ESSENTIALS OF PHYSICS

 

DEFINITION

Physics is the science aimed at describing the fundamental aspects of our universe. Physics is the branch of Science concerned with the nature and properties of matter and energy. The Physics is derived from the Greek word Physica means nature. Its Sanskrit equivalent is Bhautiki that is used to refer to the study of the physical world. We can broadly describe physics as a study of the basic laws of nature and their manifestation in different natural phenomena. Physics gives the base of all Technologies in the World and is the branch of Science that deals with all types of matter from micro to macro bodies. Physics concentrates on explaining the interaction of Matter with Energy. One important purpose of Physics is to design and conduct experiments to measure and compare physical quantities. Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. A scientist who specializes in the field of Physics is called a Physicist.

 

SCOPE

The subject matter of Physics includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms. The scope of Physics is very large. It covers from Nano sized objects to Astronomical Bodies. It explains Physical Properties in terms of Units by performing significant experiments. Physics is the study of energy, matter, and their interactions. It's a very broad field because it is concerned with and energy at all levels-from the most fundamental particles of matter to the entire universe. Some people would even argue that physics is the study of everything! Physics can help you understand just about everything in the world around you. That's because everything around you consists of matter and energy.

Basically, there are two domains of interest: (i) Macroscopic, (ii) Microscopic

The macroscopic domain includes phenomena at the laboratory, terrestrial and astronomical scales. The microscopic domain includes atomic, molecular and nuclear phenomena.

For example, consider a smart phone , physics describes how electric current interacts with the various circuits inside the device. This knowledge helps engineers select the appropriate materials and circuit layout when building the smart phone. Next, consider a GPS. Physics describes the relationship between the speed of an object, the distance over which it travels, and the time it takes to travel that distance. When you use a GPS device in a vehicle, it utilizes these physics relationships to determine the travel time from one location to another.

           

MEASUREMENTS AND UNITS

Measurements and units are fundamental aspects of Physics that allow us to quantify and express physical quantities. In Physics, measurements involve the process of determining the magnitude or value of a particular physical quantity, such as length, time, mass, temperature, or electric current. Units, on the other hand, provide a standardized way to express these measurements. They serve as reference points for comparison and ensure consistency and uniformity in communication and calculations.

Measurement : In our daily life, we need to express and compare the magnitude of different quantities; this can be done only by measuring them. Measurement is the comparison of an unknown physical quantity with a known fixed physical quantity.

Unit :  The known fixed physical quantity is called unit.

Or

The quantity used as standard for measurement is called unit.

For example, when we say that length of the class room is 8 metre. We compare the length of class room with standard quantity of length called metre.

Length of class room = 8 metre

Q = nu

Physical Quantity = Numerical value   x  unit

 Q = Physical Quantity

                        n = Numerical value

                        u = Standard unit

e.g., Mass of stool = 15 kg

Mass = Physical quantity

    15 = Numerical value

   Kg =  Standard unit

Means mass of stool is 15 times of known quantity i.e., Kg.

Characteristics of Standard Unit

 A unit selected for measuring a physical quantity should have the following properties:

(i) It should be well defined i.e., its concept should be clear.

(ii) It should not change with change in physical conditions like temperature, pressure, stress etc.

(iii) It should be suitable in size; neither too large nor too small.

(iv) It should not change with place or time.

(v) It should be reproducible.

(vi) It should be internationally accepted.

Classification of Units                      

Units can be classified into two categories:

1 . Fundamental Physical Quantity / Unit :

            It is an elementary physical quantity, which does not require any other physical quantity to express it it means it cannot be resolved further in terms of any other physical quantity. It is also known as Fundamental physical quantity.The units of fundamental physical quantities are called fundamental units.

For example, in M. K. S. system, Mass, Length and Time expressed in kilogram, metre and second respectively are fundamental units.

2 . Derived Physical Quantity / Unit :

            All those physical quantities, which can be derived from the combination of two or more fundamental quantities or can be expressed in terms of basic physical quantities, are called derived physical quantities. The units of all other physical quantities, which can be obtained from fundamental units, are called derived units.

