properties: Electric Dipole, Dipole Moment, Dielectric Constant, Polarizability, Electric 3 Orthorhombic 4(P,C,I,F)
o
Susceptibility, Displacement Vector, Types of polarization: Electronic, Ionic and Orientation 4 Monoclinic 2(P,C)
o
Polarizations and Calculation of Polarizabilities (Electronic & Ionic) -Internal Fields in Solids, Clausius 5 Triclinic 1(P)
-Mossotti Equation, Piezo-electricity and Ferro- electricity. o Co-ordination number: - (N) = 6:- is defined as number of equidistant nearest neighbors that
6 Trigonal a= b= c 1(P)
2. Magnetic Properties: Magnetic Permeability, Magnetic Field Intensity, Magnetic Field Induction, 7 Hexagonal oand o 1(P) an atom has in the given structure.
Intensity of Magnetization, Magnetic Susceptibility, Origin of Magnetic Moment, Bohr Magnetron, Total number of atoms :- (n) =1:- each corner atom is shared by 8 unit cells, the share of each
Classification of Dia, Para and Ferro Magnetic Materials on the basis of Magnetic Moment, Hysteresis corner atom to a unit cell is 1/8 th of an atom (8×1/8 =1)
Curve on the basis of Domain Theory of Ferro Magnetism, Soft and Hard Magnetic Materials, Ferrites
Nearest neighbor distance (2r):- the distance between centers of two nearest neighbor atoms
and their Applications. 3) Define a) Crystal Structure b) Lattice Parameters c) Unit Cell d) Atomic radius (r).
UNIT IV om.
1. Lasers: Characteristics of Lasers, Spontaneous and Stimulated Emission of Radiation, Meta-stable State, Atomic radius: - (r) = 2r:- is defined as the distance between nearest neighbors in a crystal.
a) Crystal structure: periodic arrangement of atoms or molecules in 3D space. Co- ordination number = N= 12
-Neon Lattice constant: - a =2r
Laser, Semiconductor Diode Laser, Applications of Lasers.
b) Lattice parameters: Number of atoms in unit cell = 8 ×1/8+ 6×1/2=4
parameters which determine the actual size of unit cell. Atomic Packing Factor (APF) =
2. Fiber Optics: Structure and Principle of Optical Fiber, Acceptance Angle, Numerical Aperture, Types
of Optical Fibers (SMSI, MMSI, MMGI), Attenuation in Optical Fibers, Application of Optical Fibers, c) Unit cell: is a minimum volume cell which on repetition gives actual crystal structure. Lattice constant =a=2r =
Optical fiber Communication Link with block diagram.
Volume of the unit cell =V= a3=
UNIT V Volume of all atoms in unit cell = v=
1. Nanotechnology: Origin of Nanotechnology, Nano Scale, Surface to Volume Ratio, Bottom-up Ex:-polonium at room temperature.
Fabrication: Sol-gel Process; Top-down Fabrication: Chemical Vapor Deposition, Physical, Chemical
and Optical properties of Nano materials, Characterization (SEM, EDAX), Applications. Body centered Cubic (BCC): Atomic Packing Factor = %
In a unit cell there are 8 atoms at 8 corners and another 1 atom at the body center. The 8 corner
atoms are shared by 8 unit cells, and as the center atom is entirely within the unit cell, it is not Ex:- Cu, Al, Pb, and Ag.
shared by any surrounding unit cell. By the above values of Atomic packing factors we can say that FCC is the closest packed
structure of all the three cubic structures.

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2) Explain the significance of Miller indices and derive an expression for interplaner Therefore In case of ionic crystals imperfections appear in crystals while maintaining the electrical
distance in terms of Miller indices for a cubic Structure. neutrality. Two types of defects (point defects) occur in ionic crystals.
i.e 1. Frenkel defect 2.Schottky defect.
Miller indices: are the reciprocals of intercepts made by the crystal planes on the
crystallographic axes when reduced to smallest integers. 3) Classify the defects and write a short note on Point defects.
Important features of Miller indices:
Miller indices represent a set of parallel equidistant planes. Defects are broadly classified into
All the parallel equidistant planes have the same Miller indices.
If a plane is parallel to any axis, then the plane intersects that axis at infinity and Miller Screw dislocation:
defects
indices along that direction is zero. Atoms are displaced in two separate planes perpendicular to each other or defects
If the miller indices of the two planes have the same ratio (844,422,211), then the planes forming a spiral around the dislocation line.
are parallel to each other. point line surface volume A screw dislocation marks the boundary between slipped and unslipped parts of the
If a plane cuts an axis on the ve side of the origin, then the corresponding index is crystal that can be produced by cutting the crystal partway and then sheering down one
ve, and is indicated by placing a minus sign above the index. lattice compo screw part relative to the other by atomic spacing horizontally.
Ex: if a plane cuts ve y-axis, then the miller index of the plane is (h l) site edgedis
sitional dis
Derivation: location Frenkel defect: When an ion is displaced from a regular lattice site to an interstitial site is
vacancy/ interstitia location
Consider a crystal in which the three axes are orthogonal and the intercepts are same. called Frenkel defect. Generally cations which are small in size are displaced to an interstitial
schottky l/frankel substituti
Take interstitial site as the interstitial space is small .A Frenkel imperfection does not change the overall
onal
the axis. electrical neutrality of the crystal.
The next plane ABC is to be compared with the reference plane which makes the Point defects: (zero dimensional defects) arises when an atom is absent from the regular Schottky defect: A pair of one cation and one anion missing from the original lattice site on
intercepts on x,y,z axes respectively. position, presence of impurity atom or atom in the wrong place during crystallization. These to the surface of the crystal so that charge neutrality is maintained in the crystal is called
are small defects which extends its influence in all directions but limited to a specific region of Schottky defect.
Let (h k l) be the miller indices.
small order (two or three atomic orders).
Vacancy: missing of an atom from its original lattice site. Generally arises due to thermal 4) Write a short note on line defects. (or) What are edge and screw dislocations?
of separation between adjacent planes. vibrations during crystallization and influenced by external parameters. Vacancies may be
with x,y,z axes respectively. single, two or more depending on crystal type. For most of the crystals, in order to create one Line defects (or) dislocations (one dimensional defect) are defined as the disturbed region
vacancy thermal energy of 1.1 eV is required. between the two perfect parts of the crystal and these defects are formed in the process of 5) .
Interstitial: this defect arises when an atom of same kind or different kind occupies the void deformation.
space between the regular atomic sites. Edge dislocation: It gives the magnitude and direction of dislocation line.
Impurity atom: an atom that does not belong to the parent lattice (original crystal). A perfect crystal is composed of several parallel vertical planes which are extended
Substitution defects: this defect arises when an impurity atom replaces or substitutes parent from top to bottom completely and parallel to side faces. The atoms are in equilibrium
atom. Ex: in brass, zinc is a substitution atom in a copper lattice positions and the bond lengths are in equilibrium value.
Interstitial impurity: this defect arises when an impurity atom which is small in size is placed If one of the vertical planes does not extend from top to bottom face of the crystal, but
between the regular atomic sites. ends in midway within the crystal, then crystal suffers with a dislocation called edge
Ex: when pentavalent and trivalent impurities are added to pure Si or Ge, we get n- type dislocation.
and P-type semiconductors. In imperfect crystal all the atoms above the dislocation plane are squeezed together and
compressed there by the bond length decreases. And all the atoms below the dislocation
plane are elongated by subjecting to the tension and thereby the bond length increases.
There are two types of edge dislocation. They are 1.Positive edge dislocation
2.Negative edge dislocation.
Positive edge dislocation: if the vertical plane starts from top of the crystal and never
According to cosine law of directions, =1
reaches to the bottom.
Therefore Negative edge dislocation: if the vertical plane starts from bottom of the crystal and never
reaches top.

In a cubic crystal a = b = c,
Therefore

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7)
At thermal equilibrium, the free energy is minimum and constant .i.e.
in (7)
)- Taking exponentials on both sides

As n

As 9) Describe De- the De-

Taking exponential on both sides

Thus
De-Broglie Hypothesis Matter waves: An electromagnetic wave behaves like particles,
particles like electrons behave like waves called matter waves, also called de-Broglie matter
waves.
The number of vacancies in a crystal is very small when compared with the number of The wave length of matter waves is derived on the analogy of radiation.
atoms. of radiation, the energy of a photon is given by
Taking exponentials on both sides 1)
Therefore
s vector: Velocity of light, Wavelength of the photon, h= constant
in the According , 2)
clockwise direction. 8)Derive an expression for the energy required to create a Schottky defect.(or) Derive an m= mass of the photon
7)Derive an expression for the energy required to create a Frenkel defect.(or) Derive an expression for the no of Schottky defects created in a crystal a at a given temperature.
coincide, then the region enclosed in the expression for the no of Frenkel defects created in a crystal a at a given temperature. Equating equations (1) and (2),

If the starting point and ending point do not coincide i.e. ppl = b. b is the quantity
p 3), P = momentum of photon
be the number of interstitial atoms,
i Ei be number of vacancies created. The total energy required to create vacancies is
indicating magnitude. and the total energy required is De-Broglie proposed the concept of matter waves, according to which a material
U= nEp
The total number of ways in which Frenkel defects can be formed is given by particle of mass
dislocation plane. called de-Broglie wavelength.
6) Derive an expression for the number of vacancies at any temperature. Or derive an ........ (2)
4) is called de-
expression for the energy formation of vacancy. The increase in entropy (s) due to Frenkel defect is given by
Wavelength is associated with moving particle and independent of charge of the
....... (3) particles.
Let v .
The total energy required for the crea This increase in entropy produces change in Free energy .. (4) Greater the mass, velocity of the particle, lesser will be the wavelength.
given as u=nEv Substitute (1),(3) in (4) De-Broglie wavelength associated with an electron:
is p By applying approximation If
--------------- (2), . then the and the work done is converted into the
Using approximation, kinetic energy of an electron.
, where K= Boltzmann constant.
Free energy (F) of the atoms in the crystal is given by . (4)
. (5). From 1 and 3
There fore
Free energy of the atoms in the crystal is given by 4)
........... (6) , substitute 2 in 5 Substitute (1),(3) in (4) 5) in (4)
By applying approximation, to eqn (6)
6)
zero, we get
Ignoring relativistic corrections, m0= rest mass of electron, 7)

