Glossary

29.4 Photon Momentum

3 min read•june 18, 2024

Photons, the particles of light, carry both energy and momentum. Their momentum is directly linked to their energy and inversely related to their wavelength. This relationship is crucial for understanding how light interacts with matter.

The showcases photons' particle-like nature as they scatter off electrons. This interaction demonstrates momentum conservation and provides evidence for light's quantum nature, supporting the concept of in .

Photon Momentum and Interactions

Photon momentum relationships

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  • (pp) directly proportional to its energy (EE) inversely proportional to its wavelength (λλ)
    • Relationship given by equation: p=Ec=hλp = \frac{E}{c} = \frac{h}{λ}
      • cc speed of light (3 × 10^8 m/s)
      • hh (6.626 × 10^-34 J⋅s)
  • As energy increases, momentum increases
    • Example: photons (high energy, short wavelength) have greater momentum than photons (low energy, long wavelength)
  • As photon wavelength increases, momentum decreases
    • Example: photons (longer wavelength) have less momentum than photons (shorter wavelength)
  • Photons are quanta of , carrying both energy and momentum

Compton effect significance

  • scattering of photon by charged particle, usually
    • During interaction, photon transfers some energy and momentum to electron
    • Photon's wavelength increases (red-shift) due to energy loss
      • Example: Incoming X-ray photon scattered by electron, resulting in lower energy X-ray photon and recoiling electron
  • Compton effect demonstrates particle-like nature of photons
    • Shows photons carry momentum can interact with matter through collisions
      • Similar to how billiard balls collide and transfer momentum
  • Compton effect provided evidence for quantum nature of light validity of photon concept
    • Helped establish wave-particle duality, a fundamental principle of
  • shift depends on scattering angle given by: Δλ=hmec(1−cos⁡θ)Δλ = \frac{h}{m_ec}(1 - \cos θ)
    • mem_e mass of electron (9.11 × 10^-31 kg)
    • θθ scattering angle (angle between incoming and scattered photon directions)
      • Example: Larger scattering angle results in greater wavelength shift

Conservation in photon interactions

  • In photon-particle interactions, total momentum conserved
    • Initial momentum of photon and particle equals final momentum of photon and particle after interaction
      • Similar to how momentum conserved in collisions between macroscopic objects (cars, balls)
  • In Compton effect, momentum conservation equation: p⃗photon,initial+p⃗electron,initial=p⃗photon,final+p⃗electron,final\vec{p}_{\text{photon,initial}} + \vec{p}_{\text{electron,initial}} = \vec{p}_{\text{photon,final}} + \vec{p}_{\text{electron,final}}
    • Initial momentum of electron usually considered zero, as typically at rest before interaction
      • Example: Electron in outer shell of atom, not moving significantly before interacting with incoming photon
  • By applying and energy, final wavelength of scattered photon kinetic energy of recoiling electron can be calculated
    • Allows for predictions of Compton effect outcomes based on initial conditions
      • Example: Calculating expected wavelength shift for specific scattering angle, or determining maximum kinetic energy of recoiling electron
  • applies to all photon interactions, including the
  • De Broglie wavelength relates particle momentum to its wavelength: λ = h/p
  • demonstrates light's particle nature through electron ejection from materials
  • Wave-particle duality explains how photons exhibit both wave-like and particle-like properties in different phenomena

Key Terms to Review (23)