For example, units of velocity, density and force are m/s, kg/m3, kg m/s2 respectively and they are examples of derived units.

Systems of Units: CGS, FPS, MKS, SI

For measurement of physical quantities, the following systems are commonly used:

 (i) C.G.S system: In this system, the unit of length is centimetre, the unit of mass is gram and the unit of time is second.

(ii) F.P.S system: In this system, the unit of length is foot, the unit of mass is pound and the unit of time is second.

(iii) M.K.S: In this system, the unit of length is metre, unit of mass is kg and the unit of time is second.

(iv) S.I System: This system is an improved and extended version of M.K.S system of units. It is called international system of unit.

S.No	Name of Physical Quantity	Unit	Symbol
1	Length	Metre	m
2	Mass	Kilogram	Kg
3	Time	Second	s
4	Temperature	Kelvin	K
5	Electric Current	Ampere	A
6	Luminous Intensity	Candela	Cd
7	Quantity of Matter	Mole	mol

 

 

 

Motion of Objects: Newtonian Mechanics and Relativistic Mechanics Perspectives

The study of motion is a fundamental aspect of Physics, and two significant frameworks that describe the motion of objects are Newtonian mechanics and Relativistic mechanics. While Newtonian mechanics provides an accurate description of everyday objects' motion at low speeds, relativistic mechanics offers a more comprehensive understanding when objects approach the speed of light.

Newtonian Mechanics :

A branch of mechanics that deals with concepts of Newton's law of motion as distance, time, and mass in a period of time are known as Newtonian mechanics. Newtonian mechanics, formulated by Sir Isaac Newton in the 17^th century, is based on three fundamental laws: the law of inertia, the relationship between force and acceleration, and the principle of action and reaction.

Newtonian mechanics is also termed, classical mechanics. This theory is classified into two terms as Newtonian kinematics and Newtonian dynamics. In dynamics Newtonian mechanics, mathematical illustrations and results derive caused due to motion, while kinetic Newtonian mechanics provides results without any motion.

Newton proposed three basic laws of motion which are commonly known as Newton’s laws of motion.

1. Newton's First law : Inertia : Every body continues in its state of rest or of uniform motion in a straight line, unless it is compelled to change that state by an external force. This tendency to resist changes in a state of motion is inertia.

Example : The electric fan continues to move for a period after electricity is turned off.

2. Newton's Second law : Force : The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.

 

 

 

 

 

Example : When we kick the ball we exert force in a specific direction, which is the direction the ball will move. In addition, the more force we apply to it and the further away the ball is.

3. Newton's Third law : Action & Reaction : To every action there is always an equal and opposite reaction. Note that action and reaction which always in pairs act on different bodies.

Example : The motion of a jet engine produces thrust and hot exhaust gases flow out the back of the engine, and a thrusting force is produced in the opposite direction.

Newtonian mechanics accurately describes object' motion at everyday speeds providing a simple understanding of motion. It has been successfully applied to a wide range of scenarios, from calculating the trajectory of projectiles to analysing the orbits of celestial bodies. However, as objects approach speeds comparable to the speed of light, Newtonian mechanics fails to provide an accurate description. At such high velocities, the predictions made by Newtonian mechanics diverge significantly from the observed behaviour of objects. This is where relativistic mechanics, developed by Albert Einstein in the early 20^th century, comes into play.

Relativistic Mechanics :

The term “relativity” refers to the fact that physical measurements are always made relative to some chosen reference frame. Einstein’s work on relativistic mechanics comprised two major advances. The first advance is the 1905 Special Theory of Relativity which refers to nonaccelerating frames of reference. The second major advance was the 1916 General Theory of Relativity which considers accelerating frames of reference and their relation to gravity.  

The main idea is that motion is always relative to some frame of reference. For example, when you are walking down the sidewalk, you are moving relative to the stationary ground, which is a frame of reference.

