Quantum Physics Photons Matter Lesson 39 by Owen Borville 1.16.2026
All bodies of matter radiate energy and the amount of radiation of a body emits depends on its temperature. A blackbody is an object that absorbs all electromagnetic radiation or light that hits it, reflecting none, and appears black. When heated, the blackbody emits thermal radiation whose spectrum depends only on temperature, as hotter bodies emit more intensely and peak at shorter wavelengths, as described by Planck's law and observed in stars and other objects.
Blackbody radiation is the emission of thermal electromagnetic radiation (EM) by an object with an emissivity of 1. This blackbody radiation led to the discovery of quantized energy. Max Plank discovered that the energy levels of the emitting atoms and molecules were quantized, with only the allowed values of E = (n+1/2)hf, where n is any non-negative integer (0, 1, 2, 3...). Planck's constant is h = 6.6 x 10^-34 J*s. Planck's blackbody radiation law is I(λ, T) = 2π hc^2/λ^5 (1/e^hc/λkBT-1)
Therefore, the oscillatory absorption and emission energies of atoms and molecules in a blackbody could increase or decrease only in steps of size ΔE = hf where f is the frequency of the oscillatory nature of the absorption and emission of EM radiation. Quantized energy levels are also identified by the atomic spectra lines, which are the EM emissions of individual atoms and molecules.
The experimental Wein's displacement law states that the hotter the body, the shorter the wavelength corresponding to the emission peak in the radiation curve: λmax T = b = 2.898x10^-3m*K, where λ is wavelength, T is temperature, and b is Wein's displacement constant.
The experimental Stefan's law states that the total power of radiation emitted across the entire spectrum of wavelengths at a given temperature is proportional to the fourth power of the Kelvin temperature of the radiating body. P(T)= σAT^4, P=power, T=temperature in K, σ=Boltzmann's constant, A=surface area.
Absorption and emission of radiation are studied as part of the model of a blackbody. The classical approach says that the exchange of energy between radiation and cavity walls is continuous. The classical approach does not explain the blackbody radiation curve. In order to explain the blackbody radiation curve, Planck assumed that the exchange of energy between radiation and cavity walls takes place only in discrete quanta of energy. Planck's hypothesis of energy quanta led to the theoretical Planck's radiation law, which agrees with the experimental blackbody radiation curve and also explains Wien's and Stefan's laws.
The photoelectric effect is the process in which EM radiation ejects electrons from a metal material surface in response to monochromatic radiation incident on the surface and it has three characteristics: (1) it is instantaneous (2) it occurs only when the radiation is above a cut-off frequency, and (3) kinetic energies of photoelectrons at the surface do not depend on the intensity of radiation. The photoelectric effect cannot be explained by classical theory. The photoelectric effect can be explained by assuming that radiation consists of photons (particles of light) and each photon carries a quantum of energy. The energy of a photon depends only on its frequency, which is the frequency of the radiation. At the surface, the entire energy of a photon is transferred to one photoelectron.
Albert Einstein proposed photons to be quanta of EM radiation having energy E = hf, where f is the frequency of the radiation. All EM radiation is composed of photons. Einstein explained that all characteristics of the photoelectric effect are due to the interaction of individual photons with individual electrons. The maximum kinetic energy KEe of ejected electrons (photoelectrons) at the metal surface is given by KE = hf - BE, (the energy-balance equation) where hf is the incident photon energy and BE(φ) is the binding energy (or work function) of the electron to the particular material. The work function is the binding energy of electrons to the metal surface. Each metal has its own characteristic work function. Kmax is directly proportional to the stopping potential (Vo) and the reverse voltage needed to halt the photocurrent: Kmax = eVo (e is the electron charge).
