Advent of Modern Physics Notes

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ADVENT OF MODERN PHYSICS

CHAPTER – 17                                                                            ADVENT OF MODERN PHYSICS

Qs. What are the basic postulates of Einstein’s Special theory of relativity. Also give the consequences of the theory.

EINSTEIN’S SPECIAL THEORY OF RELATIVITY

Introduction
Einstein examine the motion of objects in frames of references moving relative to one another. On the basis of his experimental results he proposed a special theory of relativity in the year 1905. This theory is valid specially for inertial frames and is to be modified into a general theory for accelerated frames of reference.

BASIC POSTULATES
The Einstein’s special theory of relativity is based on two assumptions known as the postulates of special relativity. The two postulates are states as follows.

First Postulate
The speed of light was regarded as the universal constant. It means that the speed of light in vacuum is the same for all observers in uniform transnational motion and is independent of the motion of the observer and the source.

Second Postulate
According to this postulate the laws of physics in the frame moving with uniform velocity can be expressed by a single set of mathematical expression.
This postulate points out if some event takes place in any of the frame and the frames are moving with uniform velocity the result of the two frames will be identical. Conversely if the frames are in accelerated motion then the result will not be identical.

MASS ENERGY RELATION
Einstein proved that energy has inertia, which is the property of matter and associated with mass. Thus mass is simply a property attributed to the total energy of the body and only total energy is required to know total mass of the body. Hence in special theory of relativity total energy and mass are related by the famous Einstein’s equation.
E = mc(2)
From this relation between mass and energy it has been predicted that any process that changed the mass by a detectable amount of energy.

Qs. Write a note on Compton Effect

COMPTON EFFECT
In 1926, Arthur Compton studies this phenomenon of change in wavelength. On the basis of his experimental results he proposed a theory based on the idea of photon theory of radiation. Since the detailed study of phenomenon was made by Compton, the effect is now known as the Compton’s Effect.

Definition
The phenomenon in which a photon (hv) strike with stationary electron and after collision both scattered in different direction in such a way v > v is known as Compton Effect.

Consideration
In order to explain this phenomenon we assume that photon strike with a stationary electron and after collision both makes an angle θ and ф with respect to their initial line of motion.

Qs. Write note on Pair Production and Annihilation of Matter.

PAIR PRODUCTION

Definition
The phenomenon in which photon collides with heavy nucleus then two material particles, electron and positron are produced, is called Pair Production.

Explanation
The positron produced during pair production has been identified to be identical with an electron in mass and carries an equal positive charge and is called the anti particle of electron. Since the process of pair production involves the creation of particle and its anti particle, therefore it is also known as materialization of energy. This phenomenon is the practical proof of Einstein’s mass energy equivalence, in which mass and energy of the system remains constant.
For the production of electron and positron 1.02 MeV energy is required. I can be calculated by the following equation
Eo = 2moC(2)
=> Eo = 2 x 9.1 x 10(-33) x (3 x 10(8))2 / 1.6 x 10(-19)
=> Eo = 1.02 x 10(6) cV
=> Eo = 1.02 MeV
If energy of photon is less than 1.02 MeV then this phenomenon cannot produce. If energy of photon is greater than 1.02 MeV then rest of energy is used to accelerate the electron and Positron. The energy conservation in Pair Production demands.
hv = e+ + e + K.E + K.E+
=> hv = moc² + moc² + K.E + K.E+
=> hv = moc² + K.E + K.E+

ANNIHILATION

Definition
The phenomenon in which electron and positron fuse together to form at least two photons, is known as Annihilation of matter.

Explanation
Annihilation is the reverse process of pair production. In Pair Annihilation a particle and one of its anti particle come close enough to be converted completely into radiation energy of the two photons moving in opposite direction conserving the total momentum of the creation and annihilation process. Each photon will have an energy equal to rest mass energy moc of an electron that is equal to 0.51 MeV.
The energy conservation equation for the process will be
(mo)e + c² + K.Ee + (mo)e-c² + (K.E_e = 2hv

Conclusion
The phenomenon of Pair Production and annihilation helps us to conclude that energy and mass are inter changeable.