In Special theory of relativity, reference frames are used to specify the relationship between a moving observer and the phenomenon under observation. A frame of reference is a system of coordinates used to identify a location or direction in space. A frame of reference is needed to describe an object’s motion. There are two types of frames of reference: inertial and non-inertial.

An inertial frame of reference is a frame where Newton’s law holds true. That means if no external force is acting on a body it will stay at rest or remain in uniform motion.

A non-inertial frame is a frame that is accelerated with respect to the assumed inertial frame of reference. Newton’s law will not hold true in these frames.

First Postulate      : The laws of Physics are the same in every inertial frame of reference.

Second Postulate : The speed of light in a vacuum is the same for all the observers, regardless of the motion of the source or the observer.

The General Theory of Relativity concerns what would happen when objects or reference frames are accelerated. One concept is that all frames of reference undergoing the same acceleration are equivalent to each other. Magnetism is a relativistic effect, and you can see this demonstrated via generators.

In conclusion, the study of motion of objects is approached through two major frameworks: Newtonian mechanics and relativistic mechanics. Newtonian mechanics accurately describes motion at everyday speeds, while relativistic mechanics provides a more comprehensive understanding when objects approach the speed of light. Both frameworks have their respective domains of applicability, with Newtonian mechanics being highly successful in describing macroscopic objects and relativistic mechanics being essential for understanding the behaviour of objects at high speeds. The combination of these two perspectives allows physicists to explore and explain the complexities of motion in the universe.

 

LAWS OF THERMODYNAMICS AND SIGNIFICANCE

            Thermodynamics in physics is a branch that deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter. Thermodynamics is only concerned with macroscopic (large-scale) changes and observations. All of thermodynamics can be expressed in terms of four quantities -Temperature (T)-Internal Energy (U) -Entropy (S)-Heat (Q).

There are four laws of thermodynamics are as follows :

1.      Zeroth law of thermodynamics

2.      First law of thermodynamics

3.      Second law of thermodynamics

4.      Third law of thermodynamics

 

 

 

1. Zeroth Law of Thermodynamics

The Zeroth law of thermodynamics states that if two bodies are individually in equilibrium with a separate third body, then the first two bodies are also in thermal equilibrium with each other.

This means that if system B is in thermal equilibrium with system A and system C is also in equilibrium with system A, then system B and C are also in thermal equilibrium with each other .

Ex : A cup of soup kept in a refrigerator overnight is said to be in thermal equilibrium with the air in the refrigerator. As heat no longer flows from the cup of soup (one source) to the refrigerator (the other source) or back

Significance : It tells about the state of thermal equilibrium of the system. It defines the exchange of heat and also defines the temperature of the system.

2. First Law of Thermodynamics

            The first law is also called as law of conservation of energy, states that energy can neither be created nor destroyed, but it can be changed from one form to another. When a definite amount of work is done, a certain amount of heat is produced and vice versa. The equivalence is given by a constant J, where J is a constant called mechanical equivalent. Thus, W= JH (J=4.2 joule/calorie or 4.2x10⁴ joule/kilo calorie).

The second statement of this law is a particular form of the general law of conservation of energy. Suppose an amount of heat dQ is supplied to a system. This is used in the following three parts:

(i) a part is used in raising the temperature of the system which is equivalent of increasing its internal kinetic energy (dU_K)

(ii) a part is used in doing internal work against molecular attraction which is equivalent of increasing its potential kinetic energy (dU_p)

(iii) the rest part is used in doing external work (dW)

dQ = dU_K + dU_p + dW

dQ = dU + dW

Where dU=dU_K + dU_p= increase in total energy of the system.

Ex : Throwing a ball from the top of a building to the ground (potential energy to kinetic energy), Photosynthesis reaction ( light energy to chemical energy), Combustion of wood (chemical energy to heat energy), etc.

 

Significance :

(i) Heat is a form of energy in transit,

(ii) Energy is conserved in thermodynamic system, and

(iii) Every thermodynamic system in equilibrium state possesses internal energy which is a function of the state of the system.