The Compton Effect describes X-rays scattered off some materials having different wavelengths than the wavelength of the incident X-rays. This phenomenon cannot be described classically. The Compton Effect is explained by assuming that radiation consists of photons that collide with weakly bound electrons in the target material. Both electron and photon are treated as relativistic particles. Conservation laws of the total energy and of momentum are obeyed in collisions. Treating the photon as a particle with momentum that can be transferred to an electron leads to a theoretical Compton shift that agrees with the wavelength shift measured in the experiment. This provides evidence that radiation consists of photons. Compton scattering is an inelastic scattering, in which scattered radiation has longer wavelength than that of incident radiation. Compton wavelength of an electron =λc = h/m0c = 0.00243 The Compton shift = Δλ = λc(1-cosθ)
Positions of absorption and emission lines in the spectrum of atomic hydrogen are predicted by the experimental Rydberg formula. Classical physics cannot explain the spectrum of atomic hydrogen. The Bohr model of hydrogen was the first model of atomic structure to correctly explain the radiation spectra of atomic hydrogen. It was preceded by the Rutherford nuclear model of the atom. In Rutherford's model, an atom consists of a positively charged point-like nucleus that contains almost the entire mass of the atom and of negative electrons that are located far away from the nucleus. The Balmer formula predicts the wavelengths of visible light from hydrogen's spectral lines.
The Bohr model of the hydrogen atom is based on three postulates (1) an electron moves around the nucleus in a circular orbit (2) an electron's angular momentum in the orbit is quantized, and (3) the change in an electron's energy as it makes a quantum jump from one orbit to another is always accompanied by the emission or absorption of a photon. Bohr's model is semi-classical because it combines the classical concept of electron orbit with the new concept of quantization.
Bohr's model of the hydrogen atom explains the emission and absorption spectra of atomic hydrogen and hydrogen-like ions with low atomic numbers. It was the first model to introduce the concept of a quantum number to describe atomic states and to postulate quantization of electron orbits in the atom. Bohr's model is an important step in the development of quantum mechanics, which deals with many-electron atoms.
Photon energy is responsible for many characteristics of EM radiation, being particularly noticeable at high frequencies. Photons have both wave and particle characteristics.
Photons have momentum, p = h/λ, where λ is the photon wavelength. Photon energy and momentum are related by p = E/c, where E = hf = hc/λ for a photon.
De Broglie's hypothesis of matter waves is that any particle of matter that has linear momentum is also a wave. The wavelength of a matter wave associated with a particle is inversely proportional to the magnitude of the particle's linear momentum. The speed of the matter wave is the speed of the particle.
Particle-Wave Duality is the concept that EM radiation or any particle of matter with linear momentum can behave like either a particle or a wave. Particles of matter also have a wavelength, called the de Broglie wavelength, λ = h/p, p = momentum. Matter also has the same interference characteristics as any other wave.
De Broglie's concept of the electron matter wave explains the quantization of the electron's angular momentum in Bohr's model of the hydrogen atom.
In the Davisson-Germer experiment, electrons are scattered off of a crystalline nickel surface. Diffraction patterns of electron matter waves are observed and give evidence for the existence of matter waves as these matter waves are observed in diffraction experiments with various particles.
Wave-particle duality exists in nature and under some experimental conditions, a particle acts as a particle and under other experimental conditions, a particle acts as a wave. Conversely, under some physical circumstances, electromagnetic radiation acts as a wave, and under other physical circumstances, radiation acts as a beam of photons.
Modern double-slit experiments with electrons demonstrated conclusively that electron-diffraction images are formed because of the wave nature of electrons. The wave-particle dual nature of particles and of radiation has no classical explanation.
Quantum theory states that the wave property is the fundamental property of all particles. A particle is considered a moving wave packet. The wave nature of particles imposes a limitation on the simultaneous measurement of the particle's position and momentum. Heisenberg's uncertainty principle sets the limits on precision in such simultaneous measurements.
Wave-particle duality phenomena is applied to many devices, such as charge-couple devices, (used in digital cameras) or in the electron microscopy of the scanning electron microscope and the transmission electron microscope.
Probability distributions for the location of particles exist rather than definite positions.
Heisenberg uncertainty principle describes the wave character of all particles and limits the precision with which certain physical quantities can be known simultaneously.
For position and momentum, the uncertainty principle is ΔxΔp>=h/4π where Δx is the uncertainty in position and Δp is the uncertainty in momentum.
For energy and time, the uncertainty principle is ΔEΔt>=h/4π where ΔE is the uncertainty in energy and Δt is the uncertainty in time. These small limits are fundamentally important on the quantum-mechanical scale.
The particle-wave duality refers to the fact that all particles, including those with mass and those without mass, have wave characteristics and this particle-wave duality is a further connection between mass and energy.