Antielectron: An antielectron, also known as a positron, is the antimatter counterpart of an electron. It has the same mass as an electron but carries a positive charge.
Compton effect: The Compton effect is the increase in wavelength (or decrease in energy) of X-rays or gamma rays when they are scattered by electrons. This phenomenon demonstrates the particle nature of light and supports the concept of photon momentum.
Compton Effect: The Compton effect is a phenomenon in which a photon interacts with a free or loosely bound electron, resulting in a change in the photon\'s wavelength and the electron\'s kinetic energy. This interaction demonstrates the particle-like nature of electromagnetic radiation.
Compton Scattering: Compton scattering is the inelastic scattering of a photon by a charged particle, typically an electron. It results in a decrease in the energy (increase in wavelength) of the scattered photon, and a corresponding increase in the energy of the recoiling electron.
Compton Wavelength: The Compton wavelength is the wavelength of a photon whose energy is equal to the rest energy of an electron. It represents the change in the wavelength of a photon when it interacts with a free electron through the Compton effect, a phenomenon that demonstrates the particle-like nature of electromagnetic radiation.
Conservation of Momentum: Conservation of momentum is a fundamental principle in physics which states that the total momentum of a closed system is constant unless an external force acts on the system. This means that the total momentum before an event, such as a collision, is equal to the total momentum after the event.
Conservation of momentum principle: The principle of conservation of momentum states that the total linear momentum of an isolated system remains constant if no external forces are acting on it. This means that the momentum before and after a collision or interaction is the same.
Electromagnetic Radiation: Electromagnetic radiation is a form of energy that is transmitted through space or a medium in the form of electric and magnetic fields oscillating perpendicular to each other. It encompasses a wide range of wavelengths and frequencies, from radio waves to gamma rays, and plays a crucial role in various physical phenomena and applications.
Electron: An electron is a fundamental subatomic particle that carries a negative electric charge and is found in all atoms, playing a crucial role in various physical and chemical phenomena. Electrons are responsible for the flow of electric current, the formation of chemical bonds, and the behavior of matter at the atomic and molecular levels. The concept of the electron is central to understanding topics such as static electricity, electric fields, magnetic fields, the photoelectric effect, quantum mechanics, and the structure of atoms. Electrons are the building blocks of matter and are essential for understanding the fundamental nature of the universe.
Infrared: Infrared (IR) is a type of electromagnetic radiation with wavelengths longer than those of visible light, but shorter than those of radio waves. It is a critical component of the electromagnetic spectrum, with significant implications in various fields, including the topics of dispersion, photon energies, and photon momentum.
Infrared radiation: Infrared radiation is a type of electromagnetic wave with wavelengths longer than visible light but shorter than microwaves. It is commonly associated with heat emission and can be detected using thermal imaging cameras.
Photoelectric effect: The photoelectric effect is the emission of electrons from a material when it is exposed to light. This phenomenon demonstrates that light can act as both a wave and a particle.
Photoelectric Effect: The photoelectric effect is a phenomenon in which electrons are emitted from the surface of a material when it is exposed to light or other electromagnetic radiation. This effect was a key piece of evidence that led to the development of the quantum theory of light and the understanding of the dual nature of light as both a particle and a wave.
Photon: A photon is a quantum of electromagnetic radiation, possessing both particle and wave properties. It has no rest mass and travels at the speed of light in a vacuum.
Photon momentum: Photon momentum is the momentum carried by a photon, despite it having no mass. It is given by $p = \frac{h}{\lambda}$, where $p$ is the momentum, $h$ is Planck's constant, and $\lambda$ is the wavelength of the photon.
Photon Momentum: Photon momentum is the momentum possessed by a photon, which is the fundamental particle of light. It is a crucial concept in quantum mechanics and the study of the wave-particle duality of light.
Planck's constant: Planck's constant is a fundamental physical constant that represents the smallest possible change in energy or action. It is a crucial parameter in quantum mechanics and is denoted by the symbol 'h'. Planck's constant establishes the relationship between the energy of a photon and its frequency, and it is a key factor in understanding the quantization of energy and the wave-particle duality of matter and energy.
Quantum mechanics: Quantum mechanics is a fundamental theory in physics that describes the behavior of particles at atomic and subatomic scales. It explains phenomena that cannot be accounted for by classical physics.
Quantum Mechanics: Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy on the atomic and subatomic scale. It is a powerful framework for understanding the properties and interactions of particles at the quantum level, which are often counterintuitive and defy classical physics.
Radio Wave: A radio wave is a type of electromagnetic radiation with wavelengths in the radio frequency (RF) portion of the electromagnetic spectrum. Radio waves are used for various communication and broadcasting applications, such as radio and television transmission, wireless networking, and remote control devices.
Ultraviolet: Ultraviolet (UV) refers to a type of electromagnetic radiation that has a wavelength shorter than visible light, ranging from about 10 nanometers to 400 nanometers. This form of radiation is crucial in various applications, including photography, sterilization, and the study of astronomical phenomena. The energy associated with UV photons is higher than that of visible light, which makes them capable of causing chemical reactions and photochemical effects.
Wave-Particle Duality: Wave-particle duality is a fundamental concept in quantum physics that describes the dual nature of light and matter, where they exhibit characteristics of both waves and particles depending on the context and experimental conditions. This principle is central to understanding the behavior of electromagnetic radiation and the properties of subatomic particles.
X-ray: X-rays are a type of electromagnetic radiation with wavelengths shorter than visible light, making them capable of penetrating various materials. They are widely used in fields such as physics, medicine, and industry, with applications ranging from medical imaging to materials analysis.
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