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By substituting the values of h=6.625 , m0= 9.1 and c= charge When electron beam accelerated by 54 V was directed to strike the given nickel crystal, Since a moving atomic particle has to be regarded as a de-Broglie wave group, there is
of electron=1.6 C a sharp max in the electron diffraction occurred at an angle of 50 0 with the incident a limit to measure particle properties. 4)
, Where V= in volt and beam. According to Born probability interpretation, the particle may be found anywhere
The incident beam and the diffracted beam make an angle of 650 with the family of within the wave group moving with group velocity.
Experimental validity: Davison and Germer Experiment: For a moving particle, the\ total energy is
The whole instrument is kept in an evacuated chamber. If the group is considered to be narrow, it is easier to locate its position, but the
The first experimental evidence of the wave nature of atomic particles was proved by Where E= total energy, V= potential energy, U= kinetic energy =
The spacing of planes in Nickel crystal as determined by x-ray diffraction is 0.091nm uncertainty in calculating its velocity and momentum increases.
C.J Davison and L.H Germer in 1927.
If the group is wide, its momentum is estimated easily, but there is great uncertainty 6), substitute (5) in (6)
They were studying scattering of electrons by a metal target and measuring the density
about the exact location of the particle. 7) Substitute (7) in (4)
of electrons scattered in different directions.
Therefore for a 54 V electron beam, the de-Broglie wavelength associated with the
electron is given by = 0.166nm Heisenberg a German scientist in 1927, gave uncertainty principle which states that
The determination of exact position and momentum of a moving particle 8)
This wavelength agrees well with the experimental value. Thus division experiment simultaneously
provides a direct verification of de-Broglie hypothesis of wave nature of moving
particles. dimension.
In general, if x represents the error in measurement of position of particle along x-
axis, and p represents error in measurement of momentum, then In three dimensions, it can be written as
10) Explain the Physical significance of
Or limitation to find the position and momentum of a particle is 9)
The wave function enables all possible information about the particle. is a
complex quantity and has no direct physical meaning. It is only a mathematical tool in
order to represent the variable physical quantities in quantum mechanics. i.e. Heisenberg uncertainty principle states that both the position and momentum
Born suggested that, the value of wave function associated with a moving particle at For a free particle, the P.E is equal to zero i.e V=0 in equation (9)
Cannot be measured simultaneously with perfect accuracy.
the position co-ordinates
the particle at ce 12) Derive an expression for Schrodinger time independent wave equation.
If represents the probability of finding the particle, then it can have two cases.
Case 1: certainty of its Presence: +ve probability 13) Derive an expression for the energy states of a Particle trapped in 1-Dimensional
Schrodinger describes the wave nature of a particle in mathematical form and is potential box:
Case 2: certainty of its absence: - ve probability, but ve probability is meaningless,
Hence the wave function is complex number and is of the form a+ib Consider a plane wave moving along +ve x- direction with velocity The equation
Even though has no physical meaning, the square of its absolute magnitude
gives a definite meaning and is obtained by multiplying the complex number with its of the wave is written in the from
complex conjugate then Where , a= amplitude of wave
particle at a place at a given instant of time. And has real and positive solutions. y=displacement of wave in y- direction
x= displacement along x- axis at any instant of time .
T (1)

then the probability of finding the particle in The wave nature of a moving particle leads to some remarkable consequences when the
From fig, the electron beam from electron gun which consists of a tungsten filament particle is restricted to a certain region of space instead of being able to move freely .i.e
1 applying when a particle bounces back and forth between the walls of a box.
2
If one dimensional motion of a particle is assumed to take place with zero potential
The accelerated electrons are collimated into a fine beam by allowing them to pass energy over a fixed distance, and if the potential energy is assumed to become infinite
Substitute (1) in (2) at the extremities of the distance, it is described as a particle in a 1-D box, and this is
The fast moving electron beam is made to strike the target (nickel crystal) capable of . = 0 if particle does not exist
the simplest example of all motions in a bound state.
rotating about an axis perpendicular to the plane of diagram. The Schrodinger wave equation will be applied to study the motion of a particle in 1-D
The electrons are scattered in all directions by atomic planes of a crystal and intensity This is called normalization condition.
box to show how quantum numbers, discrete values of energy and zero point energy
of scattered electron beam in all directions can be measured by the electron collector arise.
and can be rotated about the same axis as the target. 11 uncertainty principle? This is known as differential plane wave equation.
From a wave point of view, a particle trapped in a box is like a standing wave in a string
The collector is connected to a sensitive galvanometer whose deflection is proportional In complex wave, the
According to Classical mechanics, a moving particle at any instant has fixed position walls.
to the intensity of electron beam entering the collector. replaced by de- in eqn (3) moving freely along x- axis and is confined between
in space and definite momentum which can be determined simultaneously with any
desired accuracy. This assumption is true for objects of appreciable size, but fails in x=0 and x= a by infinitely two hard walls, so that the particle has no chance of
particles of atomic dimensions. penetrating them and bouncing back and forth between the walls of a 1-D box.

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If the particle does not lose energy when it collides with such walls, then the total energy The wave functions corresponding to are called Eigen functions of the particle, - , .
remains constant. .the integer is called the quantum number of the CB CB CB
This box can be represented by a potential well of where V is uniform inside energy level . The experimental value of ` `was obtained nearly 10 times its theoretical value. So classical
Eg =5.4 eV Eg =1.1 eV
Substituting (8) in (7), ..(10) value.
a particle is Resistivity: - According to the classical free electron theory, the resistivity is given by the
Normalization of wave function: The wave functions for the motion of the particle are VB VB VB
infinitely high V .
equation,
The boundary condition are
1) Which means the resistivity is proportional to the square root of absolute temperature. But Conductors insulators Semiconductors
2) according to theory at room temperature it does not change up to 10K and in intermediate range
Where is the probability of finding the particle. of temperature is proportional to . In case of insulator, valence band and conduction band are separated by large energy
The Schrodinger wave equation for the particle in the potential well can be written as The conductivity of semiconductors and insulators cannot be explained by the free gap, hence conductivity is zero.
According to normalization condition, the total probability that the particle is
electron theory. In case of semiconductors, the valence band and conduction band are separated by
3) somewhere in the box must be unity.
relatively narrow energy gap; hence the conductivity lies in between conductors and
In the simplest form eqn (3) can be written as 2) What are the applications of Hall Effect? insulators.
dx=1
4) Where k= propagation constant and is given by 5) Determination of the type of Semi-conductors: 5) Define the following terms.
The general solution of equation (4) is 6) From eqn(10), The Hall coefficient is -ve for an n-type semiconductor and +ve for p-type semiconductor. i. Collision time ii. Relaxation time iii. Mean free path iv .Drift velocity v. Mobility
Where A and B are arbitrary constants, and the value of these constant can be obtained Thus the sign of Hall coefficient can be used to determine whether a given Semi-conductor is
by applying the boundary conditions. n or p-type. i. Collision time: The time taken by the electron to complete one collision with the +ve ion
Substitute eqn(1) in (6) Calculation of carrier concentration: center.
B=0 in eqn (6) = = ii.Relaxation time: The time taken by the electron to reduce its velocity to 1/e of its initial
7) velocity.
Substituting eqn (2) in (7) = (for holes) iii.Mean free path: The average distance covered by the electron between two successive
The second term of the integrand expression becomes zero at both the limits. collisions.
=> n = => =
, 0 as already B=0 & if A= 0, there is no solution at all. iv.Drift velocity: The steady state velocity of the electrons in the presence of Electric field.
Determination of Mobility: v.Mobility: The steady state velocity of the electrons per unit electric field.
, i.e
Part- B (Descriptive- 10marks)
, Where Measurement of Magnetic Flux Density:
The normalized wave function is Hall Voltage is proportional to the magnetic flux density B for a given current I. So, Hall Effect 1) What are the salient features of classical free electron theory of metals? What are its
inside the box and the moving particle cannot have zero energy. can be used as the basis for the design of a magnetic flux density metal. drawbacks?
Drude and Lorentz proposed free electron theory of on the basis of some assumptions.
From (8) UNIT-2: ELECTRON THEORY, BAND THEORY & SEMI CONDUCTORS 3) Define Fermi energy level. In conductors (metals), there are large number of free electrons moving freely within
the metal i.e. the free electrons or valence electrons are free to move in the metal like
The highest energy level that can be occupied by an electron at 0 K is called Fermi energy gaseous molecules, because nuclei occupy only 15% metal space and the remaining
From (5) Part-A (SAQ-2Marks)
level. It is denoted by . 85% space is available for the electrons to move.
1) What are the failures of Classical Free electron theory? Since free electrons behave like gaseous molecules, the laws of kinetic theory of gases
4) Distinguish between conductors, Insulator and Semiconductors. can be applied. The mean K.E of a free electron is equal to that of a gas molecule at
Heat Capacities: - The internal energy of a molar substance, U = KTN same temperature.
Molar specific heat Solids are classified into three types based on energy gap. In the absence of any electric field, the electrons move randomly while undergoing
Conductors(metals) scattering at +ve ion centers. The collisions are regarded as elastic (no loss of energy).
= the discrete energy level 9)
The molar specific heat is 1.5 R theoretically, where as the experimental value obtained is too Insulators The electron speeds are distributed according to the Maxwell- Boltzmann distribution
low. This is due to the fact that all free electrons do not contribute significantly to thermal or Semiconductors law.
The lowest energy of a particle is given by putting n=1 in the eqn (9), = lowest In case of conductors, valence band and conduction band almost overlap each other and When an electric filed is applied, the free electrons are accelerated in a direction
energy, minimum energy, ground state energy or zero point energy of the system. Mean free path: - It is calculated using the formula: Tr no significance for energy gap. The two allowed bands are separated by Fermi energy opposite to that of the field.
level. Here there is no role in Eg, as a result conduction is high. The free electrons are confined to the metal due to surface potential.
= x The electrostatic force of attraction between the + ve ion cores and the free electrons is
assumed to be negligible.
= . Drawbacks:

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1. Heat capacities: - The internal energy of a molar substance, U = KTN ve. Free electron theory could not explain why certain substances behave as insulators and
some other substances as semiconductors; in spite of they have free electrons in them.
Molar specific heat
3. Define Fermi energy level. Explain Fermi Dirac distribution function.
The molar specific heat is 1.5 R theoretically, where as the experimental value obtained is too
low. This is due to the fact that all free electrons do not contribute significantly to thermal or Energy levels Fermi Dirac Distribution:
According to the Quantum theory quantization leads to discrete energy levels. The electrons
2. Mean free path: - It is calculated using the formula, nciple i.e., it
allows a maximum number of two electrons with spins in opposite directions in any energy
= x level. The pair of electrons, one with sign up and the other with spin down occupy the lowest
energy level. The next pair occupies the next level. This process goes on until all the electrons
= . in the metal occupy their position.
- , . The highest energy level that can be occupied by an electron at 0 K is called Fermi V = Vo V=Vo V = Vo V= Vo
energy level. It is denoted by . V Conclusion from Kronig Penny Model:
The experimental value of ` `was obtained nearly 10 times its theoretical value. So classical When the metal is not under the influence of an external field, all the levels above the Fermi v=0
value. energy level are empty; those lying below are completely filled. (+) v=0 (+) v=0 (+) v=0 (+) v= 0 (+) by intervals in which, there are no allowed energy levels. These are known as forbidden
3. Resistivity: - According to the classical free electron theory, the resistivity is given by the Fermi Dirac Distribution: regions.
When the material is at a temperature higher than OK, it receives thermal energy from T that the width of the allowed
equation. surroundings i.e. electrons are thermally excited. As a result, they move into the higher energy is necessary. Kronig-penny introduced a simple model for the shape of potential variation. The energy bands is increased and forbidden energy regions become narrow.
Which means the resistivity is proportional to the square root of absolute temperature. But levels which are unoccupied at OK. The occupation obeys a statistical distribution called Fermi potential inside the crystal is approximated to the shape of rectangular steps. 3) The width of the allowed band decrease with the increase of p value. When p
according to theory at room temperature it does not change up to 10K and in intermediate range Dirac distribution law. KRONIG- PENNY MODEL:- allowed energy regions become infinity narrow and the energy spectrum becomes line
of temperature is proportional to . According to this distribution law, the probability F(E) that a given energy state E is occupied Kronig penny consider a periodic arrangement of potential walls and barriers to represent spectrum.
4. The conductivity of semiconductors and insulators cannot be explained by the free electron at a temperature T is given by the potential variation exhibited by t -periodic square well potential as
theory. shown in figure. New forms of boundary conditions are developed to obtain a simple solution 5. Explain the origin of energy band formation in solids based on band theory.
2) What are the assumptions of quantum free electron theory? State its drawbacks. Here F(E) is called Fermi Dirac probability function. It indicates that the fraction of all energy known as cyclic or periodic boundary conditions.
Energy band Formation in solids:
In 1929, Somerfield stated to apply quantum mechanics to explain conductivity phenomenon
in metal. He has improved the Drude - Lorentz theory by quantizing the free electron energy
4) Explain the motion of an electron in periodic potential using Bloch theorem? (or)
and retained the classical concept of free motion of electron at a random. E1
Explain Band theory of solids in detail. (or) Discuss the Kronig- penny model for the
ASSUMPTIONS:- When two identical atoms are brought closer the outermost orbits of these atoms overlap and
motion of an electron in a periodic potential.
The electrons are free to move within the metal like gaseous molecules. They are
confined to the metal due to surface potential. corresponding to those wave functions split in to two.
Electrons in a periodic potential Bloch Theorem:
The velocity distribution of the free electrons is described by Fermi-Dirac Statistics An electron moves through + ve ions, it experiences varying potential. The potential of the
because electrons are spin half particles. electron at the +ve ions site is zero and is maximum in between two +ve ions sites.
shown in fig. If more atoms are brought together more levels are formed and for a solid of N atoms, each of
The wave functions associated with this model can be
exclusion Principle which states that no two electrons have same set of Quantum these energy levels of an atom splits into N levels of energy.
for two regions 1 and 2.
numbers.
The motion of electrons is associated with a complex wave called matter wave, (+) (+) (+) (+) ie + N atoms
according to De-Broglie hypothesis. (+) (+) (+) (+) + = 0, = E N Energy levels
The electrons cannot have all energies but will have discrete energies according to the (+) (+) (+) (+)
equation, E = n2 h2 / 8ma2. = ( 0, -b < x < o
Drawbacks: The levels are so close together that they form almost continuous band.
Conductivity: 0, = ( - E)
i.e. l These two eqs are solved by using Bloch and Kronig-penny models, and applying boundary of the physical properties of solid.
electron charge. variation. conditions the solution is
According to the above equation, polyvalent metals like Aluminum (Al) should be more p + cos = 1 physical of solids.
conductive than mono valent metals like copper (Cu). But experimentally it is not so. These two allowed energy bands are called as valence and conduction bands.
Hall coefficient: According to the free electron theory, the hall coefficients for all metals is Here p = is scattering power The band corresponding to the outermost orbit is called conduction band and the gap
negative where as there are certain metals like Be, Cd, Zn for which the Hall coefficient is + between those two allowed bands is called forbidden energy gap or band gap.

