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 ↓


Photoelectric effect


The photoelectric effect is a phenomenon in which electrons are emitted from a substance when exposed to light. Classical physics had difficulty explaining this effect, but it became an important piece of evidence for the development of quantum mechanics. It played a key role in our understanding of the wave-particle duality of light, demonstrating that light exhibits both wave-like and particle-like properties.

Understanding the basics of the photoelectric effect

When light shines on the surface of a metal, it can transfer energy to the electrons present in the metal. If the transferred energy is sufficient, it can eject electrons from the surface. This process is called the photoelectric effect. The emitted electrons are known as photoelectrons.

Classically, light was considered a wave, which led to some puzzling observations about the photoelectric effect. For example, classical wave theory predicted that the energy of emitted electrons would increase with the intensity (amplitude) of light, regardless of the frequency (color) of the light. However, experiments showed opposite results.

Experimental observations

The important observations made from the experiments on photoelectric effect are as follows:

  1. As soon as light falls on the metal, photoelectrons are emitted immediately, without any delay.
  2. The kinetic energy of the photoelectron depends on the frequency of the incident light, not its intensity. Below a certain frequency (called the threshold frequency), no electrons are emitted, regardless of the light intensity.
  3. Above the threshold frequency, the number of emitted electrons is proportional to the light intensity, but their energy increases with the frequency of the light.

These observations were inconsistent with the wave theory of light, leading to a revolutionary explanation.

Einstein's explanation using photons

Albert Einstein explained the photoelectric effect by proposing that light consists of particles called photons. Each photon has quantized energy given as follows:

E = hν

where E is the energy of the photon, h is the Planck constant, and ν (nu) is the frequency of light.

According to Einstein, an electron can absorb energy from a photon. If the absorbed energy is greater than the work function (φ) of the metal (the minimum energy required to remove the electron from the surface), the electron is ejected with kinetic energy:

KE = hν - φ

This explanation fully matched the experimental data and was an important step towards the development of quantum mechanics.

Wave–particle duality

The photoelectric effect shows the dual nature of light. Below is a simple diagram that helps in understanding this concept:

wave-like like a particle Light behaves as waves and particles

On the left, light is depicted as a wave, which shows how it can exhibit interference and diffraction. On the right, light is depicted as a particle, which is essential for understanding the photoelectric effect. This duality is a cornerstone of quantum mechanics.

Effects and applications

The understanding of the photoelectric effect has influenced many areas of physics and technology. Some of its major applications are as follows:

  • Photovoltaic cells: Devices that convert light into electricity using the photoelectric effect. Solar panels are a common example.
  • Photoelectron spectroscopy: A technique for analyzing the surface properties of materials by measuring the energy of the emitted electrons.
  • Development of quantum theory: The photoelectric effect played a vital role in the development of quantum mechanics and for this Einstein received the Nobel Prize in Physics in 1921.

Conclusion

The photoelectric effect is not only a fascinating phenomenon in its own right, but also a key piece in the puzzle of understanding the nature of light and matter. It challenges our classical intuition and introduces us to the strange but beautiful realm of quantum mechanics.

Through a simple yet powerful idea, it links our understanding of light, from waves to particles, and paves the way for numerous technological advancements and the theoretical framework of modern physics.

As we continue to explore the quantum world, insights gained from phenomena such as the photoelectric effect inspire a deeper understanding of the complex and interconnected structure of the universe.


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Photoelectric effect

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