RELATIVITY

The theory of relativity usually encompasses two theories by Albert

Einstein (1879 – 1955). The theories are Special relativity and
general relativity. Albert found that measurements of space and
time depend on the motion of the observer.

Relativity refers to the way physical measurements made in a given

reference frame are related to measurement in another reference
frame.
Reference frame- it is a space in which we are making observation and
measuring physical quantities. It is a set of coordinate system at rest
relative to each other
Types of reference frames
• Inertial reference frames: These are reference frames in which Newton’s
first law holds. i.e an inertial reference frame is either at rest or in motion
with a constant velocity
• Non- inertial frames: it is a reference frame that is accelerating, either in
a linear fashion or rotating around some axis.

Examples: Label the types of reference frames

• A train moving with constant velocity
• A rotating merry-go round
• A turning car moving with constant velocity
• The rotating earth
The principle of relativity state that the basic laws of physics are the same in all
inertial reference frames.
The Galilean transformation
• It is a method of transforming equivalent quantities (such as position and
velocity) from one inertial reference frame to another
• Galilean transformation equation for position
X = X’ + Vt
Y = Y’
Z = Z’
• Galilean velocity transformation equation for of Particle in a reference frame
Ux = U’x + V
Uy = U’y
Uz = U’z
QUESTIONS
• A boat that is initially stationary begin to move with a velocity of 10 m/s with
respect to X- axis in the +ve direction. Let the water on which it moves, be
reference frame 1 and the boat represent refence frame 2. Assume that
reference frame 1 is always stationary and at t = 0 sec, the two reference
frames coincides, if we are in reference frame 2 and an event takes place by
the boat at point (X2 = 5, Y2 = 0, Z2 = 0) after the boat travelled for 120 secs.
Find the equivalent position of this event in ref frame 1.

• At t = 0 sec, two reference frames consisting of XYZ plane coincides such that
the origin of one is found at the origin. However, as time progresses, the
second reference frame moves in the positive direction along X- axis with
velocity of 25 m/s while the first frame remains stationary. At time of t = 10
seconds, a particle within reference frame 2 has a velocity given by vector U =
(10,0,0) m/s. find the equivalent velocity U of the particle with respect to
reference frame 1
 Einstein Postulates
Einstein develop the theory of special relativity from two main
postulates
• Postulate one: The principle of relativity - The basic laws of
physics are the same in all inertial reference frames.
• Postulate two: Constancy of the speed of light - Light can move
through empty space and without the presence of a medium.
Light travels through empty space with constant velocity C that is
independent of the speed of observers or source of light
The special theory of relativity deals with inertial frames and the
general theory deals with non -inertial (accelerating) reference
frames.
 Simultaneity
• The time interval between two events and the simultaneity of two
events depends on the observer’s reference frame. An event is
something that happens at a particular place at a particular time. Two
events are said to occur simultaneously if they occur at exactly the
same time.

∆�0
• ∆� = = �∆�0
�2
1− 2
�
�
• ∆�0 = 2
�
• Where � is the length contraction constant.
 Lorentz transformation
• Lorentz used Einstein’s postulate to establish new relationship
between space-time coordinate in inertial frames.
• Lorentz transformation is a mathematical method of relating quantities
between inertial reference frames while utilising the special theory of
relativity.
• X = �(x’ + Vt)
• Y = Y’
• Z = Z’
�′ +�
•�= ��′
1+ 2
�
 QUESTION
• A space ship takes off from the earth and travels with a velocity 0.7 c
along the X-axis. It then releases a missile straight ahead that moves
with a velocity of 0.8 c with respect to the space ship. Calculate the
speed of the missile with respect to the earth.
Consequences of Lorentz transformation
1. Length contraction – it is the phenomenon of a decrease in length of an object as
measured by an observer which is travelling at any non -zero velocity relative to the
object.
�2 �0
� = �0 1 − =
�2 �
QUESTIONS
• A spaceship flies past Earth at a speed of 0.990C. A crew member on board the
spaceship measure its length, obtaining the value 400 m. what length do
observers on earth measure

• Suppose a space has a length of 50 m while it is stationary on earth. Find the

velocity that is required to decrease the length of the ship to 10 m.
 2. Time dilation
• This is the difference of elapsed time between two events as measured by
observers either moving relative to each other or differently situated from
gravitational mass or masses. It explains that moving clock runs slowly