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6. What is effective mass of an electron? Derive an expression for the effective mass of n= (2 ) exp (EF/KT) dx At low temperature, there are no excitations of the electrons from donor level to the
an electron. conduction band.
Hence, density of empty donors and the electron density in conduction band should be
Effective mass of the electron moving in a crystal lattice: n= (2 ) exp( same
i.e. 2 ) 3/2 exp = Nd exp
Using gamma function, it can be shown that Taking log on both the sides & rearranging
Acceleration of the electron in the crystal is given by a = F/m = Ee/m ½
= (KT) ³/2 - -log Nd log 2 ) 3/2
But acceleration of the electron is not constant because of the velocity changes i.e., the
½
electron move faster near the +ve ions in the crystal. Since the electric field and charge Hence, n = (2 ) exp ( (KT)³/2 = log
of the electron are invariant, the effective mass of the electron change accordingly. No of electrons per unit volume is given by
i.e F = a (1)
n= 2 ) exp 2Ef ( + ) KT log 2
Consider A semi conductor in which holes in the valance band and electrons in the conduction
band are solely created by thermal excitations is called intrinsic semiconductors i.e., A The expression for no of holes in the valance band is given by the expression
V= = , w = angular frequency, k = wave propagation vector At absolute zero
pure semi-conductor is considered as intrinsic semiconductor. P= 2 ) exp
i.e. Fermi level lies exactly at the middle of donor level and the bottom of the
Frequency of the complex wave v = E/h dv=1/hdE The no. of electrons moving into the conduction band is equal to the no. of holes created In Intrinsic semi conductor n=p then the Intrinsic carrier concentration is n=p=ni; Conduction band .
in the valence band. ni2 ) 3( ) 3/2 exp Substituting equation 2 in eqn. 1 & re-arranging,
The Fermi level lies exactly in the middle of forbidden energy gap.
Intrinsic semi-conductors are not of practical use in view of their poor conductivity. ni2 )3( ) 3/2 exp N = (2Nd) ½ ) 3/4 exp
SO, a = =( ) Carrier concentration in intrinsic semi-conductors: Here Ec - Ev = Eg (forbidden energy gap ) Hence the density of the electrons in the conduction band is proportional to the square
In the conduction band, the level density D (E) at an energy E is given by the expression. Hence ni = 2 ) 3/2 ( ) ¾ exp root of the donor concentration.
a= ( )
dE Fermi Level: In Intrinsic semi conductor n=p and assuming the effective mass of e and hole to
Wave propagation vector k = 9. Derive an expression for carrier concentration in p-type extrinsic semiconductors?
The probability of an energy level filled with electrons is given by Fermi-Dirac be same, i.e. =
k= P= function. Exp = exp P-type semi-conductors are fabricated by addition of trivalent atoms like Al as impurity
`P` is momentum, ` ` is de-Broglie wavelength . F (E) = EF Ec = Ev- EF to the intrinsic semi-conductor.
= = . 2 EF = Ev+Ec Hence, holes are majority charge carriers and free electrons are minority charge
energies E and E+dE is carriers.
EF =
Expression for Carrier concentration in P type semi-conductors:
Since is the rate of change of momentum, which is nothing but force `F`. n = D(E) F(E) dE Thus the Fermi level is located half way between the valance band and conduction band and
In this type of semi-conductor, there will be there will be acceptor levels formed at an
its position is independent of the temperature.
a= F energy Ea.
n= (2me) E dE Na represents no. of impurities per unit volume of semi-conductor.
8. Derive an expression for carrier concentration in n-type extrinsic semiconductors?
At low temperatures, all the acceptor levels are empty.
a= ) When pentavalent impurities like P, As, Sb is added to the intrinsic semi-conductors, With increase of temperature, acceptor atoms get ionized i.e. the electrons moves from
The number of electrons in the conduction band is obtained by making integration resultant semi conductor is called N-Type semi-conductor. valance band and occupy the vacant sites in the acceptor energy levels, there by leaving
The concentration of free electrons is more when compared to concentration of holes. holes in the valence band
i.e. F = a (2) Density of holes in the valance band is given by
the bottom of the conduction band we write E- Ec for E -type semi conductors:
Compare 1 & 2 In this type of semi conductor, there will be donor levels formed at an energy Ed. P=2 ) 3/2 exp
n= (2 ) represents no. of impurities per unit volume of semi conductor.
Effective mass Since Ef lies below the acceptor levels, the density of ionized acceptors is given by
For all possible temperatures E- >>>> KT At low temperature all donor levels are filled with electrons, with increase of Na F (Ea) = Na exp
Hence F (E) = exp - ( = exp temperature, more and more donor atoms get ionized and the density of electrons in the
7. Derive an expression for carrier concentration of intrinsic semiconductors? conduction band increases. Hence, density of holes in the valance band is equal to the density of ionized acceptors.
Equation 1 becomes Density of electrons in the conduction band is given by 2 ) 3/2 exp = Naexp
Intrinsic Semi conductors: n= (2 )
n= 2 ) 3/2 exp 1
n = (2 ) exp (EF/KT) The Fermi level (EF) lies in between Ed & Ec
To solve this Integral Part The density of empty donor levels is given by
E-Ec = x Nd [ 1-F(Ed d [ 1-1+ exp ] = Nd [ 1-F(Ed)] Nd exp
E = Ec+x
dE = dX

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In P-tpe semi- -direction. The Hall coefficient is -ve for an n-type semiconductor and +ve for p-type semiconductor. 2) Write a short note on Ferro Electricity.
As they move Thus the sign of Hall coefficient can be used to determine whether a given Semi-conductor is
due to the magnetic field. n or p-type. Ferro Electricity: Substances exhibiting electronic polarization even in the absence of
This force drives the holes down to the lower face. As a result, the lower face becomes Calculation of carrier concentration: external field are called Ferroelectric Materials. This phenomenon is known as Ferroelectricity.
+vely charged and ve charge on the upper surface creating the hall field in the Y- = = Examples: Rochelle salt (NaKC 4H4O6.4H2O), Lead Titanate, PbTiO3, Lead zirconate Titanate
direction. The Hall field exerts an upward force on holes equal to Ee. (PZT), Lead lanthanum zirconate Titanate (PLZT).
In the steady sate, two forces just balance and as a result, no further increase of + ve = (for holes) Properties
charge occurs on Face1. Have peculiarly large dielectric constant.
=> n =
In N type semiconductor, the majority charge carriers are electrons experiences a force They exhibit hysteresis phenomena like ferromagnetic materials.
in the downward direction and lower face gets vely charged. As a result, Hall field => =
will be in the Y direction. Determination of Mobility: 3) Write a short note on Piezo Electricity.
Demonstration: If the conduction is due to one type carriers, ex: electrons
Consider a rectangular slab of n-type semi conductor carrying current in the + ve X- Piezo Electricity: When certain crystals are subjected to stress, the electric charges appear on
i.e. 2 = direction. their surface with certain distance of separation. This is called the piezoelectric effect. The
-direction as shown then under the influence of crystals exhibiting Piezo electric effect are called piezoelectric crystals and this phenomenon
Taking log, = log 2 magnetic field, electrons experience a force given by = -Bev. is called Piezo electricity. Examples: Quartz, Rochelle salt, Tourmaline.
As a result of force acting on the electrons in the Y direction as a consequence the Non-Centro Symmetric crystals are exhibiting this property.
At 0o K, E f = lower face of the specimen gets vely charged and upper surface is + vely charged. Measurement of Magnetic Flux Density:
4) Define the following terms (a) Magnetic flux (b) Magnetic induction(c) Magnetic field
Hence a potential called the Hall Voltage present between the top and bottom faces Hall Voltage is proportional to the magnetic flux density B for a given current I. so, Hall Effect
i.e. At 0 K, Fermi level lies exactly at the middle of the acceptor level and in the top strength (d) Intensity of magnetization(e) Magnetic susceptibility(f) Magnetic
of the specimen. can be used as the basis for the design of a magnetic flux density metal.
of the valance band. permeability of medium
The Hall field , exerts an upward force on the electrons given by F= -e
Sub. eqn. 2 in eqn. 1 & re-arranging, P=(2Na) ½ ) 3/4 exp The two opposing forces and establish an equilibrium under which
Thus the density of the holes in the valance band is proportional to the square root of | | =| | i.e -Bev =-e UNIT- 3: DIELECTRIC PROPERTIES & MAGNETIC MATERIALS Magnetic flux( : The number of lines passing normally through an area. Its unit is Weber.
the acceptor concentration. Magnetic induction (or) Magnetic flux density (B): The magnetic induction in any material
= BV Part-A (SAQ-2Marks) is the number of lines of magnetic force passing through unit area perpendicularly. Its unit is
10. Explain Hall Effect in detail? What are its applications? Weber/ or tesla.
(1)Define the following terms (i)Electric dipole (ii)Dipole moment (iii) Dielectric constant Magnetic field intensity (or) strength (H): Magnetic field intensity at any point in the
= (iv)Polarization (v)Polarization vector(vi) Electric displacement vector. magnetic field is the force experienced by a unit North Pole placed at that point. Its unit is
= d ampere
= Bvd Electric dipole: Two equal and opposite charges small in magnitude and separated by a small Magnetization (or) Intensity of magnetization (I): The term of magnetization is the process
distance constitute a electric dipole. of converting a non magnetic material into a magnetic material.
Dipole moment: The product of magnitude of both charge and the distance between the two It is also defined as the magnetic moment per unit volume. . Its units is ampere
charges. i.e. µ = q r. Magnetic : The ratio of intensity of magnetization (I) produced to the
J= nev = V It is a vector quantity. magnetic field strength (H) in which the material is placed.
=> = = The direction of µ is from negative to positive.
Hall Coefficient: Dielectric constant: : Dielectric constant is the ratio between the permittivity of the
Hall field , for a given material depends on the current density J and the applied medium to the permittivity of the free space. = Magnetic permeability of medium (µ): It is defined as the ratio of magnetic induction B in a
magnetic field B. substance to the applied magnetic field intensity.
Since it is the ratio of same quantity, has no unit.
Hall-Effect: i.e. Polarization: The process of producing electric dipoles which are oriented along the field
When a material carrying current is subjected to a magnetic field in a direction = direction is called polarization in dielectrics. 5) What are ferrites? Mention any two applications.
perpendicular to direction of current, an electric field is developed across the material Since, = , = Polarization vector (P): The dipole moment per unit volume of the dielectric material is called
polarization vector P. Ferri magnetic substances are the materials in which the atomic or ionic dipoles in one
in a direction perpendicular to both the direction of magnetic field and current direction.
= direction are having unequal magnitudes. This alignment of dipole gives a net
-
Explanation: J= , = = )B magnetization and those magnetic substances which have two or more different kind
If µ is the average dipole moment per molecule and N is the number of molecules per unit of atoms. These are also called Ferrites.
Consider a semi-conductor, and current passes along the X-axis and a magnetic field
Bz is applied along the Z-direction, a field Ey is called the Hall field which is developed volume, then polarization vector,
in the Y-direction. i.e =
Electric displacement vector is a quantity which is a very convenient function for analyzing
Applications:
Determination of the type of Semi-conductors: the electrostatic field in the dielectrics and is given by D= E+P