Qs. Write note on Uncertainty Principle

UNCERTAINTY PRINCIPLE

Introduction
In classical physics we can easily determine the momentum and position of moving body simultaneously with accuracy, that no uncertainties are involved in it. But for a light particle is found that however refined we make our instruments there is a fundamental limitation to the accuracy with which the positron and momentum can be known simultaneously.
This limitation was first expressed by Hersenberg in 1927 and is known as Uncertainty Principle.

Statement
It is impossible to measure with accuracy both positron and momentum of a particle simultaneously.

Consideration
Consider a slit of thickness Δy placed near to a screen. Now a particle bean strikes the slit then after diffraction at very small angle, it reaches at points A.

Proof
As we know that momentum is a vector quantity, therefore, it can be resolved into two components. Consider ΔOAB.
tan θ = Perpendicular / Base
=> tan θ P(y) / P(x)
Since θ is very small, therefore
tan θ ≈ θ
=> θ P(y) / P(x)
=> Py = Px θ ——- (I)
From the condition of interference,
mλ = d sin θ
For first maximum,
m = 1
=> λ = Δy sin θ
But,
sin θ ≈ θ
=> λ = Δy θ
=> θ = λ / Δy
Substituting the value of θ in eq (I)
=> P(y) = P(x) λ / Δy
=> P(y)Δy = P(x) λ
From Debroglie’s wave equation
λ = h / P(x)
=> λP(y)Δy = P(x) h / P(x)
=> P(y)Δy = h
Similarly,
P(x)Δx = h
And,
P(z)Δz = h

Conclusion
The uncertainty principle is of no importance in our daily life because plank’s constant h is very small and so the uncertainties in position and momentum of even light objects are far too small to be experimentally observed.

Qs. State and explain Debroglie’s Hypothesis.

DEBROGLIE’S HYPOTHESIS


Introduction
In 1924, Debroglie proposed an idea called Debroglie’s Hypothesis.

Statement
If light can have particle behaviour then material particles such as electrons and protons etc can also behave in a wave like manner.

Mathematical Form
According to Debroglie’s Hypothesis a particle like electron can possesses a momentum given by
P = mv = h / λ
Where m is the mass of particle. This relation has related the electron a particle and the wave character of a frequency. Thus we can write down the wave length associated with the particle i.e.
λ = h / mv

Conclusion
The Debroglie’s relation was initially developed for the electron but it is valid for all material objects including particles. However for massive materials the associated wavelength is too small to be measured.

Qs. Define and Explain Photoelectric Effect

PHOTOELECTRIC EFFECT


Introduction
In 1887, Hertz discovered the phenomenon of emission of electrons. When ultra violet light falls on certain metals. On the basis of his experimental results, he proposed the phenomenon of photoelectric effect.

Definition
The emission of electrons from a solid or liquid surface when it is subjected to electromagnetic radiation is known as Photo-electric effect.

Experiment
Consider a glass tube in which two electrodes are suspended connected to a positive and negative terminal of a battery. A milliammeter is connected in series with the circuit to detect the flow of current.
When ultra violet rays strike the negative plate, then electrons emit. These electrons are repelled by the negative (-) plate and attracted by the positive plate. Hence, current flows in the circuit. The effect is known as Photoelectric effect.