3. Second Law of Thermodynamics

The Second Law of Thermodynamics states that the state of entropy of the entire universe, will always increase over time.

For a spontaneous process, ΔS_system + ΔS_surroundings > 0.

This law can be stated in the following two ways :

Kelvin's statement of second law :

We know that a heat engine takes heat from the source, converts a part into mechanical work and the balance is rejected to the sink. As the engine absorbs more and more heat from the source, the temperature of source continuously falls and after sometime becomes as that of surroundings. Now no heat flow will be possible. In this case, the engine stops working, i.e., no work can be obtained from the engine. This consideration led Kelvin to state the second law as:

“It is impossible to derive a continuous supply of work by cooling a body to a temperature lower that of the coldest of its surroundings. ”

Clausius statement of second law :

The Clausius statement of second law is based on the working of refrigerator. In refrigerator, the transfer of heat takes place from a cold body to a hot body with the aid of an external agency. No refrigerator so far has been constructed which can transfer heat from a cold body to a hot body without the aid of external agency. This consideration led Clausius to state the second laws as:

"It is impossible for a self acting machine unaided by any external agency to convert heat from a cold body to a hot body."

Ex : Air leaks from the balloon on its own. The air leaks from the balloon on its own after some time. The air never goes inside the balloon on its own. It is an example of spontaneous process and it  based on the Entropy statement of second law of thermodynamics.

Significance :

1. The entropy change in an isolated system can only be positive or zero.

2. The change in enthalpy conveniently quantifies the heat flow of reactions.

 

4. Third Law of Thermodynamics

            The third law is also called as Nernst law. The third law of thermodynamics states that as the temperature approaches absolute zero, the change in entropy of a pure crystalline substance becomes zero.

LimT –>0  S = 0

The change in entropy is equal to the heat absorbed divided by the temperature of the process.

Ex : Steam/vapors of water are the gaseous forms of water at high temperatures as the molecules within steam are randomly moving, thus it will have high entropy.

Significance :

1. The third law provides an absolute reference point for the determination of entropy at any other temperature.

2. It explains the behavior of solids at very low temperature.

 

ACOUSTIC WAVES AND ELECTROMAGNETIC WAVES

Acoustic waves and electromagnetic waves are two distinct types of waves that propagate through different mediums and have distinct characteristics.

Acoustic Waves :

Acoustics is the science of sound which deals with the process of generation, transmission and reception of sound in a room or in a hall. Acoustic waves, also known as sound waves, are mechanical waves that require a medium, such as air, water, or solids, for their propagation. Sound is a wave phenomenon. Generally, the sound we hear in our day to day life travels through air in the form of longitudinal waves. These waves are produced by the vibration or disturbance of particles in the medium, which creates a series of compressions and rarefactions that travel through the medium. Acoustic waves exhibit properties such as frequency, wavelength, amplitude, and velocity. They can be characterized by their pitch (related to frequency) and loudness (related to amplitude).

A sound wave is similar in nature to a slinky wave for a variety of reasons. First, there is a medium which carries the disturbance from one location to another. Typically, this medium is air; though it could be any materials such as water or steel. Second, there is an original source of the wave, some vibrating object capable of disturbing the first particle of the medium. Third, the sound wave is transported from one location to another by means of the particle interaction. If the sound wave is moving through air, then as one air particle is displaced from its equilibrium position, it exerts a push or pull on its nearest neighbours, causing them to be displaced from their equilibrium position. This particle interaction continues throughout the entire medium, with each particle interacting and causing a disturbance of its nearest neighbours.

Velocity of Sound through various media :

In general, velocity of sound through any medium is

V =

where, E is the modulus of elasticity and p its density.

In Solids

V =

where, Y is the Young's modulus and p its density.

In Fluids

V =

where, K is the bulk modulus of fluids and p its density.

Acoustic waves are responsible for our perception of sound and are extensively used in fields such as music, communication, and medical imaging (ultrasound).