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Applications of ferrites: Substitute Q from 5 in 3 we get (a)Ferro Electricity: Substances exhibiting electronic polarization even in the absence of
They are used to produce ultrasonics by magnetization principle. external field are called Ferroelectric Materials. This phenomenon is known as Ferroelectricity.
Coulomb force = ( ----------6
Ferrites are used in audio and video transformers. Examples: Rochelle salt (NaKC4H4O6.4H2O), Lead Titanate, PbTiO3, Lead zirconate Titanate
At equilibrium Lorentz force= Coulomb force (PZT), Lead lanthanum zirconate Titanate (PLZT).
Part- B (Descriptive- 10marks) -ZeE= Properties:
Have peculiarly large dielectric constant.
(1) Define polarization? Explain the various types of polarization in dielectrics? X= ----------------------------------7 They exhibit hysteresis phenomena like ferromagnetic materials.
Therefore the displacement of electron cloud x is proportional to the applied electric
Polarization: The process of producing electric dipoles which are oriented along the field field E.
direction is called polarization in dielectrics. Dipole moment:
Types of Polarizations: Therefore induced dipole moment µ= E. Now the two electric charges +Ze and Ze are displaced by a distance under the
Polarization occurs due to several atomic mechanisms. When the specimen is placed inside Where is the electronic polarizability. influence of the field and form a dipole.
electric field, mainly three types of polarizations are possible. Those are Electronic polarizability is proportional to the volume of atoms. Induced dipole moment = magnitude of charge × displacement = Ze X -----------8
Electronic polarization Polarizability is independent of temperature. Substitute the value of X from 7 in 8 we have
Ionic polarization The polarization is not zero even when external field is zero.
Orientational or Dipolar polarization = Ze × Ferroelectrics follow Curie-Weiss law, the electric susceptibility
Calculation of electronic polarizability:
Electronic polarization: = Here C=Curie temperature, = transition temperature, above which Ferro electric
Electronic polarization occurs due to the displacement of negatively charged electron (I)Without Electric field: = E--------------------------------9 substance becomes Para electric substances. Spontaneous polarization becomes zero at
in opposite direction. = is called electronic polarizability transition temperature.
When an external field is applied and there by creates a dipole moment in the dielectric. Let us consider a classical model of an atom. Assume the charge of the nucleus is +Ze Calculation of ionic polarization: All Ferro electric materials are Pyro electric; however the converse is not true.
Therefore induced dipole moment µ= E. and the nucleus is surrounded by an electron cloud of charge Ze which is distributed Ionic polarization is due to the displacement of cations and anions in opposite directions They exhibit the phenomenon of Double refraction.
Where is the electronic polarizability. in sphere of radius R. and occurs in an ionic solid.
Electronic polarizability is proportional to the volume of atoms. The charge density of the charged sphere = Suppose an electric field is applied in the +ve x direction, the +ve ions move to the right (b)Piezoelectricity:
This Polarization is independent of temperature. by x1 and the ve ions move to the left by x2.
Ionic polarization: Charge density -------------------1 Assuming the each unit cell has one cation and one anion, the resultant dipole moment When certain crystals are subjected to stress, the electric charges appear on their surface
This is due to the displacement of cations and anions in opposite directions and occurs (II) With Electric field: per unit cell due to ionic displacement is given by x1+ x2) ------------1 with certain distance of separation. This is called the piezoelectric effect. The crystals
in an ionic solid. This type of polarization occurs in ionic dielectrics like Nacl. 1 2 exhibiting Piezo electric effect are called piezoelectric crystals and this phenomenon is
When such a dielectric material is subjected to an external electric field, adjacent ions When the dielectric is placed in an electric field E, two phenomena occurs due to the applied field, -------------------------2 called Piezo electricity.
of opposite sign undergoes displacement and this displacement results either increase Hence Examples: Quartz, Rochelle salt, tourmaline are piezoelectric substances.
or decrease in the distance of separation between ions. Lorentz force due to the electric field tends to separate the nucleus and the electron Piezoelectric strains are very small, and the corresponding electric fields are very large.
cloud from their equilibrium position. Restoring force constants depend upon the mass of the ion and angular frequency of the
If x1 and x2 are the displacements of positive and negative ions in an ionic crystal due Non-Centro Symmetric crystals are exhibiting this property.
to the application of electric field E, then dipole moment ). After the separation, an attractive coulomb force arises between the nucleus and molecule in which ions are present.
electron cloud which tries to maintain the original equilibrium position. Explanation:
Orientational or Dipolar polarization: -----------------------3, where .
Let x be the displacement made by the electron cloud from the positive core .Since the
This type of polarization occurs in materials with polar molecules.
nucleus is heavy it will not move when compared to the movement of electron cloud ---------------------------4, Where -ve ion.
Without the external field the molecules are oriented at random. So the net dipole here x<<R, where R is the radius of the atom.
moment is zero.
Since the Lorentz and coulombs forces are equal and opposite in nature, equilibrium is ---------------------------5
When external field is applied the polar molecules orient favorably into the field
reached.
direction. The process of orientation becomes easy at high temperature. And ---------------------------6
At equilibrium Lorentz force = Coulomb force
Hence the Orientational polarizability is strongly dependent on temperature. = Lorentz force = charge field = -ZeE--------------2
Coulomb force=charge × field = +Ze× Structure of Quartz

Then Coulomb force=charge X ---3 In 3-dimensional lattices of quartz crystal before the constraint is applied the dipole
(2) Derive the expression for electronic and ionic polarizations. Thus the ionic polarizability is inversely proportional to square of the natural
Here the total number of negative charges (Q) encloses in the sphere of radius R is moment at each lattice point is zero.
Electronic polarization and calculation of Electronic polarizability: frequency of the ionic molecule and is reduced mass is equal to . When pressure is applied along X-axis the angle increases giving rise to polarization
X= charge density of the electron × volume of the sphere ---------------4 along Y-axis.
Electronic polarization occurs due to the displacement negative electron cloud of each (3) Write a short note on (a) Ferro electricity (b) Piezo electricity. In structure with centre of symmetry, the opposite ends are identical in any direction.
atom with respect to its nucleus in the presence of electric field. When an external field Substitute from 1 in 4 we get So constraints do not produce any polarization.
is applied and there by creates a dipole moment in the dielectric. Q= × , i.e Q= -------------------------------5

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(4) Define the local/internal field of cubic structure and derive the expression for it? Or Let us consider small area ds on the surface of the sphere. This area is confined within Classification of magnetic materials:
Derive the expression for local field in a symmetrical dielectric material? an angle d , making an angle with the direction of field E. By the application of magnetic field some materials will not show any effect that are When placed inside a magnetic field it attracts the magnetic lines of force.
charge on the area ds. Polarization P is parallel to E. PN is the component of called non magnetic materials and those which show some effects are called magnetic Examples: Aluminum, Manganese, oxygen.
Local Field: In presence of Electric field, every dipole experiences its own medium polarization perpendicular to the area ds. materials. Ferromagnetism:
of influence called Local field or internal field. Polarization is defined as the surface charges per unit area. All magnetic materials magnetized in the presence of external magnetic field. Ferromagnetism arises when the magnetic moments of adjacent atoms are arranged in
Depending on the direction and magnitude of magnetization and also the effect of a regular order i.e all pointing in the same direction.
INTERNAL FIELD OR LOCAL FIELD: E= = temperature on magnetic properties, all magnetic materials are classified into Dia, Para The ferromagnetic substances posses a magnetic moment even in the absence of the
and Ferro magnetic materials. applied magnetic field, this magnetization is known as the spontaneous magnetization.
Electric field intensity at c due to charge q' is given by coulombs law .Electric field Two more classes of materials have structure very close to Ferro magnetic materials,
intensity E is along the radius r. E is resolved into two components. but shows quiet different magnetic properties. They are Anti-Ferro magnetic and Ferri adjacent atoms, coupling their magnetic moment together in rigid parallelism.
Component of intensity parallel to the field direction Ex = E cos . magnetic materials. Properties of ferromagnetic materials:
Component perpendicular to the field direction Ey = E sin . Diamagnetism: In ferromagnetic materials, large magnetization occurs in the direction of the field.
The perpendicular components Ey and ( Ey) are in opposite directions and hence cancel The number of orientations of electronic orbits in an atom be such that vector sum of Strong attraction is the characteristic property of ferromagnetism.
each other the parallel components alone are taken into consideration. By revolving ds magnetic moment is zero They exhibit spontaneous magnetization.
about AB, we get a ring of area dA and radius The external field will cause a rotation action on the individual electronic orbits this The relative permeability is very high for Ferro magnetic.
produces an induced magnetic moment which is in the direction opposite to the field The magnetic susceptibility is positive and very high.
and hence tends to decrease the magnetic induction present in the substance. Magnetic susceptibility is fairly high and constant up to a certain temperature according
Ring area dA = Circumference Thickness Thus the diamagnetism is the phenomena by which the induced magnetic moment is
When an external electric field is applied across a dielectric, the intensity of electric the equation = C= curie constant Curie temperature.
= 2 y rd sin = y/r always in the opposite direction of the applied field.
field felt by a given atom is not equal to the applied electric field E, because the atoms = 2 r sin .rd y = r sin Properties of diamagnetic materials: Ferromagnetism is due to the existence of magnetic domains which can be
are surrounded on all sides by other polarized atoms. dA = 2 r2 sin d Diamagnetic material gets magnetized in a direction opposite to the magnetic field. spontaneously magnetized.
The internal field Eint is defined as the electric field acting on the atom is equal to the Weak repulsion is the characteristic property of diamagnetism. Exhibit hysteresis phenomenon.
sum of the electric fields created by the neighboring polarized atoms and the applied Electric field intensity = Spin alignment is parallel in the same direction
Permanent dipoles are absent.
field. This field is responsible for polarizing the atom. Electric field intensity due to whole sphere is = Relative permeability is less than one but positive.
Where Eint is called internal field or Lorentz field. The magnetic susceptibility is negative and small. It is not affected by temperature. When placed inside a magnetic field they attract the magnetic lines of forces very
= strongly.
Diamagnetism is universal i.e. all materials when exposed to external magnetic fields,
LORENTZ METHOD TO FIND INTERNAL FIELD: tend to develop magnetic moments opposite in the direction to the applied field. Examples: Iron, Nickel, Cobalt.
When placed inside a magnetic field, magnetic lines of force are repelled.
A dielectric material is placed in an external electric field. It is placed in between two (7)Explain the hysteresis curve based on domain theory of ferromagnetism?
Para magnetism:
plates of a parallel plate capacitor. (5) Derive the Clasius-Mosotti relation based on local field? (Or) Derive an expression (OR)
The number of orientations of orbital and spin magnetic moments be such that the
relating macroscopic dielectric constant and microscopic polarizability in case of Explain the hysteresis in a ferromagnetic material.
vector sum of magnetic moment is not zero and there is a resultant magnetic moment
sphere is greater than the radius of the atom. symmetrical dielectric material? in each atom even in the absence of applied field. Domain theory of ferromagnetism:
Thus there are many atomic dipoles within the sphere. Electric field at the centre of the Let us consider the elemental dielectric having cubic structure as diamond, si, carbon The net magnetic moments of the atoms are arranged in random directions because of According to Weiss, the specimen of ferromagnetic material having number regions or
sphere is called internal field which is made up of the following four factors. etc. which have cubic structure. Since there is no ions or no permanent dipoles in these domains which are spontaneously magnetized. In each domain spontaneous
thermal fluctuations, in the absence of external magnetic field. Hence there is no
material the ionic polarizability & orientational polarizability are zero. magnetization is due to parallel alignment of all magnetic dipoles.
magnetization.
Eint = E1 + E2 + E3 + E4 ------------------- (1) i.e. If we apply the external magnetic field there is an enormous magnetic moment along The direction of spontaneous magnetization varies from domain to domain.
Polarization = the field direction and the magnetic induction will be increase. Thus induced magnetism The resultant magnetization may hence be zero or nearly zero.
E1 = Electric field due to the charges on the capacitor plates (externally applied). is the source of par magnetism. When an external field is applied there are two possible ways for the alignment of
E2 = Electric field due to polarized charges on the plane surface of the dielectric. p= ------------- (1) domains.
Properties of paramagnetic materials:
E3 = Electric field due to polarized charges induced on the surface of the sphere. Paramagnetic materials get magnetized in the direction of the magnetic field. (i)By motion of domain walls: The volume of domains that are favorably oriented with respect
We know and ------------------- (2) to the magnetizing field increases at the cost of those that are unfavorably oriented.
E4 = Electric field due to permanent dipoles of atoms inside the sphere. Weak attraction is characteristic property of Para magnetism.
Paramagnetic material has magnetic dipoles. [Fig (b)]
We can take E = E1 + E2, where E1 is the field externally applied and E2 is the field due Relative permeability is greater than one but small i.e. this indicate that when (ii)By rotation of domains: when the applied magnetic field is strong, rotation of the direction
to the polarized charges on the plane surface of the dielectric. paramagnetic substance is placed in a uniform magnetic field, the field inside the of magnetization occurs in the direction of the field. [Fig(c)]
If we consider the dielectric as highly symmetric then the dipoles present inside the material will be more than the applied field. H H H
sphere will cancel each other. The magnetic susceptibility is small and positive. The magnetic susceptibility of
o E4 = 0. paramagnetic is
o Equation (1) becomes called curie law, c is called Curie constant.
E int = E + E3 ------- (2) (6) Explain the classification of magnetic materials on the basis of magnetic moment and Paramagnetic susceptibility is independent of the applied field strength.
To find E3: mention the important properties of various magnetic materials? Spin alignment is random Fig (a) fig (b) fig(c)

