# Wave-particle duality

Wave-particle duality is a fundamental concept in quantum mechanics that describes the dual nature of particles, which can exhibit both wave-like and particle-like behaviour.

• Wave-particle duality refers to the phenomenon where entities like light can exhibit characteristics of both waves and particles.
•  Electromagnetic radiation, including light, is often described using wave properties. However, when it interacts with matter, it behaves like particles.
•  A photon is a quantum of electromagnetic radiation and represents the smallest discrete amount of light energy.
• When a photon is absorbed by matter, the energy becomes localized at specific points. This phenomenon is termed ‘wave function collapse.’ It describes the transition of a quantum system from a superposition of states to a definite state upon measurement.
• Wave-particle duality is a fundamental aspect of quantum mechanics and applies to all particles, not just light. Particles like electrons also exhibit wave-like and particle-like behaviour.
• The double-slit experiment is an experiment in quantum physics that demonstrates the wave-like behaviour of particles, including photons and electrons, and is a key illustration of wave-particle duality.

Concepts used to describe light as waves and particles can be paired to illustrate the wave-particle character of light

##### Explanation
FrequencyEnergyFrequency is related to the energy of a photon. Higher frequency light corresponds to higher energy photons. This is described by Planck's equation E = hf, where E is energy, h is Planck's constant, and f is frequency.
WavelengthMomentumThe wavelength of a wave is inversely proportional to its momentum. This is described by the de Broglie wavelength formula λ = h/p, where λ is wavelength, h is Planck's constant, and p is momentum.
Wave speedMomentumThe speed of a wave is related to its momentum through its frequency and wavelength. For light, the speed of propagation (c, the speed of light) is equal to its frequency times wavelength (c = λf), which is also related to its momentum as described above.
AmplitudeIntensityThe amplitude of a wave determines its intensity, which is related to the brightness or energy density of light. Higher amplitude corresponds to higher intensity.
PeriodLifetimeThe period of a wave is the time it takes for one complete cycle. In the context of light particles (photons), their "lifetime" refers to the duration of their existence before they are absorbed or undergo a different process.
PhaseQuantum statePhase refers to the position of a point in a wave cycle, and it can be related to the quantum state of a particle. In quantum mechanics, a particle's state is described by a complex-valued wavefunction, and the phase of this wavefunction is significant in determining probabilities and interference patterns.

These pairings are all based on the wave-particle duality of matter, which states that all objects have both wave-like and particle-like properties.

The specific pairings in the table can be derived from the following equations:

• E = hf (Planck’s equation describes the relationship between the energy of a photon and its frequency.)
• p = h/λ (de Broglie wavelength equation describes the relationship between the momentum of a particle and its wavelength.)
• p = mv (momentum equation describes the relationship between the momentum of a particle and its mass and velocity.)
• I = 1/2 cε_0 E^2 (intensity equation describes the relationship between the intensity of an electromagnetic wave and its electric field.)

where:

• E is energy
• f is frequency
• p is momentum
• m is mass
• v is velocity
• λ is wavelength
• I is intensity
• c is the speed of light
• ε_0 is the permittivity of free space. The permittivity of free space, also known as the electric constant, is a fundamental constant of nature. It is a measure of how easily an electric field can penetrate a vacuum.

The equation E = hf tells us that the energy of a particle is proportional to its frequency. This means that the higher the frequency of a particle, the more energy it has. This is why high-frequency radiation, such as gamma rays and X-rays, is so dangerous.

The equation p = h/λ tells us that the momentum of a particle is inversely proportional to its wavelength. This means that the shorter the wavelength of a particle, the more momentum it has. This is why high-energy particles, such as protons and electrons, can be used to accelerate other particles to high speeds.

• Wave-particle duality is a fundamental concept in quantum mechanics that describes the dual nature of particles, which can exhibit both wave-like and particle-like behaviour.
• Wave-particle duality refers to the phenomenon where entities like light can exhibit characteristics of both waves and particles.
•  Electromagnetic radiation, including light, is often described using wave properties. However, when it interacts with matter, it behaves like particles.
•  A photon is a quantum of electromagnetic radiation and represents the smallest discrete amount of light energy.
• When a photon is absorbed by matter, the energy becomes localized at specific points. This phenomenon is termed ‘wave function collapse.’ It describes the transition of a quantum system from a superposition of states to a definite state upon measurement.
• Wave-particle duality is a fundamental aspect of quantum mechanics and applies to all particles, not just light. Particles like electrons also exhibit wave-like and particle-like behaviour.