Electromagnetic Waves

            Electromagnetic waves are a form of radiation that travel though the universe. They are formed when an electric field couples with a magnetic field. Both electricity and magnetism can be static but when they change or move together, they make waves. Magnetic and electric fields of an electromagnetic wave are perpendicular to each other and to the direction of the wave. Unlike Acoustic waves, electromagnetic waves do not need molecules to travel. They can travel through air, solid objects, and even space, making them very useful for a lot of technologies. They can travel through a vacuum, such as in the case of light from the sun reaching the earth. Electromagnetic waves encompass a wide range of frequencies, forming the electromagnetic spectrum, which includes radio waves, microwaves, infrared waves, visible light, ultraviolet, X-rays, and gamma rays.

Radio Waves : These types of waves are used to broadcast signals for radio and television. This wave has the longest wavelength. These are having a frequency range of < 3x10¹¹ Hz and are having a Wavelength range of  > 1mm.

Microwaves : These electromagnetic waves are in the use of cooking, radar, telephone, and other signals. These are having a frequency range of 3x10¹¹ – 10¹³ Hz and are having a Wavelength range of  1mm – 25 μm .

Infrared Waves : These waves are sometimes referred as heat waves. It is used widely in night vision goggles. These devices can read and capture the infrared light emitted by our skin and objects with heat. In space, infrared light helps to map interstellar dust. These are having a frequency range of 10¹³ – 10¹⁴ Hz and are having a Wavelength range of  25 μm – 2.5 μm .

Visible Rays : Visible light can be detected by our eyes. Light bulbs, stars, etc., emit visible light. These are having a frequency range of 4 x 10¹⁴ – 7.5 x 10¹⁴ Hz and are having a Wavelength range of  750 nm – 400 nm .

Ultraviolet Rays : The Sun is the main source of ultraviolet radiation. But fortunately, most of it is absorbed in the ozone layer. It causes skin tanning and burns. Scientists use this radiation in fluorescent tubes. These are having a frequency range of 10¹⁵ – 10¹⁷ Hz and are having a Wavelength range of  400 nm – 1 nm .

X-rays : X-rays can be used in many instances. For example, a doctor can use an X-ray machine to take an image of our bones or teeth. Airport security personnel use it to see through and check bags. These are having a frequency range of 10¹⁷ – 10²⁰ Hz and are having a Wavelength range of  1 nm – 1 pm .

Gamma Rays : These are used in medicine to destroy cancer cells. This wave has the shortest wavelength. These are having a frequency range of 10²⁰ – 10²⁴ Hz and are having a Wavelength range of  < 10^-12 m .

In summary, acoustic waves are mechanical waves that require a medium for propagation and are responsible for our perception of sound. Electromagnetic waves, on the other hand, are waves of varying electric and magnetic fields that can propagate through a vacuum and cover a wide range of frequencies in the electromagnetic spectrum. Both types of waves have distinct characteristics and applications in various fields of science, technology, and everyday life.

ELECTRIC AND MAGNETIC FIELDS AND THEIR INTERACTIONS

            Electric and magnetic fields are fundamental components of electromagnetism and play a crucial role in the interactions between charged particles and the transmission of electromagnetic waves.

Electric Field

            An electric field is a region in which an electric charge experiences a force. Faraday introduced the concept of electric field. The electric field E at a point is defined as the electric force F experienced by a positive test charge q₀ placed at that point divided by the magnitude of the test charge.

          The electric field E is a vector quantity and has the same direction as the electric force F. Note that the electric field is due to an external charge and not due to the test charge. The test charge q₀ should, therefore, be so small in magnitude that it does not disturb the field due to external charge. In SI system, the force is in newton and the charge is in coulomb. Therefore, according to equation the electric field has the unit newton per coulomb. The direction of E is same as that of F.

Let us now examine why the test charge q₀ should be infinitesimally small. Fig. (a) shows a uniformly charged metallic sphere with charge q and a test charge q_o (<< q). It means that charge density per unit area is same around points A, B, C and D. The test charge q_o must measure the force F without disturbing the charge distribution on sphere. Fig. (b) shows the situation when q≈q₀. In this case, the presence of the test charge modifies the surface charge density. As result, the electrical force experienced by the test charge q_o will also change, say from F to F´. That is, the force in the presence of the charge different from that in absence. But without q₀ force cannot be measured.