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Hysteresis curves Hysteresis loss: It is the loss of energy in taking a ferromagnetic body through a 1) Explain i) Metastable state ii) optical pumping iii) population inversion
complete cycle of magnetization and this loss is represented by the area enclosed by the
hysteresis loop. Metastable state: The excited state, which has a long life time, is known as metastable state.
Optical pumping: This process is required to achieve population inversion and used in Ruby
(8) Write short notes on Ferri magnetic materials? What their applications? laser.

Ferri magnetic substances are the materials in which the atomic or ionic dipoles in one excited sta
direction are having unequal magnitudes. This alignment of dipole gives a net Population Inversion:
magnetization and those magnetic substances which have two or more different kind of Generally, number of atoms in the ground state is greater than the number of atoms in higher
atoms. These are also called Ferrites. energy states.
Hard magnetic materials Soft magnetic materials But in order to produce a laser beam, the minimum requirement is stimulated emission.
Stimulated emission takes place only if the number of atoms in the higher energy level is greater
than the number of atoms in the lower energy level.
(i)Hard magnetic materials have large hysteresis (i)Soft magnetic materials have low hysteresis Simply population inversion is nothing but number of atoms in higher energy level is greater
In Ferri magnetic materials there, they may have large net magnetization as compared loss due to large hysteresis is loop area. Loss due to small hysteresis loop area. than the number of atom in lower energy level.
to anti Ferro magnetic materials. 2) Define spontaneous and stimulated emission of radiation?
Ferrimagnetic materials generally known as ferrites consist of two or more different (ii)In these materials the domain wall movement (ii)In these materials the domain wall movement
kind of atoms their formula is . is difficult because of presence of impurities and is relatively easier, even for small changes in the Spontaneous Emission:
Where stands for a suitable divalent metal ion such as , , , , crystal imperfection and it is irreversible in magnetizing field the magnetization changes by coming down to ground state by itself without any external agency, such an emission is called
etc, is a trivalent ferric ion. nature. large amount. spontaneous emission. Atom* atom + hv.
Hysteresis: Lagging of magnetization behind the magnetizing field (H). Applications of ferrites: Photons released in spontaneous emission are not coherent. Hence spontaneous emission is not
When a Ferro magnetic material is subjected to external field, there is an increase in the They are used to produce ultrasonics by magnetization principle. useful for producing lasers.
value of the resultant magnetic moment due to two processes. Ferrites are used in audio and video transformers. (iii) The coercivity and retentivity are large. (iii)The coercivity and retentivity are small Stimulated Emission: When an atom in the excited state, emits two photons of same energy
The movement of domain walls Ferrites rods are used in radio receivers to increase the sensitivity. Hence these materials cannot be easily magne- .Hence these materials can be easily magnetized
Rotation of domain walls They are also used for power limiting and harmonic generation. tised and demagnetized and demagnetized. emission is called stimulated emission. Atom* atom + 2hv.
When a weak magnetic field is applied, the domains are aligned parallel to the field and Ferrites are used in computers and data processing circuits.
magnetization grows at the expense of the less favorably oriented domains. Ferrites are used in switching circuits and in storage devices of computers. (iv) In these materials, because of the presence (iv)These materials are free from irregularities; In the two photons one photon induces the stimulated emission and the second one is
This results in the Bloch wall (or) domain wall movement and the weak field is removed Ferrites are not metals but their resistivity lies in the range of insulators or of impurities and crystal imperfection the the magneto static energy is small.
the domains reverse back to their original state. This reversible wall displacement is released by the transition of atom from higher energy level to lower energy level.
semiconductors. mechanical strain is more. Hence magneto static
indicated by OA the magnetization curve. (9) Write short notes on soft and hard magnetic materials? Both the photons are strictly coherent. Hence stimulated emission is responsible for
energy is large.
When the field becomes stronger than the domain wall movement, it is mostly (Or) laser production.
(v)These materials have small values of (v)These materials have large values of
reversible movement. This is indicated by path AB of the graph. The phenomenon of Distinguish soft and hard magnetic materials.
susceptibility and permeability. susceptibility and permeability. 3) Explain the basic principle of optical fiber?
hysteresis is due to the irreversibility.
At the point B all domains have got magnetized, application of higher field rotates the Hard and soft magnetic materials: (vi)These are used to make permanent magnets. (vi)These are used to make electronic magnets.
domains into the field direction indicated by BC. Once the domains rotation is complete Optical fibers are the waveguides through which electromagnetic waves of optical
Example Example
the specimen is saturated denoted by C. The process of magnetization of a Ferro or Ferri magnetic material consist of moving 1. copper nickel iron alloy 1. iron silicon alloys frequency range can be guided through them to travel long distances.
Thus the specimen is said to be attain the maximum magnetization. At this position if domains walls so that favorably oriented domains grow and shrink. If the domain walls 2. copper nickel cobalt alloy 2. ferrites An optical fiber works on the principle of total internal reflection (TIR).
the external field is removed (H=0), the magnetic induction B will not fall rapidly to are easy to move and coercive field is low and the material is easy to magnetize. Such 3.iron-nickel-aluminum alloys with certain 3.garnets Total Internal Reflection: when a ray of light travels from a denser medium into a rarer
zero ,but falls to D rather than O. This shows that even when the applied field is zero a material is called soft magnetic material. amount of cobalt called alnico alloy
the material still have some magnetic induction (OD) which is called residual medium and if the angle of incidence is greater than the critical angle then the light gets
If it is difficult to move the domain walls, the coercive field is large then the material totally reflected into the denser medium
magnetism or retentivity. (vii) Applications: For production of permanent (Vii)Applications: Mainly used in
Actually after the removal of the external field the specimen will try to attain the is magnetically hard .These are called hard magnetic material.
magnets used in magnetic detectors, electromagnetic machinery and transformer
original configuration by the movement of domain walls. But this movement is stopped microphones flux meters, voltage regulators, cores. They are used in switching circuits, 4) Explain i) Numerical Aperture ii) Acceptance angle
due to the presence of impurities, lattice imperfections. damping devices, magnetic separators, and loud microwave insulators and matrix storage of
Therefore to overcome this, large amount of reverse magnetic field ( ) is applied to speakers. computers. i) Numerical Aperture:
the specimen .The amount of energy spent to reduce the magnetization (B) to zero is Numerical aperture of a fiber is a measure of its light gathering power.

HSTERESIS: lagging of magnetization (B) behind the magnetizing field (H) is called UNIT- 4 : LASERS & OPTICAL FIBERS The light gathering ability of optical fiber depends on two factors i.e.,
hysteresis. Core diameter
Part-A (SAQ-2Marks) NA

