Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Quantum mechanics → Wave–particle duality ↓


Compton scattering


Compton scattering is a fundamental concept in quantum mechanics that demonstrates the wave-particle duality of electromagnetic radiation, particularly X-rays and gamma rays. Named after Arthur H. Compton, who discovered the phenomenon in 1923, Compton scattering shows the interaction between electromagnetic radiation and matter, providing evidence for the particle nature of light.

Historical background

By the early 20th century, the wave nature of light was well established through experiments such as Young's double-slit experiment and the interference and diffraction of light. However, the discovery of the photoelectric effect by Albert Einstein, where light was shown to eject electrons from metal surfaces, suggested that light also behaved like a particle. Compton scattering further demonstrated this particle-like behavior, providing additional support for the concept of wave-particle duality.

What is Compton scattering?

Compton scattering is the inelastic scattering of a photon, typically an X-ray or gamma-ray photon, by a target, typically an electron. During this scattering process, the photon transfers some of its energy to the electron, resulting in a change in the wavelength and direction of the photon. This change in wavelength is known as the Compton shift.

Understanding the Compton Effect

Before delving deeper, let's start with a simple analogy. Imagine that a billiard ball, which represents a photon, collides with another billiard ball, which represents an electron. After the collision, both balls reverse their direction, and the photon (the billiard ball) loses some of its energy to the electron (another billiard ball). In Compton scattering, the photon, like the billiard ball, also loses energy, resulting in an increase in the wavelength of light. The wavelength of the photon after the collision is longer than its original wavelength.

Mathematical representation

The change in wavelength (Compton shift) can be calculated using the Compton equation:

Δλ = λ' - λ = (h / (m_e * c)) * (1 - cos θ)

Where:

  • Δλ is the change in wavelength.
  • λ' is the wavelength after scattering.
  • λ is the initial wavelength before scattering.
  • h is the Planck constant (~6.626 x 10 -34 J s).
  • m_e is the electron rest mass (~9.109 x 10 -31 kg).
  • c is the speed of light in a vacuum (~3 x 10 8 m / s).
  • θ is the angle at which the photon is scattered.

Wave–particle duality

Wave-particle duality is a core principle of quantum mechanics, which proposes that every particle or quantum entity exhibits both wave and particle properties. In the context of Compton scattering, this principle is illustrated by the fact that electromagnetic radiation (traditionally described as waves) can also exhibit particle-like properties, such as momentum and energy transfer.

Wave nature vs particle nature

Earlier experiments such as diffraction and interference highlighted the wave properties of light. However, phenomena such as the photoelectric effect and Compton scattering emphasize the particle properties of light by demonstrating energy quantization.

Visual representation

Let's imagine the Compton scattering process:

Incoming photon Electron Scattered photons Recoil Electron

Examples of Compton scattering

Now, let's look at some text examples to get a deeper insight into the significance of Compton scattering:

Example 1: X-ray scattering experiment

Suppose we perform an experiment using X-rays with an initial wavelength of 0.1 nm, directed at a target containing free electrons. When these X-rays are scattered at an angle of 90°, the wavelength shift is calculated using the Compton equation:

Δλ = (6.626 x 10^-34 Js) / ((9.109 x 10^-31 kg) * (3 x 10^8 m/s)) * (1 - cos 90°)

The resulting Δλ from this calculation is approximately 0.00243 nm.

Example 2: Gamma-ray scattering

Consider gamma rays with a wavelength of 0.01 nm incident on a metal surface, where they scatter at 45° angle. The wavelength shift is calculated similarly:

Δλ = (6.626 x 10^-34 Js) / ((9.109 x 10^-31 kg) * (3 x 10^8 m/s)) * (1 - cos 45°)

Here, the calculated Δλ is about 0.00172 nm.

Implications and applications

Compton scattering has important implications in a variety of areas of science and technology, including:

Health care

In medical imaging, especially in the field of X-ray technology and radiation therapy, understanding Compton scattering helps to design better diagnostic tools and treatment methods. Scattering effects must be considered to optimize image quality and minimize patient radiation exposure.

Astrophysics

Compton scattering plays an important role in astrophysics, where it helps explain the behavior of cosmic X-rays and gamma rays when interacting with matter in space. This understanding allows researchers to infer the properties of celestial objects and the conditions of the interstellar medium.

Conclusion

Compton scattering is a cornerstone of modern physics, illustrating the wave-particle duality of electromagnetic radiation. By probing the exchange of energy and momentum between photons and electrons, it enriches our perception of the microscopic world. Beyond its theoretical significance, Compton scattering impacts practical applications ranging from medical imaging to astrophysics, underscoring its continued importance in both scientific exploration and technological innovation.


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Compton scattering

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