 

 

 

 

b) Redistribution of charge on the sphere when another charge is brought near it.

(a) Uniformly charged metallic sphere and a test charge

 

 

                           

         Let there be a point charge q. A test charge q_o is placed at distance r from q. The force experienced by the test charge is given by

          The electric field is defined as the force per unit charge.

            If q is positive, the field E will be directed away from it. If q is negative, the field E will be directed towards it.

 

 

 

 

 

 

Magnetic Field

            A magnetic field, is a region in which a magnetic material or a moving charged particle experiences a force. Keep a small magnetic needle near a bar magnet. The magnetic needle rotates and stops in a particular direction only. This shows that a force acts on the magnetic needle that makes it rotate and rest in a particular direction only. This force is called torque. The region around the magnetic where the force on the magnetic needle occurs and the needle stops at a specific direction, is called a magnetic field. The direction of magnetic field is represented by magnetic line of forces. As shown in fig., the direction of magnetic needle changes continuously and it takes the curved path while moving from north to south. This curved path is known as magnetic line of forces. Tangent line draw at any point on magnetic line of force, represent the direction of magnetic field at that point. These magnetic line of forces have following properties.

1. Magnetic line of forces always start from north pole and end at south pole of the magnet.

2. These line of forces never intersect each other.

3. Near the poles magnetic lines are very near to each other which shows that magnetic field at the poles is stronger as compare to other parts.

Magnetic field around the current carrying wire :

Magnetic Field around the Current carrying wire If an electric current is made to flow in a wire, magnetic field produce around it. For seeing this take a conducting wire (like copper). Now with the help of connecting wires attach this to the two ends of a battery. Keep a magnetic needle parallel to the conducting copper wire .When the circuit is complete the magnetic needle shows deflection. This shows that when electric current flows through a conductor, magnetic field is produced around the conductor. Thus magnetic field is an effect of flow of electric current through conducting wire. In the year 1820 a scientist from Denmark named H.C. Oersted observed this effect for the first time. The principle of the magnetic effect of electric current used in many appliances like motor etc.

In summary, electric and magnetic fields are interconnected and form the basis of electromagnetism. They play a crucial role in the interactions between charged particles, the generation of electromagnetic waves, and the operation of various devices. Understanding their properties and interactions is essential for the study of electromagnetism and the development of technologies that rely on electromagnetic phenomena.

 

BEHAVIOUR OF ATOMIC AND NUCLEAR PARTICLES

Dalton Atomic Theory :

The theory proposed in the year 1803 considered the atom to be the smallest indivisible constituent of all matter. However, towards the end of nineteenth century, certain experiments showed that an atom is neither the smallest nor indivisible particle of matter as stated by Dalton. It was shown to be made up of even smaller particles. These subatomic particles were called electrons, protons and neutrons. The electrons are negatively charged whereas the protons are positively charged. The neutrons on the other hand are uncharged in nature.

 

 

Protons :

Protons and Neutrons together make up the nucleus of an atom and hence are called nucleons. Some important points regarding the discovery and properties of protons are listed below.

·         Protons are positively charged subatomic particles.

·         The number of protons in an atom is equal to the number of electrons in it.

·         The discovery of protons is credited to Ernest Rutherford.

·         Protons can be produced via the removal of an electron from a hydrogen atom.

·         The mass of a proton is 1.676 x 10^-24 Kg.

·         The charge of a proton is + 1.602 x 10^-19 Coulombs.

Electrons :

            Electrons are subatomic particles that revolve around the nucleus of an atom. Ions can be formed either by the loss or gain of electrons. Electrons of different atoms come together to participate in chemical bonding. A few points detailing the discovery and the properties of electrons are listed below.

·         Electrons are negatively charged subatomic particles.

