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29.2 The Photoelectric Effect

3 min read•june 18, 2024

The reveals light's particle-like nature. When light hits a metal, it can kick out electrons, but only if it has enough energy. This energy depends on light's frequency, not its brightness.

Understanding the is crucial for grasping . It shows how light behaves as both a wave and a particle, challenging classical physics and paving the way for modern theory.

The Photoelectric Effect

Photoelectric effect and light particles

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  • Light behaves as discrete particles called photons
    • Each carries a specific amount of energy determined by its frequency (visible light, ultraviolet)
    • Photons interact with electrons in a metal surface (gold, zinc), causing them to be ejected as
  • Increasing light intensity increases the number of electrons ejected but does not increase their kinetic energy
    • More photons interact with more electrons, resulting in a greater number of ejected electrons
    • This suggests that individual photons are responsible for ejecting electrons, not the overall intensity of light
  • A minimum frequency of light is required to eject electrons from a metal surface
    • This is specific to the metal and is related to its (energy needed to remove an )
    • Below this frequency, no electrons are ejected regardless of light intensity (infrared light)
    • This supports the idea that photons must have a minimum energy to overcome the work function and eject electrons

Energy calculations for photons

  • The energy of a photon EE is directly proportional to its frequency ff
    • E=hfE = hf, where hh is 6.626×10−346.626 \times 10^{-34} J⋅\cdots
  • is inversely proportional to its wavelength λ\lambda
    • E=hcλE = \frac{hc}{\lambda}, where cc is the speed of light 3.0×1083.0 \times 10^8 m/s
  • To calculate photon energy from frequency:
    1. Multiply the frequency by Planck's constant
    2. Example: A photon with a frequency of 6.0×10146.0 \times 10^{14} Hz has an energy of E=6.626×10−34E = 6.626 \times 10^{-34} J⋅\cdots \times 6.0 \times 10^{14}HzHz= 3.98 \times 10^{-19}$ J
  • To calculate photon energy from wavelength:
    1. Divide the product of Planck's constant and the speed of light by the wavelength
    2. Example: A photon with a wavelength of 500 nm has an energy of E=6.626×10−34 J⋅s×3.0×108 m/s500×10−9 m=3.98×10−19E = \frac{6.626 \times 10^{-34} \text{ J} \cdot \text{s} \times 3.0 \times 10^8 \text{ m/s}}{500 \times 10^{-9} \text{ m}} = 3.98 \times 10^{-19} J

Light properties in photoelectric effect

  • Changing light frequency affects the kinetic energy of ejected electrons
    • If the frequency is above the threshold frequency (ultraviolet light), increasing it will increase the kinetic energy of ejected electrons
    • If the frequency is below the threshold frequency (infrared light), no electrons will be ejected regardless of the intensity
  • Changing light intensity affects the number of electrons ejected
    • Increasing intensity (brighter light) will increase the number of photons incident on the metal surface
    • More photons will interact with more electrons, causing a greater number of electrons to be ejected
    • However, increasing intensity does not change the kinetic energy of individual ejected electrons
  • The maximum kinetic energy KEmaxKE_{max} of ejected electrons is related to the photon energy and the metal's work function ϕ\phi
    • KEmax=hf−ϕKE_{max} = hf - \phi
    • If the photon energy hfhf is greater than the work function, the excess energy is converted into the kinetic energy of the ejected electron
    • If the photon energy is less than the work function, no electrons will be ejected (red light on zinc)

Experimental setup and measurements

  • The photoelectric effect is typically studied using a - system in a vacuum tube
    • The cathode is the metal surface from which electrons are ejected
    • The anode collects the ejected electrons, creating a measurable current
  • A can be applied to measure the maximum kinetic energy of ejected electrons
    • This is the minimum voltage needed to prevent any electrons from reaching the anode
    • The stopping potential is directly related to the maximum kinetic energy of the photoelectrons
  • , such as visible light or X-rays, is used to induce the photoelectric effect
    • Different types of radiation have varying frequencies and energies, affecting their ability to eject electrons from the metal surface