All bodies of matter radiate energy and the amount of radiation of a body emits depends on its temperature. A blackbody is an object that absorbs all electromagnetic radiation or light that hits it, reflecting none, and appears black. When heated, the blackbody emits thermal radiation whose spectrum depends only on temperature, as hotter bodies emit more intensely and peak at shorter wavelengths, as described by Planck's law and observed in stars and other objects.
Blackbody radiation is the emission of thermal electromagnetic radiation (EM) by an object with an emissivity of 1. This blackbody radiation led to the discovery of quantized energy. Max Plank discovered that the energy levels of the emitting atoms and molecules were quantized, with only the allowed values of E = (n+1/2)hf, where n is any non-negative integer (0, 1, 2, 3...). Planck's constant is h = 6.6 x 10^-34 J*s. Planck's blackbody radiation law is I(λ, T) = 2π hc^2/λ^5 (1/e^hc/λkBT-1)
Therefore, the oscillatory absorption and emission energies of atoms and molecules in a blackbody could increase or decrease only in steps of size ΔE = hf where f is the frequency of the oscillatory nature of the absorption and emission of EM radiation. Quantized energy levels are also identified by the atomic spectra lines, which are the EM emissions of individual atoms and molecules.
The experimental Wein's displacement law states that the hotter the body, the shorter the wavelength corresponding to the emission peak in the radiation curve: λmax T = b = 2.898x10^-3m*K, where λ is wavelength, T is temperature, and b is Wein's displacement constant.
The experimental Stefan's law states that the total power of radiation emitted across the entire spectrum of wavelengths at a given temperature is proportional to the fourth power of the Kelvin temperature of the radiating body. P(T)= σAT^4, P=power, T=temperature in K, σ=Boltzmann's constant, A=surface area.
Absorption and emission of radiation are studied as part of the model of a blackbody. The classical approach says that the exchange of energy between radiation and cavity walls is continuous. The classical approach does not explain the blackbody radiation curve. In order to explain the blackbody radiation curve, Planck assumed that the exchange of energy between radiation and cavity walls takes place only in discrete quanta of energy. Planck's hypothesis of energy quanta led to the theoretical Planck's radiation law, which agrees with the experimental blackbody radiation curve and also explains Wien's and Stefan's laws.
The photoelectric effect is the process in which EM radiation ejects electrons from a metal material surface in response to monochromatic radiation incident on the surface and it has three characteristics: (1) it is instantaneous (2) it occurs only when the radiation is above a cut-off frequency, and (3) kinetic energies of photoelectrons at the surface do not depend on the intensity of radiation. The photoelectric effect cannot be explained by classical theory. The photoelectric effect can be explained by assuming that radiation consists of photons (particles of light) and each photon carries a quantum of energy. The energy of a photon depends only on its frequency, which is the frequency of the radiation. At the surface, the entire energy of a photon is transferred to one photoelectron.
Albert Einstein proposed photons to be quanta of EM radiation having energy E = hf, where f is the frequency of the radiation. All EM radiation is composed of photons. Einstein explained that all characteristics of the photoelectric effect are due to the interaction of individual photons with individual electrons. The maximum kinetic energy KEe of ejected electrons (photoelectrons) at the metal surface is given by KE = hf - BE, (the energy-balance equation) where hf is the incident photon energy and BE(φ) is the binding energy (or work function) of the electron to the particular material. The work function is the binding energy of electrons to the metal surface. Each metal has its own characteristic work function. Kmax is directly proportional to the stopping potential (Vo) and the reverse voltage needed to halt the photocurrent: Kmax = eVo (e is the electron charge).
