Electron spin

Electron spin is an intrinsic property of electrons, along with their mass and charge. Spin is not a classical rotation. It’s a quantum property and shouldn’t be interpreted literally as spinning. It is quantized, meaning it can only have certain discrete values.

  • A single orbital can only contain a maximum of two electrons (Pauli Exclusion Principle) and they can not have the same spin. This means that two electrons in the same orbital must have opposite spins.
  • The spin of an electron plays a key role in atomic structure and chemical bonding.
  • It is common to illustrate the spin of an electron using clockwise and anti-clockwise arrows. These are an analogy that serves as a way of understanding the two possible spin states.
  • A quantum number (ms) represents this property, with +1/2 representing spin up (represented by an arrow pointing clockwise) and -1/2 representing spin down (represented by an arrow pointing anti-clockwise).
  • In an atom, electrons are identified and described using four quantum numbers. These numbers provide information about the electron’s energy and location within the atom. Here’s a breakdown of each number:
Principal Quantum Number (n)
  • Determines the energy level of the electron. Larger values of n correspond to higher energy levels, further away from the nucleus.
  • Allowed values: positive integers starting from 1 (n = 1, 2, 3, …).
  • Example: Electrons in the innermost shell (1s) have n = 1, while those in the second shell (2s, 2p) have n = 2.
Azimuthal Quantum Number (l)
  • Defines the sub-shell (or orbital type) the electron occupies within a principal energy level. Different sub-shells have distinct shapes and capacities.
  • Allowed values: 0 ≤ l ≤ (n – 1). So, l = 0 for s orbitals, l = 1 for p orbitals, and so on.
  • Example: In the second energy level (n = 2), an electron with l = 0 occupies the 2s sub-shell (spherical), while one with l = 1 occupies a 2p sub-shell (dumbbell-shaped).
Magnetic Quantum Number (ml)
  • Specifies the orientation of the electron’s orbital within a subshell. Different ml values represent different possible orientations in space.
  • Allowed values: For example, a p orbital (l = 1) can have ml = -1, 0, or 1, corresponding to three different spatial orientations.
  • Example: Electrons in a p orbital with ml = 0 lie along the z-axis, while those with ml = ±1 lie in the x-y plane at different angles.
Electron Spin Quantum Number (ms)
  • Describes the intrinsic spin of the electron, a fundamental property unrelated to its motion.
  • Allowed values: ±1/2. Represents two possible spin states, often visualized as “up” and “down”.
  • Example: Two electrons in the same orbital must have opposite spin states (+1/2 and -1/2) according to the Pauli Exclusion Principle.
Related diagrams

Each diagram below can be viewed on its own page with a full explanation.

LMS colour space

The LMS colour space is a practical implementation of trichromatic colour theory that enables the full range of human observable colours to be specified by measuring the responsiveness of the L, M and S cones to each wavelength of light within the visible spectrum.

  • The LMS colour space was one of the first systematic demonstrations of trichromatic colour theory.
  • LMS describes how the three types of cone photoreceptors (L, M and S cone types) in a human eye respond given any particular light stimuli.
  • The method used in the development of the LMS colour space produced a generalized representation of human colour perception.
  • The underlying principle was that any colour can be described in physiological terms by measuring the response of the L, M and S cone cells in the human eye’s retina to different wavelengths of light.
  • The initial source of data for the LMS colour space was taken from experiments that compared the spectral sensitivity of subjects with normal sensitivity with other subjects experiencing forms of colour blindness.
  • A more recent technique used to collect data for LMS belongs to the field of visual psychophysics and is known as heterochromatic flicker photometry. It provides extensive and accurate spectral sensitivity data obtained from cellular material removed from the eye.
  • The LMS colour space describes human observable colours using three parameters, known as tristimulus colour values, each component of which corresponds with the response of the L, M and S cone types.
Tristimulus colour values
  • Tristimulus colour values have three components corresponding with the response of the L, M and S cone types. Each response is measured against a scale with values between 0 and 1.
  • LMS tristimulus colour values for a monochromatic red, green and blue stimulus might appear as follows:
    • Red: wavelength  = 635 nanometres: L = 0.3278612, M = 0.0444877, S = 0.0
    • Green: wavelength = 520 nanometres:  L = 0.6285647, M = 0.8166012, S = 0.02920317
    • Blue: wavelength= 450 nanometres: L = 0.04986433, M = 0.08705225, S = 0.9553885
    • Data from: https://cie.co.at/datatable/cie-2006-lms-cone-fundamentals-2-field-size-terms-energy
  • Tristimulus colour values can be thought of as colour-matching functions. If you know a tristimulus colour value then you can predict the corresponding colour experience.
Limitations of the LMS colour space
  • The LMS colour space provides an accurate physiological description of human colour perception but has limitations related to the fact that some colours in the visible spectrum appear brighter than others.
  • Whilst the achievements of the research that produced the LMS colour space underpin much of the subsequent developments within the field, LMS has been superseded by the CIE (1931) XYZ colour space.
  • The CIE (1931) XYZ colour space addresses the limitations of the LMS colour space by sacrificing physiologically accurate measurements of colour perceptions in favour of a solution better suited to everyday colour management..
  • The XYZ tristimulus colour parameters replace the LMS tristimulus colour parameters
  • XYZ is a more convenient representation and the CIE XYZ colour plot defines all the possible colours a human observer can see. For a given luminance Y, the XZ value specifies all possible chromaticity values one can see.
  • There is a simple linear transformation, via a 3 x 3 matrix, between LMS and XYZ.