Maximum K.E of Electrons
The maximum K.E. of electrons can be achieved by reversing the polarity of the circuit. When ultra violet rays strike the positive (+) electrode. The kinetic energy possessed by the electrons can be achieved if it is balanced by the voltage. So we increase the voltage to such an extent that no electrons emit out. At this stage K.E. is maximum and can be calculated by
K.E(MAX) = Voe
=> 1/2 mv² = Voe
Where,
m = mass of electron
e = charge of electron
v = velocity of electron
Vo = voltage of circuit

Results Obtained
The conclusions that were made from the experiment on Photoelectric effect are
1. Increasing the intensity of source of light increases the number of photoelectrons but not the velocity with which it leaves the metallic surface.
2. For each substance, there is a certain frequency called the threshold frequency below which the effect does not occur.
3. The higher the frequency of incident ray, the greater the K.E of electrons.
Photoelectric effect could not be explained on the basis of classical wave theory, because according to the theory:
There should be no threshold frequency because by that time electrons might escape from the metallic surface by absorbing enough energy.
The velocity of photelectrons should depend upon the intensity of the incident ray rather than the frequency.

Qs. Give Einstein’s explanation of the photoelectrons effect on the basis of quantum theory of radiation.

EINSTEIN’S EXPLANATION OF PHOTOELECTRONS EFFECT

Introduction
Albert Einstein was successful in providing an explanation of the photoelectric effect. He proposed his description on the basis of quantum theory of radiation.

Explanation
Einstein explained the photoelectric effect on the basis of following postulates.
1. An electron absorbs neither one whole photon or it absorbs none.
2. An electron cannot absorb more than one photon.
3. After absorbing a photon, it acquires energy (hv) equal to photon. The energy is either used up in ejecting the electrons or it dissipates within the metal surface.
4. An electron may lose some of its energy before leaving the metal surface and is ejected with a kinetic energy less than hv.
5. If the energy of the photon is less than the energy required to overcome the forces then the electron will not emit.

Mathematical Expression
The energy of the electron is given as
Total Energy = Work Function + K.E
=> hv = фo + 1/2 mv²
фo = hvo
=> hv = hvo + 1/2 mv²
=> hv – hvo = 1/2 mv²
=> h(v-vo) = 1/2 mv²
Since, K.E = 1/2 mv² = Voe and v = c/λ
=> h [c/λ - c/λo] = Voc
=> hc [1/λ - 1/λ] = Voc
The above equation is known as Einstein’s Photoelectric Equation.

Qs. What is a Photo Cell? Also Write its Uses.

PHOTO CELL

Construction
The Photocell or photo tube consist of an evacuated glass tube fitted with an anode and a concave metallic cathode of an appropriate surface.
The material of the cathode can be chosen to respond to the frequency range over which the photocell operates.

Working
When light of suitable frequency fall on the cathode photoelectrons are emitted which are attracted by the positive anode and current flows in the external circuit. The current would cease to flow if the light beam is interrupted.

USES OF PHOTO CELL

1. Simple Photo Cell
A simple photo cell can be used in any situation where beam of light falling on a cell is interrupted or broken. Examples are given below.
To count vehicles passing a road or items running on a conveyer belt.
To open door automatically.
To operate burglar alarm etc.

2. Photo Conducting Cell
In this cell internal photoelectric effect liberates free charge carrier in a material and its electrical conductivity increases as much as 10,000 times, Its uses are
For detection and measurement of infrared radiations where the wavelength is of the order of 10(-6) m.
As relays for switching on artificial lighting, such as streetlights.

3. Photo Voltaic Cell
Such cells are used as exposure meters to set the aperture of the camera.

4. Other Uses
Photocells are used for the production of pictures in television cameras and the sound tracks on motion pictures. The sound information is stored on the film in the form

Statement
Radiant energy comes out in discreat amounts or guanta of energy. The energy E content of each quantum was directly proportional to the frequency v.

Mathematical Form
E ∞ v
=> E = hv ——– (I)
Where h = Plank’s constant = 6.63 x 10(-34) Js. Since,
c = vλ
=> v = c / λ
Thus equation (I) becomes
E = hc / λ
Where,
c = velocity of light = 3 x 10(8) m/s.
λ = wavelength of radiation
The energy of ‘n’ photons is given by
E = nλy
Where,
n = 0, 1, 2, 3 ………