• The greater the mass of an object, the more energy is required to

accelerate that object to a high velocity. Ordinary macroscopic objects have
velocities much smaller than the speed of light so, time dialation is difficult
to measure.
• Elementary particles on the other hand have very small masses and
require considerably less energy to accelerate them to high speeds.
Therefore, time dialation for subatomic particles is easier to measure.
Muon is one of such elementary particles that is unstable and decays
rather quickly. A muon lifetime while at rest is 2.2��. according to the
equation of time dialation, when muon travels at high velocities, its
lifetime should increase because time slows down for object moving
very fast as compared to their stationary counterparts.
• The time interval ∆�0 between two events that occur at the same place (X’1 = X’2)
in S’ is measured to be
∆�0 = t’2 – t’1 ∆�0
∆� =
�2
1− 2
�
QUESTION
• If the muon is accelerated to a speed of 70 % of the speed of light in a vacuum,
find the lifetime of the muon at this speed.
• A spaceship just returned to earth from a ten year long voyage (according to
observers on earth), if the spaceship velocity was 0.75c, how many years have
elapsed for the crew on the ship
• A light year is defined as the distance light would travel in one year. If a spaceship
can travel at a velocity of 0.99c, find the time it would take for a spaceship to travel
50 light years by using
(a) Classical physics and (b) using theory of relativity
 ATOMS
• All matter is composed of atoms.

• Smallest particle into which an element can be divided and still be

the same substance.

• All substances are made of atoms.

• Atoms are small particles that cannot be created or destroyed.

• Atoms of the same element are exactly alike.

• Atoms join with other atoms to make new substances

• Atoms are an ordered collection of various subatomic particles. The central nucleus
contains the protons and neutrons, around this are electrons
• AMU stands for Atomic Mass Unit, the unit used to measure the mass of protons and
neutrons.
ØProtons
• positively charged particles
• found in the nucleus
• mass is 1 AMU
Ø Neutrons
• no charge (neutral)
• found in the nucleus
• mass is 1 AMU
Ø Electrons
• Negatively charged
• Found around the nucleus in energy levels within the electron cloud.
• Mass is very small, almost zero
Atoms are neutral because the number of protons equals the number of electrons.
• The atomic number is the number of protons

• The atomic mass is equal to the number of protons and neutrons

• Electrons in an atom can only exist in certain energy levels

• Electrons on the outermost energy level are called valence electrons and
determine how the atom will react with other atoms

• Electrons reside in “orbitals” surrounding the nucleus of the atom.

• There are four types of electron orbitals: s, p, d, and f. An orbital describes

the probability of finding the electron at a certain location around the nucleus
 Photons
• A photon is the discrete Packets or quantum of electromagnetic radiation. It
is the basic unit of all light.
• Photons are always in motion and, in a vacuum, travel at a constant speed to
all observers of 2.998 x 108 m/s. This is commonly referred to as the speed of
light, denoted by the letter c.
• Energy of a photon= hf
Planck’s constant: h = 6.626 x 10-34 J s
Questions

1. Find the energy of the following;

Ø4.3 x 1013 Hz (v) light (6980 nm = 6.98 μm).
Ø670 nm (λ) diode laser.
ØViolet light from a mercury lamp has a wavelength of 436 nm
2. The earth receives 1.4 KW of energy from the sun, if it is assumed
that the sunlight consist of monochromatic radiation of wavelength
600 nm, how many photons arrive at the earth every second