·         An equal number of electrons and protons are found in the atoms of all elements.

·         J.J. Thomson is credited with the discovery of electrons since he was the first person to calculate the mass and the charge of an electron.

·         The mass of an electron is negligible when compared to the mass of a proton. It is found to have a mass equal to (1/1837) times the mass of a proton (9.1095X10^-31 kg ).

·          The charge of an electron is equal to - 1.602 x 10^-19 Coulombs.

Neutrons :

            Neutrons, along with protons, make up the nucleons. Neutrons are named for their neutral nature-unlike protons and electrons, they do not carry any charge. The discovery and general properties of neutrons are discussed below.

·         Neutrons are neutrally charged subatomic particles.

·         The masses of two different isotopes of an element vary due to the difference in the number of neutrons in their respective nuclei.

·         The neutron was discovered by James Chadwick in 1932.

·         They were discovered in an experiment wherein a thin sheet of beryllium was bombarded with alpha particles.

·         The mass of a neutron is 1.676 x 10^-24 Kg.

The table below gives relative masses and relative charges for protons, neutrons, and electrons:    

Particle	Charge	Relative charge	Symbol	Mass in kg
Electron	-1.602 x 10-19 C	-1	e	9.109 x 10-31 kg
Proton	+1.602 x 10-19 C	+1	p	1.672 x 10-27 kg
Neutron	0	0	n	1.674 x 10-27 kg

           If beams of the three types of particles, all with the same energy, are passed between two electrically charged plates, the following is observed:

·         Protons are deflected on a curved path toward the negative plate.

·         Electrons are deflected on a curved path toward the positive plate.

·         Neutrons continue in a straight line.

 

WAVE-PARTICLE DUALITY

Wave-particle duality is a fundamental concept in quantum mechanics that states that particles, such as electrons and photons, can exhibit both wave-like and particle-like properties, depending on the experimental setup or observation. This concept challenges the classical notion that particles and waves are separate and distinct entities.

To understand the wave and particle duality, it is necessary to know what is a particle and what is a wave.

The concept of a particle is easy to grasp. It has mass, it is located at some definite point, it can move from one place to another, it gives energy when slowed down or stopped. Thus, the particle is specified by (i) mass m (ii)velocity v (iii) momentum p and (iv)energy E.

The concept of a wave is a bit more difficult than that of a particle. A wave is spread out over a relatively large region of space. Actually a wave is nothing but rather a spread out disturbance. A wave is specified by its (1) frequency, (ii) wavelength, (iii) phase of wave velocity, (iv) amplitude, and (v) intensity.

Photo-Electric effect: The emission of electrons from a metal plate when illuminated by light of suitable wavelength (or frequency) is called photoelectric effect. The emitted electrons are called as photoelectrons and phenomenon is called as photo-electric effect.

Compton effect: When a monochromatic beam of high frequency radiation (X-rays, Gamma-rays, etc.) is scattered by a substance, the scattered radiation contains two components-one having a lower frequency or greater wavelength and the other having the same frequency or wavelength. The radiation of unchanged frequency in the scattered beam is known as unmodified radiation while the radiation of lower frequency or slightly higher wavelength is called as modified radiation. This phenomenon is known as Compton effect.

            Both Photoelectric effect and the Compton effect emphasize the corpuscular/particle nature of the electron, while Davisson and Germer (1925) observed diffraction of electrons from a nickel crystal, which points to the wave nature of the electrons. de Broglie (1923) put forth a hypothesis of wave-particle duality.

According to de-Broglie’s hypothesis, a moving particle is associated with a wave characteristics and vice versa, which is known as de-Broglie wave.

The wavelength of matter wave is given by

where p is the momentum, m and v are mass and velocity of the particle respectively, h is the Planck’s constant.