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NA is defined as sine of the acceptance angle In metallic cables only 48 conversations can be made at once without cross talks where 4. Coherence: If any wave appears as pure sine wave for longtime and infinite space, then it
i.e., NA = Sin A i.e NA = n12-n22 as in optical fibers more than 15000 conversations can be made at once without cross is said to be perfectly coherent.
The efficiency of optical fiber is expressed in terms of NA; it is called as figure of merit of talks. Practically, no wave is perfectly coherent including lasers. But compared to other light sources,
optical fiber. Light cannot enter through the surface of the optical fiber except at the entry interface lasers have high degree of coherence because all the energy is concentrated within the small
ii) Acceptance Angle: i.e., interference b/w different communication channels is absent. Hence purity of light region. There are two independent concepts of coherence.
All right rays falling on optical fiber are not transmitted through the fiber. signal is protected. i) Temporal coherence (criteria of time)
Only those light rays making i > c at the core-cladding interface are transmitted through the Optical signal do not produce sparks like electrical signals and hence it is safe to use ii) Spatial coherence (criteria of space)
fiber by undergoing TIR. For which angle of incidence, the refraction angle is greater than 90 0 optical fibers.
will be propagated through TIR. External disturbances from TV or Radio Stations power electronic systems and 4) Explain the concept of population inversion and pumping in lasers?
There by Acceptance Angle is defined as: The maximum angle of incidence to the axis of lightening cannot damage the signals as in case of metallic cables.
optical fiber at which the light ray may enter the fiber so that it can be propagated through TIR. Materials used in the manufacture of optical fibers are SiO2, plastic, glasses which are Population Inversion:
cheaper & available in plenty. 3) What are the characteristics/striking features/Properties of Laser Light? Generally, number of atoms in the ground state is greater than the number of atoms in
5. What are the main sections of optical fiber? Describe the step index optical fiber? higher energy states.
Characteristics of Laser Beam: Some of the special properties which distinguish lasers from But in order to produce a laser beam, the minimum requirement is stimulated emission.
Part- B (Descriptive- 10marks) ordinary light sources are characterized by:
An optical fiber consists of three (3) co-axial regions. Stimulated emission takes place only if the number of atoms in the higher energy level
The inner most region is the light- 1. Directionality is greater than the number of atoms in the lower energy level.
1) What is Acronym of a Laser, absorption, spontaneous and stimulated emissions? 2. High Intensity
a middle co- Simply population inversion is nothing but number of atoms in higher energy level is
3. Mono- chromacity greater than the number of atom in lower energy level.
Laser: Laser means Light Amplification by Stimulated Emission of Radiation. 4. Coherence
Sheath protects the core & cladding regions from external contaminations, in addition Absorption: So, if there is a population inversion there by only stimulated emission will able to
to providing mechanical strength to the fiber. from the external agency and excited into the higher energy levels from ground state, produce laser beam.
1.Directionality:
The refractive index of core (n1) is always greater than the refractive index of cladding then this process is known as absorption. Atom + hv atom* Population inversion is associated with three Phenomenon.
(n2) i.e., n1 > n2 to observe the light propagation structure of optical fiber. Spontaneous Emission: When an atom in the excited state emits a photon of energy o Stimulated emission
Step Index optical fiber: o Amplification
Based on variation in the core refractive index (n1), optical fibers are divided in to two types emission is called spontaneous emission. Atom* atom + hv o Pumping Process
1. Step index fiber Photons released in spontaneous emission are not coherent. Hence spontaneous Stimulated Emission: If majority of atoms are present in higher energy state than the
2. Graded index fiber emission is not useful for producing lasers. process becomes very easy.
Step index fibers have both single & multimode propagations. Stimulated Emission: When an atom in the excited state, emits two photons of same 2
represents number of atoms in the excited state than the amplification of light takes
agency, such an emission is called stimulated emission. Atom* atom + 2hv place only when N2 > N1.
6) Write a short note on attenuation in optical fibers. In the two photons one photon induces the stimulated emission and the second one is If N2 > N1, there will be a population inversion so induced beam and induced emission
released by the transition of atom from higher energy level to lower energy level. Laser emits radiation only in one direction. The directionality of laser beam is expressed in are in the same directions and strictly coherent than the resultant laser is said to be
Usually, the power of light at the output end of optical fiber is less than the power launched at terms of angle of divergence ( ) amplified.
Both the photons are strictly coherent. Hence stimulated emission is responsible for
the input end, then the signal is said to be attenuated. laser production. Divergence or Angular Spread is given by = r2-r1/d2-d1
Where d1, d2 are any two distances from the laser source emitted and r1, r2 are the radii of beam average in any particulars energy state at equilibrium temperature as
Attenuation: It is the ratio of input optical power (Pi) in to the fiber to the power of light spots at a distance d1 and d2 respectively as shown in above figure. Laser light having less
2) Explain principle of laser/lasing action? 2-E1/KT) = /KT)
coming out at the output end (Po). divergence, it means that laser light having more directionality.
10 Pi / Po db/km. 2. High Intensity: Generally, light from conventional source spread uniformly in all directions.
Laser Production Principle:
Attenuation is mainly due to For example, take 100 watt bulb and look at a distance of 30 cm, the power enter into the eye /KT)
Two coherent photons produced in the stimulated emission, interacts with other two
1. Absorption. is less than thousand of a watt. This is due to uniform distribution of light in all directions.
excited atoms, resulting in four coherent photons.
2. Scattering. But in case of lasers, light is a narrow beam and its energy is concentrated within the small Pumping Process:
Thus, coherent photons are multiplied in a lasing medium. The continuous successive
3. Bending. region. The concentration of energy accounts for greater intensity of lasers. This process is required to achieve population inversion.
emission of photons results for the production of laser beam.
3. Monochromacity: The light emitted by laser is highly monochromatic than any of the other
7) Write down advantages of fiber optics in communication system Or What are the conventional monochromatic light. A comparison b/w normal light and laser beam, ordinary
Advantages of optical fibers over metallic cables ? sodium (Na) light emits radiation at wave length of 5893A0 with the line width of 1A0. But He- Pumping can be done by number of ways
Optical fibers allow light signals of frequencies over a wide range and hence greater Ne laser of wave length 6328A0 with a narrow width of only 10-7 A0 i.e., Monochromacity of i) Optical Pumping excitation by strong source of light (flashing of a
volume of information can be transmitted either in digital form or in analog form within laser is 10 million times better than normal light. Camera)
a short time. The degree of Monochromacity of the light is estimated by line of width (spreading frequency ii) Electrical Pumping excitation by electron impact
of line). iii) Chemical Pumping excitation by chemical reactions
iv) Direct Conversion Electrical energy is directly converted into

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Due to stimulated emission the transition of atoms take place from metastable state to The flash lamp is switched on, a few thousand joules of energy is discharged in a few
Inversion is achieved in forward bias. ground state, there by emitting laser beam. milliseconds.
Construction: A part of this energy excites the Cr3+ Ions to excited state from their ground state and
5 the rest heats up the apparatus can be cooled by the cooling arrangement by passing
or liquid nitrogen.
Derive the relation between the probabilities of spontaneous emission and stimulated The chromium ions respond to this flash light having wavelength 5600
A0(Green),[4200 A0(Red)Also]
When the Cr3+ Ions are excited to energy level E3 from E1 the population in E3 increases.
Cr3+ Ions stay here(E3) for a very short time of the order of 10-8 sec, then they drop to
In 1917, Einstein predicted the existence of two different kinds of processes by which the level E2 which is metastable state of lifetime 10-3 sec .Here the transitions from E3
an atom emits radiation. to E2 is non radiative in nature.
Transition b/w the atomic energy states is statistical process. It is not possible to predict As the lifetime of the state E2 is much longer, the number of ions in this state goes on
which particular atom will make a transition from one state to another state at a increasing while in the ground state (E1) goes on decreasing. By this process population
particular instant. For an assembly of very large number of atoms it is possible to inversion is achieved between E2 & E1.
calculate the rate of transitions b/w two states. When an excited ion passes spontaneously from the metastable state E2 to the ground
Einstein was the first to calculate the probability of such transition, assuming the atomic state E1 it emits a photon of wavelength 6943A0.
system to be in equilibrium with electromagnetic radiation. This photon travels through the ruby rod and if it is moving parallel to the axis of the
ab = Q
Fig: He-Ne laser
crystal, is reflected back & forth by silvered ends until it stimulates an excited ion in E2
N1B12 t, Where N1 The first gas laser to be operated successfully was the He-Ne laser in 1961 by the
1 and causes it to emit fresh photon in phase with the earlier photon. This stimulated scientist A. Jawan.
beam and B12 = Probability of an absorption transition coefficient. transition triggers the laser Transition.
The number of spontaneous transitions Nsp In this method, two gases helium & Neon were mixed in the ratio 10:1 in a discharge
The process is repeated again and again, because the photons repeatedly move along tube made of quartz crystal.
no. of atoms N2 lying in excited state. Nsp = A21N2 t, Where A21 = probability of Ruby is a crystal of aluminum oxide (Al2O3) in which some of the aluminum ions (Al3+)
the crystal being reflected from ends. The photons thus get multiplied.
spontaneous transition. is replaced by chromium ions (Cr3+). This is done by doping small amount (0.05%) of The dimensions of the discharge tube are nearly 80 cm length and 1.5 cm diameter,
chromium oxide (Cr2O3) in the melt of purified Al2O3. When the photon beam becomes sufficiently intense, such that a part of it emerges
The number of stimulated transitions Nst occurring during the time t may be written through the partially silvered end of the crystal. = Tan-1(n) ,Where n = refractive
as: Nst = B21N2 t, Where B21 = probability of stimulated emission. These chromium ions give the pink color to the crystal. Laser rods are prepared from a index of the window substance.
single crystal of pink ruby. Al2O3 does not participate in the laser action. It only acts as The purpose of placing Brewster windows on either side of the discharge tube is to get
Under the thermal equilibrium number of upward transitions = number of downward 7) Describe the principle, construction and working of He-Ne laser with relevant energy
the host. plane polarized laser output.
transitions per unit volume per second. level diagram?
The ruby crystal is in the form of cylinder. Length of ruby crystal is usually 2 cm to 30 Two concave mirrors M1 & M2 are made of dielectric material arranged on both sides
So, we can write: A21N2+B21N2Q = B12N1Q 1
cm and diameter 0.5 cm to 2 cm. of the discharge tube so that their foci lines within the interior of discharge tube.
Q = A21N2 / B12N1 - B21N2 ----------------> 2 He-Le Laser:
The ends of ruby crystal are polished, grounded and made flat. One of the two concave mirrors M1 is thick so that all the incident photons are reflected
Dividing by B21N2 in all terms, Q = (A21/ B21) x 1 / (B12N1 / B21N2) 1 --------> 3 Principle: This laser is based on the principle of stimulated emission, produced in the
The one of the ends is completely silvered while the other one is partially silvered to back into lasing medium.
By substituting N1/N2 = exp (h /kT) from Boltzmann Distribution law, active medium of gas. Here, the population inversion achieved due to the interaction
get the efficient output. Thus the two polished ends act as optical resonator system. The thin mirror M2 allows part of the incident radiation to be transmitted to get laser
Q = (A21/ B21) 1/( B12 / B21) exp (h /kT) 1 ------------> 4 between the two gases which have closer higher energy levels.
A helical flash lamp filled with xenon is used as a pumping source. The ruby crystal is output.
Above equation must agree with planks energy distribution radiation formula. placed inside a xenon flash lamp. Thus, optical pumping is used to achieve population Construction:
Working:
Q = 3 2C3 1/exp (h /kT) -1 ------------------------> 5 inversion in ruby laser.
From equations 4 & 5, B12 = B21, we get A21/ B21 = 3 2C3 As very high temperature is produced during the operation of the laser, the rod is
The co-efficients A21, B12, B21 are known as Einstein coefficients. surrounded by liquid nitrogen to cool the apparatus.
Note: Since we are applying same amount of energy (Q) and observing in the same time Working with Energy Level Diagram (ELD):
( t), number of atoms excited into higher energy levels (absorption) = number of atoms
that made transition into lower energy levels (stimulated emission)
B12 = B21 i.e. absorption = stimulated emission
6) Describe the principle, construction and working of ruby laser with relevant energy
level diagram?

Ruby Laser: It is a 3 level solid state laser, discovered by Dr.T.Maiman in 1960.