3. A radio station emits waves of frequency 96 MHZ at a rate of 100

KW. Calculate the number of photons emitted per second.
 Absorption and emission of light
• Atoms and molecules absorb and emit light in the ultraviolet
(UV), visible (vis), infrared (IR), and microwave (μwave)
regions of the electromagnetic spectrum.
• Absorption or emission of light in the UV and visible regions
involves movement of electrons in the atom or molecule.
• One reason UV light is so damaging is that the light has
enough energy to break chemical bonds—biological and
chemical systems
Einstein model of photoelectric effect
• Light is not waves but energy “packets” (“photons”) each photon has
energy = hf.
• This demonstrate the particle nature of light.
• In Photoelectric effect, Photoelectron is ejected (instantly) through
the complete absorption of one photon.
• hf = KE + φ
• KEmax = hf – φ (recall: KEmax = eVo)
• eVo = hf – φ
Questions
• Calculate the incident photon energy when sodium is illuminated by
the radiation of wavelength 150 nm. (give your answer in eV)
• A metal having a work function of 5.76 eV is illuminated with
radiation of 7.88 eV. The kinetic energy of the electrons emitted from
the metal surface is………………..
• If a photon of wavelength 525 nm hit a metallic cesium (work
function is 3.43 x 19−19 J. what is the velocity of the photoelectron
produced.
• What is the frequency of a light wave whose wavelength
is 5.00 � 10−7 m and velocity is 3.00 � 108 m/s
 Semiconductors
• Materials that permit flow of electrons are called conductors (e.g., gold,
silver, copper, etc.).
• Materials that block flow of electrons are called insulators (e.g., rubber,
glass, Teflon, mica, etc.).
•Materials whose conductivity falls between those of conductors and
insulators are called semiconductors.
•Semiconductors are “part-time”conductors whose conductivity can be
controlled
Conductors
• Gold, Aluminium, Silver, Copper, all these metals allow an electric current to flow
through them.
• There is no forbidden gap between the valence band and conduction band which
results in the overlapping of both the bands. The number of free electrons available
at room temperature is large.
Insulators
• Glass and wood are examples of the insulator. These substances do not allow
electricity to pass through them. They have high resistivity and very low conductivity.
• The energy gap in the insulator is very high up to 7eV. The material cannot conduct
because the movement of the electrons from the valence band to the conduction
band is not possible.
Semiconductors
• Germanium and Silicon are the most preferable material whose electrical properties
lie in between semiconductors and insulators. The energy band diagram of
semiconductor is shown where the conduction band is empty and the valence band
is completely filled but the forbidden gap between the two bands is very small that
is about 1eV. For Germanium, the forbidden gap is 0.72eV and for Silicon, it is 1.1eV.
Thus, semiconductor requires small conductivity.
• Energy Band Theory
• According to Bohr’s theory, every shell of an atom contains a discrete
amount of energy at different levels. Energy band theory explains the
interaction of electrons between the outermost shell and the innermost
shell. Based on the energy band theory, there are three different energy
bands:
• Valence band
• Forbidden energy gap
• Conduction band
 Classification of Energy Bands
Valence Band
• The electrons in the outermost shell are known as valence electrons. These valence
electrons contain a series of energy levels and form an energy band known as valence
band. The valence band has the highest occupied energy.
Conduction Band
• The valence electrons are not tightly held to the nucleus due to which a few of these
valence electrons leave the outermost orbit even at room temperature and become
free electrons. The free electrons conduct current in conductors and are therefore
known as conduction electrons. The conduction band is one that contains conduction
electrons and has the lowest occupied energy levels.
Forbidden Energy Gap
• The gap between the valence band and the conduction band is referred to as
forbidden gap. As the name suggests, the forbidden gap doesn’t have any energy and
no electrons stay in this band. If the forbidden energy gap is greater, then the valence
band electrons are tightly bound or firmly attached to the nucleus. We require some
amount of external energy that is equal to the forbidden energy gap.
 Types of Semiconductors
Semiconductors can be classified as:
• Intrinsic Semiconductor
• Extrinsic Semiconductor
Intrinsic Semiconductor
• An intrinsic type of semiconductor material is made to be very pure
chemically. It is made up of only a single type of element
• Germanium (Ge) and Silicon (Si) are the most common type of intrinsic
semiconductor elements. They have four valence electrons (tetravalent).
They are bound to the atom by covalent bond at absolute zero
temperature.
• When the temperature rises, due to collisions, few electrons are
unbounded and become free to move through the lattice, thus creating
an absence in its original position (hole). These free electrons and holes
contribute to the conduction of electricity in the semiconductor. The
negative and positive charge carriers are equal in number.
• The thermal energy is capable of ionizing a few atoms in the lattice, and
hence their conductivity is less
• Extrinsic Semiconductor
• The conductivity of semiconductors can be greatly improved by
introducing a small number of suitable replacement atoms called
IMPURITIES. The process of adding impurity atoms to the pure
semiconductor is called DOPING. Usually, only 1 atom in 107 is replaced
by a dopant atom in the doped semiconductor. An extrinsic
semiconductor can be further classified into:
• N-type Semiconductor
• P-type Semiconductor
N-Type Semiconductor
• Mainly due to electrons
• Entirely neutral
• I = Ih and nh >> ne
• Majority – Electrons and Minority – Holes
• When a pure semiconductor (Silicon or Germanium) is doped by pentavalent
impurity (P, As, Sb, Bi) then, four electrons out of five valence electrons bonds
with the four electrons of Ge or Si.
• The fifth electron of the dopant is set free. Thus, the impurity atom donates a
free electron for conduction in the lattice and is called “Donar“.
• Since the number of free electron increases by the addition of an impurity, the
negative charge carriers increase. Hence, it is called n-type semiconductor.
P-Type Semiconductor
• Mainly due to holes
• Entirely neutral
• I = Ih and nh >> ne
• Majority – Holes and Minority – Electrons
• When a pure semiconductor is doped with a trivalent impurity (B, Al, In,
Ga ) then, the three valence electrons of the impurity bonds with three of
the four valence electrons of the semiconductor.
• This leaves an absence of electron (hole) in the impurity. These impurity
atoms which are ready to accept bonded electrons are called “Acceptors“.
• With the increase in the number of impurities, holes (the positive charge
carriers) are increased. Hence, it is called p-type semiconductor.
Thank you