The Uncertainty Principle

            In 1927, Heisenberg proposed a very interesting principle, which is a direct consequence of the dual nature of matter, known as uncertainty principle. In classical mechanics, moving particle has a fixed position in space and a definite momentum. However, in wave mechanics the particle is described in terms of a wavepacket. According to Born's. probability interpretation, the particle may be found anywhere within the wavepacket. When the wavepacket is small, the position of the particle may be fixed but the particle will spread rapidly and hence the velocity becomes indeterminate. On the other hand, when the wavepacket is large, the velocity can be fixed but there is large indefiniteness in position. In this way certainty of momentum involves uncertainty in momentum or velocity and certainty of momentum involves and uncertainty in position. This shows that it is impossible to know where within the wavepacket the particle is and what is its exact momentum. Hence we can measure either the position or the momentum of a particle with any desired degree of accuracy.

            According to Heisenberg uncertainty principle, it is impossible to measure both the position and momentum a particle simultaneously to any desired degree of accuracy.

where p_x is the uncertainty in determining the momentum and x is the uncertainty in determining the position of the particle.

If one tries to define exactly the position of a body, then the uncertainty in its momentum becomes very large and vice versa.

where  and  are uncertainties in determining the energy and time while  and  are uncertainties in determining the angular momentum and angle.

 

THEORIES AND UNDERSTANDING OF THE UNIVERSE

Throughout history, humanity has developed various theories and understandings of the universe in an attempt to comprehend its origins, structure, and evolution. These theories have evolved with scientific advancements and observations. Here, we will explore some of the key theories and understandings of the universe.

1. Heaven and Earth

The least that we know is that the universe is around 13.7 billion years old, and here is A Study on the Theories of Development of the Universe that will help us understand more.

Different civilizations are Mayas, Chinese, Incas, Arabs, Greeks, and Egyptians believed in a supreme power who created everything. They had different beliefs and explanations regarding the shape of the earth. They believed that heaven, hell and earth were in the middle. For them, the earth was a flat surface and the sky above, and hell under the ground.

2. Geocentric Model:

            Then came the geocentric model The Greeks proposed that the earth was not flat somewhat spherical Different celestial bodies were revolving around the earth in orbit and the presence of stars in the sky.This model persisted for centuries but was later challenged by emerging scientific observations.

3. Heliocentric Model: The heliocentric model, championed by Nicolaus Copernicus in the 16^th century, proposed that the sun was at the centre of the solar system, and the planets, including earth, orbited around it. The theory also states that stars are fixed at a distance. Many years later, around 2 thousand years. Copernicus set his Heliocentric theory, which was approved post his death. This model provided a simpler explanation for the observed movements of celestial bodies.

4. Big Bang Theory: The universe consists of everything you can think of: nature, the work!, oceans, and even our solar system.

But how did it all begin? A Study on the Theories of Development of the Universe shows that the most sought-after theory is the Big Bang Theory. This theory explains that the universe was born out of a hot and highly dense point that was not more than a few millimetres wide. Around 13.7 billion years ago, this point exploded, which created four significant constituents of the universe: Matter, Energy, Time, and Space.

The Big Bang theory is an effort to explain what happened at the very beginning of our universe. Discoveries in astronomy and physics have shown beyond a reasonable doubt that our universe did in fact have a beginning. According to the standard theory, our universe sprang into existence as 'singularity' around 13.7 billion years ago. Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something-a singularity. We don't know where it came from not why did it appear. After its initial appearance, it apparently inflated (the 'Big Bang'), expanded and cooled, going from very, very small and very, very hot, to the size and temperature of our current universe. It continues to expand and cool to this day and we are inside of it: incredible creatures living on a unique planet, circling a beautiful star clustered together with several the hundred billion other stars in a galaxy soaring through the cosmos.

5. Inflationary Theory: The inflationary Universe theory purports that the Universe underwent a short and sudden episode of great expansion right after the Big Bang. This phenomenon is called inflation and is believed to happen just
10^-36 seconds after the Big Bang. The inflationary theory is an extension of the Big Bang theory, proposed by physicist Alan Guth in the 1980’s. It suggests that the universe underwent a period of rapid expansion or inflation shortly after the Big Bang. This theory helps explain the observed uniformity and flatness of the universe on large scales.