The Compton Effect describes X-rays scattered off some materials having different wavelengths than the wavelength of the incident X-rays. This phenomenon cannot be described classically. The Compton Effect is explained by assuming that radiation consists of photons that collide with weakly bound electrons in the target material. Both electron and photon are treated as relativistic particles. Conservation laws of the total energy and of momentum are obeyed in collisions. Treating the photon as a particle with momentum that can be transferred to an electron leads to a theoretical Compton shift that agrees with the wavelength shift measured in the experiment. This provides evidence that radiation consists of photons. Compton scattering is an inelastic scattering, in which scattered radiation has longer wavelength than that of incident radiation. Compton wavelength of an electron =λc = h/m0c = 0.00243 The Compton shift = Δλ = λc(1-cosθ)
Positions of absorption and emission lines in the spectrum of atomic hydrogen are predicted by the experimental Rydberg formula. Classical physics cannot explain the spectrum of atomic hydrogen. The Bohr model of hydrogen was the first model of atomic structure to correctly explain the radiation spectra of atomic hydrogen. It was preceded by the Rutherford nuclear model of the atom. In Rutherford's model, an atom consists of a positively charged point-like nucleus that contains almost the entire mass of the atom and of negative electrons that are located far away from the nucleus. The Balmer formula predicts the wavelengths of visible light from hydrogen's spectral lines.
The Bohr model of the hydrogen atom is based on three postulates (1) an electron moves around the nucleus in a circular orbit (2) an electron's angular momentum in the orbit is quantized, and (3) the change in an electron's energy as it makes a quantum jump from one orbit to another is always accompanied by the emission or absorption of a photon. Bohr's model is semi-classical because it combines the classical concept of electron orbit with the new concept of quantization.
Bohr's model of the hydrogen atom explains the emission and absorption spectra of atomic hydrogen and hydrogen-like ions with low atomic numbers. It was the first model to introduce the concept of a quantum number to describe atomic states and to postulate quantization of electron orbits in the atom. Bohr's model is an important step in the development of quantum mechanics, which deals with many-electron atoms.
Photon energy is responsible for many characteristics of EM radiation, being particularly noticeable at high frequencies. Photons have both wave and particle characteristics.
Photons have momentum, p = h/λ, where λ is the photon wavelength. Photon energy and momentum are related by p = E/c, where E = hf = hc/λ for a photon.
De Broglie's hypothesis of matter waves is that any particle of matter that has linear momentum is also a wave. The wavelength of a matter wave associated with a particle is inversely proportional to the magnitude of the particle's linear momentum. The speed of the matter wave is the speed of the particle.
Particle-Wave Duality is the concept that EM radiation or any particle of matter with linear momentum can behave like either a particle or a wave. Particles of matter also have a wavelength, called the de Broglie wavelength, λ = h/p, p = momentum. Matter also has the same interference characteristics as any other wave.
De Broglie's concept of the electron matter wave explains the quantization of the electron's angular momentum in Bohr's model of the hydrogen atom.
In the Davisson-Germer experiment, electrons are scattered off of a crystalline nickel surface. Diffraction patterns of electron matter waves are observed and give evidence for the existence of matter waves as these matter waves are observed in diffraction experiments with various particles.
Wave-particle duality exists in nature and under some experimental conditions, a particle acts as a particle and under other experimental conditions, a particle acts as a wave. Conversely, under some physical circumstances, electromagnetic radiation acts as a wave, and under other physical circumstances, radiation acts as a beam of photons.
Modern double-slit experiments with electrons demonstrated conclusively that electron-diffraction images are formed because of the wave nature of electrons. The wave-particle dual nature of particles and of radiation has no classical explanation.
Quantum theory states that the wave property is the fundamental property of all particles. A particle is considered a moving wave packet. The wave nature of particles imposes a limitation on the simultaneous measurement of the particle's position and momentum. Heisenberg's uncertainty principle sets the limits on precision in such simultaneous measurements.
Wave-particle duality phenomena is applied to many devices, such as charge-couple devices, (used in digital cameras) or in the electron microscopy of the scanning electron microscope and the transmission electron microscope.
Probability distributions for the location of particles exist rather than definite positions.
Heisenberg uncertainty principle describes the wave character of all particles and limits the precision with which certain physical quantities can be known simultaneously.
For position and momentum, the uncertainty principle is ΔxΔp>=h/4π where Δx is the uncertainty in position and Δp is the uncertainty in momentum.
For energy and time, the uncertainty principle is ΔEΔt>=h/4π where ΔE is the uncertainty in energy and Δt is the uncertainty in time. These small limits are fundamentally important on the quantum-mechanical scale.
The particle-wave duality refers to the fact that all particles, including those with mass and those without mass, have wave characteristics and this particle-wave duality is a further connection between mass and energy.