Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Modern Physics ↓


Wave–particle duality


Wave-particle duality is a fundamental concept of quantum physics that describes how elementary particles and some larger composite particles exhibit both wave-like and particle-like properties. Before delving into the intricacies of this phenomenon, let's dive into the basics by understanding waves and particles separately.

Particle

In classical physics, a particle is often thought of as a small, localized object that can be given a number of physical properties, such as volume or mass. Particles are the building blocks of matter and obey Newtonian mechanics. They have specific locations and can be counted, and they have momentum and energy.

Waves

Unlike particles, waves are disturbances that travel through a medium or vacuum and can transport energy. They are characterized by parameters such as frequency, wavelength and amplitude. Waves can superimpose on top of each other and interfere, causing constructive or destructive interference.

Wave

Dualism

The concept of wave–particle duality arose from experiments and theories that demonstrated that light and particles have both wave and particle characteristics, depending on the conditions of the experiment.

Double-slit experiment

Example: The double-slit experiment is one of the most famous experiments demonstrating wave-particle duality. When light passes through two slits and onto a screen, it creates an interference pattern indicating wave behavior. However, when individual photons (light particles) are sent through the slits, they create the same pattern over time, indicating that each photon acts as a wave.
Screen

The double-slit experiment was first performed by Thomas Young in 1801 to show that light can exhibit characteristics of both waves and particles. This experiment is a cornerstone in the development of quantum mechanics.

Mathematical representation

In quantum mechanics, particles are represented as wave functions (Ψ), which describe the probability of finding a particle at a specific point in space. The wave function allows us to calculate the probability of events associated with the particle, such as position and momentum.

Ψ(x, t) = A * e^(i(kx - ωt))

Here, A is the amplitude of the wave function, i is the imaginary unit, k is the wave number, ω is the angular frequency, x is the position, and t is time. Using the wave function, quantum mechanics can predict the probabilities of different outcomes.

Wave-particle duality in light

Light is a prime example of wave-particle duality. It has long been known that light exhibits wave-like properties such as interference and diffraction. However, experiments also show that light exhibits particle-like properties.

Photoelectric effect

Example: In the photoelectric effect, it is observed that light falling on a metal surface can knock out electrons. This phenomenon cannot be explained by the wave theory alone, suggesting that light consists of particles called photons. Each photon carries a discrete amount of energy given by Planck's relation:
E = hν
where E is the energy, h is the Planck constant, and ν (nu) is the frequency of light.

Albert Einstein was awarded the Nobel Prize in Physics in 1921 for explaining the photoelectric effect based on the particle theory of light.

Wave-particle duality in matter

Not only does light exhibit wave-particle duality, but so do materials such as electrons. Louis de Broglie proposed that all matter exhibits wave behavior.

De Broglie wavelength

De Broglie suggested that particles also have a wavelength, known as the de Broglie wavelength, and so might exhibit wave-like properties. The de Broglie wavelength of a particle is given by:

λ = h / p

where λ (lambda) is the wavelength, h is Planck's constant, and p is the momentum of the particle. This relation means that particles with higher momentum have shorter wavelengths.

Electron

The wave behavior of particles has been observed in many experiments. The diffraction and interference patterns produced by beams of electrons are clear evidence of their wave-like properties.

Effect of wave–particle duality

Wave-particle duality has profound implications for our understanding of the universe. It exposes the limitations of classical physics and the traditional categories of waves and particles. Quantum mechanics, the framework that includes wave-particle duality, allows for dual interpretations and possibilities rather than definite states.

Heisenberg uncertainty principle

One of the most important consequences of wave-particle duality is the Heisenberg uncertainty principle. It states that it is not possible to determine both the position (x) and momentum (p) of a particle with infinite precision at the same time. The more precisely one of these properties is measured, the less precisely the other can be controlled, known, or predicted.

Δx Δp ≥ ħ / 2

where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and ħ is (h-times) the reduced Planck constant.

Conclusion

Wave-particle duality is a key concept in quantum physics that shows how our classical intuitions fail at the microscopic level. Particles of matter and light exhibit both wave-like and particle-like properties, leading to the development of new theories that redefine our understanding of the universe. Understanding wave-particle duality helps explain the nature of quantum objects, leading to revolutionary techniques and approaches to understanding the physical world.


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Wave–particle duality

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