Principle:
The chromium Ions raised to excited states by optical pumping using xenon flash lamp
Then the atoms are accumulated at metastable state by non-radiative transition. Fig: Energy Level Diagram of Ruby Laser

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8) Describe the principle, construction and working of Semiconductor laser with relevant Hetrojunction means the material on one side of the junction differs from that on the Identification of tumors and curification.
energy level diagram? other side.i.e;Ga-AS on one side and GaAlAs on other side. Used to detect and remove stones in kidneys.
Generation amd recombination tales place very fastly. Used to detect tumors in brain.
Semi Conductor Laser: Working: 3. Industry:
Semiconductor lasers are of two types, Except the Construction, Principle and working Used to make holes in diamond and hard steel.
are same for both. Used to detect flaws on the surface of aero planes and submarines.
1. Homojunction semiconductor Laser 4. Chemical &Biological:
2. Hetrojunction semiconductor Laser Lasers have wide chemical applications. They can initiate or fasten chemical reactions.
Used in the separation of isotopes.
Principle: Lasers can be used to find the size & shape biological cells such as erythrocytes.
After the invention of semi conductor leaser in 1961, laser have become at common
use. 10. with the help of a suitable diagram explain the principle, structure and working of
In conventional lasers, lasers are generated due to transition of electrons from higher to an optical fiber as a wave guide?
lower energy level. Fig a) when no biasing
But in semi-conductor lasers the transition takes place from conduction band to valence Principle: Optical fibers are the waveguides through which electromagnetic waves of
band. optical frequency range can be guided through them to travel long distances.
Fig:(E.L.D) Energy Level Diagram corresponding to He-Ne laser The basic mechanism responsible for light emission from a semi conductor laser is the An optical fiber works on the principle of total internal reflection (TIR).
The discharge tube is filled with Helium at a pressure of 1 mm of Hg & Neon at 0.1mm recombination o -junction when current is passed through the diode. Total Internal Reflection: when a ray of light travels from a denser medium into a
of Hg. Stimulated emission can occur when the incident radiation stimulates an e in conduction rarer medium and if the angle of incidence is greater than the critical angle then the
When electric discharge is set-up in the tube, the electrons present in the electric field band to make a transition into valence band in that process radiation will be emitted. light gets totally reflected into the denser medium
make collisions with the ground state He atoms. When current is passed through PN Structure & Working:
Hence ground state He atoms get excited to the higher energy levels F1 (2S1), F2 (2S3). holes will increase the density of e in CB & holes in VB. At some value of current the An optical fiber consists of three (3) co-axial regions.
Here Ne atoms are active centers. stimulated emission rate will exceed the absorption rate. The inner most region is the light-guiding region known
As the current is further increased at some threshold value of current the amplification a middle co-
The excited He atoms make collision with the ground state Ne atoms and bring the Ne
atoms into the excited states E4 & E6. will takes place and laser begin to emit coherent radiation. Fig b) with biasing
The energy levels E4 & E6 of Ne are the metastable states and the Ne atoms are directly The properties of semi conductor laser depends upon the energy gap When a forward bias with the source is applied to a semiconductor, e from N-region & Sheath protects the core & cladding regions from external contaminations, in addition
pumped into these energy levels. holes from P-region move to cross the junction in opposite directions. to providing mechanical strength to the fiber.
Since the Ne atoms are excited directly into the levels E4 & E6, these energy levels are Fabrication/construction: s combine recombination is possible due to transition of The refractive index of core (n1) is always greater than the refractive index of cladding
more populated than the lower energy levels E3&E5. e from CB to VB. (n2) i.e., n1 > n2 to observe the light propagation structure of optical fiber.
Therefore, the population inversion is achieved between E6&E5,E6&E3,E4&E3 For low currents the population inversion does not take place hence only spontaneous When light enters through one end of optical fiber it undergoes successive total internal
emission takes place and photon released are not coherent. -
The transition between these levels produces wavelengths of 3390 A0,6328 A0,1150 A0
respectively. When forward current is further increased beyond the certain threshold value
population inversion takes place and coherent photons are released.
Now The Ne atoms undergo transition from E3 to E2 and E5 to E2 in the form of fast
decay giving photons by spontaneous emission. These photons are absorbed by optical The energy gap of Gallium Arsenide (Ga-As) is 1.487eV and corresponding
elements placed inside the laser system. wavelength of radiation is 6435 A0 which is responsible for laser emission.
The Ne atoms are returned to the ground state(E1) from E2 by non radiative diffusion
9) Mention some important applications of Lasers in various fields?
and collision process, therefore there is no emission of radiation.
Some optical elements placed inside the laser system are used to absorb the IR laser Applications of Lasers: Lasers have wide applications in different branches of science
wavelengths 3390 A0, 1150 A0. Fig:Homojunction Semiconductor Laser and engineering because of the following.
Hence the output of He-Ne laser contains only a single wavelength of 6328A0. Very narrow band width
The released photons are transmitted through the concave mirror M 2 there by producing Homojunction Semiconductor Laser: High directionality
laser. Ga As is heavily doped with impurities in both P & N regions. N region is doped with 11) Define and derive the expressions for acceptance angle and numerical Aperture?
Extreme brightness
A continuous laser beam of red color at a wavelength of 6328A0. tellurium & P region by Germanium. 1. Communication:
By the application of large potential difference, Ne atoms are pumped into higher The concentration of doping is of the order of 1017 to 1019 impure atoms per cm. Lasers are used in optical communications, due to narrow band width. Expressions for acceptance angle & Numerical Aperture (NA):
energy levels continuously. The size of the d The laser beam can be used for the communication b/w earth & moon (or) other
A Laser beam of power 0.5 to 50 MW comes out from He-Ne laser. varies from 1 to 100 Am. Acceptance Angle:
satellites due to the narrow angular speed.
These values depend on diffusion condition and 40 mp at the time of fabrication. All right rays falling on optical fiber are not transmitted through the fiber. Only those
Used to establish communication between submarines i.e; under water communication.
Hetrojunction Semiconductor Laser: 2. Medical: light rays making i > c at the core-cladding interface are transmitted through the

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fiber by undergoing TIR. For which angle of incidence, the refraction angle is greater Numerical aperture of a fiber is a measure of its light gathering power. Refractive index increases from one end of core diameter to center and attains
than 900 will be propagated through TIR. maximum value at the centre. Again refractive index decreases as moving away from
There by Acceptance Angle is defined as: The maximum angle of incidence to the center to towards the other end of the core diameter.
axis of optical fiber at which the light ray may enter the fiber so that it can be The light gathering ability of optical fiber depends on two factors i.e., The refractive index variation is represented as n(r) = n1(1- 1/2 = n2
propagated through TIR. Core diameter & NA. 1-n2/n1
NA is defined as sine of the acceptance angle i.e., NA = Sin A The number of modes is given by the expression N = 4.9[d(NA)/ ]2
NA = n12-n22 Where d = core diameter,
The efficiency of optical fiber is expressed in terms of NA, so it is called as figure of Structure:
merit of optical fiber. i) Core Diameter: 30 to 100 m
# NA is also expressed like this: NA = n12-n22 = (n1-n2) (n1+n2) ii) Cladding Diameter: 105 to 150 m
Fractional index change = n1 n2 / n1 = n1 n2 = n1 iii) Sheath Diameter: 250 to 1000 m
Then NA = n1 (n1 + n2) iv) NA: 0.2 to 0.3
Fig: Refractive index profile & propagation in single mode, step index& graded index fibers
Let n1 = n2, then n1 + n2 = 2n1 Performance Characteristics:
Then NA = n1 2n1 = n1 2 = n1 2 i) Band Width: 300 MHZ Km to 3 GHZ Km.
a) Single Mode Step Index Fiber:
ii) Attenuation: 2 to 10 dB/km.
The variation of the refractive index of a step index fiber as a function of distance can
12) How optical fibers are classified on the basis of refractive index profile? iii) Applications: These are ideally suited for medium to high band width applications using
be mathematically represented as longitudinal cross section.
Or incoherent and coherent multimode sources.
Note: Mode of propagation: It is defined as the number of paths available for the light ray to
Describe the Step index and graded index optical fibers in detail and explain the transfer through the optical fiber.
transmission of signal through them? 13) Distinguish Step index & Graded index fibers And Single mode & Multi mode fibers?
Structure:
i) Core Diameter: 8 to 12 m, usually 8.5 m Step Index Graded Index
Classification of Optical Fibers: ii) Cladding Diameter: Around 125 m
Based on variation in the core refractive index (n1), optical fibers are divided in to two iii) Sheath Diameter: 250 to 1000 m
Consider the optical fiber with core refractive index n1 and cladding refractive index types 1. RI of core is uniform throughout except 1. Refractive index varies gradually with
iv) NA: 0.08 to 0.15 usually 0.10 at one stage. radial distance.
n2. Light is incident on the axis of optical fiber at an angle 1. It can produce an angle 1. Step index fiber Performance Characteristics:
2. Graded index fiber 2. Single & multimode propagations exist. 2. It is a multi mode fiber.
of refraction 2. i) Band Width: Greater than 500 MHZ Km.
Based on mode of propagation, fibers are further classified in to 3. Used for short distance applications. 3. Used for long distance applications.
ii) Attenuation: 2 to 5 dB / Km. 4. Attenuation losses are of the order 100 4. 4. Attenuation losses are of the order 10
At air-core interface (A), nosin 1 = n1sins 2 - -----------------------1 1. Single mode propagation iii) Applications: These fibers are ideally suited for high band width applications using single
2. Multi mode propagation dB/km. dB/km.
At core-clad interface (B), for TIR, n1sin (90- 2) = n2sin 900 mode injection coherent (LASER) sources. 5. Mer4dinol rays propagation takes place. 5. Skew rays propagation takes place.
n1 cos 2 = n2, cos 2 = n2/n1 ------------------------------ 2 Step index fibers have both single & multimode propagations. B) Multi Mode Step Index Fibers: 6. Easy to manufacture. 6. Difficult to manufacture.
0Sin 1 = n1 -cos2 2------------------------------3 Graded index fibers have multimode propagation only These fibers have reasonably large core diameters and large NA to facilitate efficient Single Mode Multi Mode
Substituting 3 in 2 , n0Sin 1 = n1 -n22/n12 All together in total three (3) types of fibers transmission to incoherent or coherent light sources.
n0Sin 1 2
1 - n2
2 1. Single mode step index fiber These fibers allow finite number of modes. 1. Core diameter is small. 1. Core diameter is large.
For air n0=1, then sin 1 = 12- n22 2. Multi mode step index fiber Normalized frequency (NF) is the cut off frequency, below which a particular mode 2. Signal entry is difficult. 2. Signal entry is easy.
-1 2 2 3. Multi mode graded index fiber cannot exist. This is related to NA, Radius of the core, and wave length of light as 3. Exists in step index fiber. 3. Exists in both step & graded index fibers.
1 = A = Sin 1 - n2 , Here A is called Acceptance angle
Transmission of Signal in Optical Fibers: NF =2 Where a = radius of core 4. Light must be coherent. 4.Light source may be coherent or
This gives max value of external incident angle for which light will propagate in the 1. Step Index Fiber: The refractive index of core material is uniform throughout and
fiber. Structure: incoherent source .
undergoes a sudden change in the form of step at the core-clad interface. i) Core Diameter: 50 to 200 m
Numerical Aperture (NA):
ii) Cladding Diameter: 125 to 400 m
iii) Sheath Diameter: 250 to 1000 m 14) What are the Advantages of optical fibers over metallic cables?
iv) NA: 0.16 to 0.5
Performance Characteristics: Optical fibers allow light signals of frequencies over a wide range and hence greater
i) Band Width: 6 to 50 MHZ Km. volume of information can be transmitted either in digital form or in analog form within
ii) Attenuation: 2.6 to 50 db/km. a short time.
iii) Applications: These fibers are ideally suited for limited band width and relatively low cost In metallic cables only 48 conversations can be made at once without cross talks where
applications. as in optical fibers more than 15000 conversations can be made at once without cross
c) Multi Mode Graded Index Fibers: talks.
In case of graded index fibers, the refractive index of core is made to vary as a function Light cannot enter through the surface of the optical fiber except at the entry interface
of radial distance from the centre of the optical fiber. i.e., interference b/w different communication channels is absent. Hence purity of light
signal is protected.