Key Terms to Review (23)

Albert Einstein: Albert Einstein was a theoretical physicist who developed the theory of relativity, fundamentally changing our understanding of space, time, and energy. His work laid the foundation for modern physics, influencing concepts such as the nature of light, the structure of atoms, and the gravitational interaction between masses.
Anode: An anode is an electrode through which conventional current flows into a polarized electrical device. It plays a crucial role in various phenomena, particularly in the emission of electrons in the photoelectric effect, the generation of X-rays in certain types of tubes, and the detection of radiation in detectors. Understanding the function and characteristics of anodes is essential to grasp how electrical devices operate and interact with light and radiation.
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.
Cathode: The cathode is the negatively charged electrode in an electrical device, such as a vacuum tube, X-ray tube, or photodetector. It is the source of electrons that are emitted or accelerated in the device, playing a crucial role in the photoelectric effect, X-ray generation, and radiation detection.
Cathode-ray tubes: Cathode-ray tubes (CRTs) are vacuum tubes that contain one or more electron guns and a phosphorescent screen used to display images. They were instrumental in the discovery of the electron and played a key role in early atomic physics experiments.
Einstein's Photoelectric Equation: Einstein's photoelectric equation is a fundamental equation that describes the relationship between the energy of photoelectrons emitted from a metal surface and the frequency of the incident light. It is a crucial equation in understanding the photoelectric effect, which is the emission of electrons from a metal surface when it is exposed to light.
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.
Max Planck: Max Planck was a German physicist who is considered the father of quantum theory. His groundbreaking work in the early 20th century laid the foundation for understanding the behavior of energy and matter at the atomic and subatomic levels, which had profound implications across various fields of physics, including the electromagnetic spectrum, the quantization of energy, the photoelectric effect, and photon energies.
Millikan's experiment: Millikan's experiment, conducted by Robert A. Millikan in 1909, was a pivotal scientific study that measured the elementary electric charge of the electron. By using charged oil droplets suspended in an electric field, Millikan was able to determine the charge on individual electrons and provide strong evidence for the quantization of electric charge. This experiment was fundamental in supporting the particle theory of electricity and also connected to the understanding of the photoelectric effect by illustrating the discrete nature of electric charge.
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.
Photoelectrons: Photoelectrons are electrons that are emitted from the surface of a material when it is exposed to light. This phenomenon is known as the photoelectric effect, which was a key discovery in the development of quantum mechanics.
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 energy: Photon energy is the amount of energy carried by a single photon, proportional to its frequency and inversely proportional to its wavelength. It can be calculated using the equation $E = hf$, where $E$ is the photon energy, $h$ is Planck's constant, and $f$ is the frequency of the photon.
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: A quantum refers to the smallest discrete unit of energy or matter in the realm of quantum mechanics, a fundamental aspect of physics that describes the behavior of particles at microscopic scales. This concept highlights how energy and particles can exist in quantized states rather than continuously, influencing various phenomena such as the photoelectric effect. Understanding quantum behavior is essential for explaining how light interacts with matter and leads to the emission of electrons from surfaces when exposed to electromagnetic radiation.
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.
Stopping Potential: Stopping potential is the minimum potential difference required to just prevent the emission of photoelectrons from a metal surface when it is illuminated by light. It is a key concept in understanding the photoelectric effect and the particle-wave duality of light.
Threshold Frequency: The threshold frequency is the minimum frequency of light that can eject an electron from the surface of a material during the photoelectric effect. This frequency is a characteristic property of the material and is the lowest frequency at which the photoelectric effect can occur.
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.
Work Function: The work function is the minimum energy required to remove an electron from a material's surface. It is a fundamental property that describes the energetics of electron emission from a solid or liquid material and is crucial in understanding phenomena such as the photoelectric effect and the particle-wave duality of light and matter.
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Glossary
Glossary
29.3 Photon Energies and the Electromagnetic Spectrum