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Optical signal do not produce sparks like electrical signals and hence it is safe to use 1. Absorption Losses: In glass fibers, three different absorptions take place. Nano Technology can be defined as the design, characterization, production and
optical fibers. Ultra violet absorption: Absorption of UV radiation around 0.14µm results in the ionization Surface to volume ratio is very important in Nanotechnology because it shows direct application of structures, devices and system by controlling shape and size at the nano
External disturbances from TV or Radio Stations power electronic systems and of valence electrons. effect on material properties. meter scale.
lightening cannot damage the signals as in case of metallic cables. Infrared absorption: Absorption of IR photons by atoms within the glass molecules causes Starting from bulk, the first effect of reducing particle size is to create more surface Various forms of Nano materials :
Materials used in the manufacture of optical fibers are SiO2, plastic, glasses which are heating. This produces absorption peak at 8µm, also minor peaks at 3.2, 3.8 and 4.4µm. sites i.e. surface to volume ratio increases. As a result inter atomic spacing decreases One dimension surface coatings and films
cheaper & available in plenty. Ion resonance/OH- absorption: The OH- ions of water, trapped during manufacturing causes with size and change in surface pressure shows effect on material properties. Two dimensions Nano wires, Nano tubes
absorption at 0.95, 1.25 and 1.39µm. Then the properties such as physical, chemical, Optical, Electrical, Magnetic and Three dimensions Nano particles i.e. precipitates, colloids, quantum dots etc.
15) How optical fibers are used in communication field? Or Explain optical fiber 2. Scattering Losses: Mechanical properties are changed with size. Approaches of Nano technology:
communication link with help of block diagram. The molten glass, when it is converted in to thin fiber under proper tension creates sub Two main approaches are used in Nano technology
microscopic variations in the density of glass leads to losses. 3. What are the important applications of Nano Technology? 1. Bottom up : Materials and devices are built from molecular components
Optical Fiber Communication Link: The dopents added to the glass to vary the refractive index also leads to the inhomogenities in which assemble chemically using principles of molecular recognition.
the fiber. As a result losses occur. Nano materials possess unique, beneficial chemical, physical and mechanical properties; 2. Top down : Nano objects are constructed from larger entities without Atomic level
4
) they can be used for a wide variety of applications. control.
3. Bending Losses: Manufacture of efficient computer clips. Basic Principles of Nano Technology:
In a bent fiber, there is a loss in power of the transmitted signal called as Bending Loss. Used in production of better insulation materials. It uses a basic u
According to the theory of light, the part of the wave front travelling in cladding (rarer medium) Used ion high definition plasma TV, to improve the pixel size. 10-9. They are very small, about 40,000 times smaller than the width of an average
should travel with more velocity than the wave front in the core (denser medium). But human hair. Based on Nano meters, i.e., considered as basic principle, chemistry, health
Used in the manufacture of low-cost flat panel displays.
Cutting tools made of Nano materials are tougher and harder. sciences, material science, space programs and engineering applications are designed.
with higher velocity than the other part.
So the part of wave front travelling in cladding medium lost in the form of radiation leads to Nano technology is used for the manufacture of high energy density batteries.
Nano materials are sued to produce high power magnets. Organic Nano materials (fullerenes)
bending losses. Inorganic Nano materials
Used to improve fuel efficiency in auto mobiles.
Fig:Block Diagram of Optical fiber communication link Used to manufacture aerospace components.
2. Explain Bottom-up and Top-down fabrication with examples.
Optical fiber is an ideal communication medium by systems that require high data capacity, Used to produce longer lasting satellites.
fast operation and to travel long distances with a minimum number of repeaters. Used to produce medical implants. Materials will be fabricated by using any one of the following approaches.
Encoder: It is an electronic system that converts the analog information signals, such as voice Used in the preparation of Nano drugs.
Bottom up: Materials and devices are built from molecular components which
of telephone user, in to binary data. The binary data consists of series of electrical pulses. assemble chemically using principles of molecular recognition.(Refers to build up
Transmitter: Transmitter consists of a driver which is a powerful amplifier along with light Part- B (Descriptive- 10marks) Nano material from bottom i.e. atom by atom, cluster by cluster)
source. The o/p of amplifier feeds to light source, which converts electrical pulses in to light
pulses. 1. Explain the basic concepts, origin and importance of Nanotechnology.
Source to Fiber Connector: It is a special connector that sends the light from sources to fiber.
The connector acts as temporary joint b/w the fiber and light source, misalignment of this joint, Nano means 10-9 i.e., A Nanometer (nm) is one thousand millionth of the meter (i.e. 10-
9
leads to loss of signal., m)
Fiber to Detector Connector: It is also temporary joint, which collects the source from fiber. Atoms are extremely small and the diameter of a single atom can vary from 0.1 to 0.5
Receiver: Receiver consists of a detector followed by amplifier. This combination converts UNIT-5 :Science & Technology of Nano Materials nm depending on the type of the element. The radius of the atom can be half the distance
light pulses in to electrical pulses. between neighboring atoms when they present in the solid phase.
Decoder: Electrical pulses containing information are fed to the electronic circuit called Part-A (SAQ-2Marks) At the Nano-scale, materials exhibit different or New Properties, changed properties
decoder. Decoder converts binary data of electrical pulses in to analog information signals. include grater material strength, enhanced reactivity, better catalytic functioning and
1. Define the terms a) Nano Materials b) Nano Science c) Nano Technology higher conductivity.
16) Write a short note on attenuation in optical fibers. The first concept related to Nano technology was proposed by the scientist Richard
a) Nano Materials: Nano materials can be defined as the materials which have structured
Usually, the power of light at the output end of optical fiber is less than the power launched at Components with size less than 100 nm at least in one dimension. to Feynman, all materials are composed of grains, which in turn comprise of many
the input end, then the signal is said to be attenuated. b) Nano Science: Nano Science can be defined as the study and manipulation of materials atoms.
Attenuation: It is the ratio of input optical power (Pi) in to the fiber to the power of light at atomic, molecular and micro molecular scales, where the properties different from Nano materials can be defined as the materials which have structured components with
coming out at the output end (Po). those at bulk scale. size less than 100 nm at least in one dimension. Example: Sol-Gel process
c) Nano Technology: Nano Technology can be defined as the design, characterization,
10 Pi / Po db/km. Nano Science can be defined as the study and manipulation of materials at atomic, Sol-Gel process:
Attenuation is mainly due to Production and application of structures, devices and system by controlling shape and molecular and micro molecular scales, where the properties different from those at Bulk
1. Absorption. Size at the Nano meter scale. scale. This is an example for Bottom-Up approach comes under chemical method.
2. Scattering. In solutions, molecules of Nanometer size are dispersed and move randomly, hence the
3. Bending. 2. Briefly write about surface to volume ratio and its importance in Nano technology.
solutions are clear.

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In colloids, the molecules of size ranging from 20µm to 100µm are suspended in a Due to increase in chemical activity, Nano-materials can be used as catalyst.
solvent. Nano materials contains small particles may be useful in hydrogen storage devices in
When mixed with a liquid, colloids look cloudy or even milky. A colloid that suspended metals.
iii) Optical Properties:
- hat keep their shape. Depending upon the particle site, different colours are seen i.e., Gold Nano spheres of
- 100 nm appears orange in colour while 50 nm Nano spheres appears green in colour.
c) Growth of particles d) Agglomeration of particles. The linear and non linear optical properties of materials can change with its size i.e.,
The rate of hydrolysis and condensation reactions are depends on various factors such Nano crystalline systems have novel optical properties.
as pH, temperature, molar reaction, catalyst and process of drying. iv) Electrical Properties:
Under proper conditions, fine Nano particles are produced. The change in electrical properties in Nano materials is electrical conductivity increases
with reduction in particle size.
Top down: Nano objects are constructed from larger entities without atomic level control. v) Magnetic Properties:
(Refers to slicing or successive cutting of Bulk material in to Nano sized particles.)
The strength of the magnet, coercively and saturation magnetization values increases
Under these two approaches any one of the three following methods will be employed with decrease in the grain size.
for material fabrication. Small particles are more magnetic than the bulk material.
vi) Mechanical Properties:
1. Chemical Methods:
Sol-gel processes Materials made up of with small grains have more strength.
Chemical combustion Because of the Nano size, many of the mechanical properties such as hardness, elastic
Spray pyrolysis modules, scratch resistance, fatigue strength are modified.
2. Mechanical Methods: Super plasticity is achieved with help of Nano technology (i.e. poly crystalline materials
Grinding exhibit very large texture deformations without necking or fracture).
Milling
Mechanical alloying 5. Explain SEM and EDAX techniques for characterization of Nano materials.
Scanning electron Microscopy (SEM): Working:
3. Physical Methods:
Electrical wire explosion method The image of the sample in SEM is produced by scanning the sample with a focused Electron source produces a stream of monochromatic electrons.
Chemical vapour deposition electron beam and detecting the secondary/back scattered electrons. Electrons are attracted and travel through anode there by attains directionality.
Laser ablation When electron beam is incident on surface of bulk material, scattered electrons carries Condenser lens eliminates high angled electrons from the beam so electron beam
Example: Chemical Vapor Deposition (CVD) information. becomes thin and coherent.
Chemical Vapor Deposition (CVD): 3. Explain the different properties of Nano materials based on surface to volume ratio When electron beam is incident on surface of Nano material, the electrons are A set of coils acts as electro static lens, scans and weeps the beam in grid fashion and
(Or) Explain the difference in properties of a material on Nano and in bulk scale. transmitted then such electrons are utilized for sample analysis. This technique is allowed to pass through objective lens in wide way.
This is an example for Top-Down approach comes under Physical method. known as Transmission electron Microscopy (TEM). Then such a beam of electrons strikes the sample, interaction takes place in smooth way
In this method, Nano particles are deposited from gas phase. Materials are heated to Nano materials have properties that are different from those of bulk materials. This is and this process is displayed on CRT.
form a gas and then allowed to deposit on a solid surface, usually under vaccum due to increase in surface to volume ratio and the change in inter planar spacing. Nano This process is repeated several times i.e. 30times/Sec to get accurate results.
condition. materials properties are depend on their size & structure. Applications: SEM gives useful information on
This deposition may be either physical/chemical. Starting from bulk, the first effect of reducing particle size is to create more surface 1. Topography: Surface features of the object.
In deposition by chemical reaction new product is formed. Production of pure metal sites i.e. surface to volume ratio increases. As a result inter atomic spacing decreases 2. Morphology: Shape, Size and arrangement of particles.
powders is also possible using this method. with size and change in surface pressure shows effect on material properties. 3. Composition: Composition and their relative ratio.
CVD can also be used to grow surfaces. The object to be coated is placed inside the Then the properties such as physical, chemical, Optical, Electrical, Magnetic and 4. Crystallographic Information: Arrangement of atoms and their order.
chemical vapour and may react with substrate atoms. Mechanical properties are changed with size. Energy Dispersive X-Ray analysis (EDAX/EDX) :
Then the atoms or molecules grow on the surface of the substrate depends on alignment i) Physical Properties: This technique is used for identifying the Elemental composition of the sample.
of atoms or molecules of the substrates. The first effect of reducing particle size is to create more surface sites i.e., surface to volume EDX system works an integrated feature of SEM.
ratio increases. This changes the surface pressure and results a change in the inter particle Principle:
spacing. During EDX analysis, the sample is bombarded with electron beam inside the SEM.
As a result, the thermodynamic properties may change for example melting point decreases The bombarded electrons collide with the specimen atoms and show the alignment of
with size. the sample in the form of spectrum.
ii) Chemical Properties: The spectrum intensity depends on energy and speed of the electrons used for collision
Increase in surface to volume ratio & variations in geometry have a strong effect on with the sample.
catalytic properties i.e., increases the chemical activity of the material During the collisions between electrons and sample atom own electrons, some of the
inner shell electrons are ejected and those places are occupied by outer electrons.
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Thus the transfer of outer electrons gives some of its energy by emitting an X-ray.
The sample EDX spectrum is shown in figure.

Then SEM/TEM technique is used for complete analysis.

Applications of EDX:
1. Classification of materials.
2. Structural analysis
3. Composition investigation.
4. Failure and defect analysis.
5. Identification of corrosion and oxidation problems.
6. Examination of surface Morphology.

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