Particle physics

Particle Physics is a branch of physics that studies the fundamental constituents of matter and energy and their interactions.

  • Particle physics is an experimental sub-field of quantum mechanics often associated with the Large Hadron Collider at CERN.
  • The Large Hadron Collider is a particle accelerator, which collides particles at high energies. These collisions create new particles, which are then studied by detectors. The detectors measure the properties of the new particles, such as their mass, energy, and charge.
  • The Standard Model serves as the theoretical framework employed by particle physicists to investigate fundamental forces and particles.
  • Among the most important discoveries of particle physics was the discovery of the photon and the dual nature of light (both a wave and particle).

Particle physics

Particle physics is a branch of physics that studies the fundamental constituents of matter and energy and their interactions.

  • Particle physics is an experimental sub-field of quantum mechanics often associated with the Large Hadron Collider at CERN.
  • Large Hadron Collider is a particle accelerator, which collides particles at high energies. These collisions create new particles, which are then studied by detectors. The detectors measure the properties of the new particles, such as their mass, energy, and charge.
  • The Standard Model serves as the theoretical framework used by particle physicists to investigate fundamental forces and particles.
  • Among the most important discoveries of particle physics was the discovery of the photon and the dual nature of light (both a wave and particle).

Perceived colour

Perceived colour refers to what an observer sees in any given situation and so is a subjective experience.

  • Our ability to perceive and distinguish between colours is crucial to how we experience and understand the world.
  • Perceived colour is influenced by the range and mixture of wavelengths and intensities of light that enter the eye.
  • Perceived colour can be influenced by the properties of light, objects, and the attributes of visual perception.
  • Colour perception tends to prioritize information that is important to an observer, but it may not always be objectively accurate.
  • The perceived colour of an object can be influenced by factors, such as the size, shape, and structure of objects, their position and orientation, and the direction of incident light.
  • Colour perception can be described by chromatic colour names (such as pink, orange, brown, green, blue, and purple) and achromatic colour names (such as black, grey or white).
  • Perceived colour is often a combination of chromatic and achromatic content.
  • The state of adaptation of an observer’s visual system can affect colour perception, such as when fatigued cells in the retina produce after-images.
  • An observer’s expectations, priorities, current activities, recollections, and previous experiences can all influence perceived colour.
  • The International Commission on Illumination (CIE) defines perceived colour as having three main characteristics: hue, brightness (or lightness), and colourfulness (or saturation/chroma).
  • Here at lightcolourvision.org we often characterise colour in terms of hue, saturation and brightness and so align our discussions with the HSB colour model.

Perceived colour

Perceived colour refers to what an observer sees in any given situation and so is a subjective experience.

  • Our ability to perceive and distinguish between colours is crucial to how we experience and understand the world.
  • Perceived colour is influenced by the range and mixture of wavelengths and intensities of light that enter the eye.
  • Perceived colour can be influenced by the properties of light, objects, and the attributes of visual perception.
  • Colour perception tends to prioritize information that is important to an observer, but it may not always be objectively accurate.
  • The perceived colour of an object can be influenced by factors, such as the size, shape, and structure of objects, their position and orientation, and the direction of incident light.
  • Colour perception can be described by chromatic colour names (such as pink, orange, brown, green, blue, and purple) and achromatic colour names (such as black, grey or white).
  • Perceived colour is often a combination of chromatic and achromatic content.
  • The state of adaptation of an observer’s visual system can affect colour perception, such as when fatigued cells in the retina produce after-images.
  • An observer’s expectations, priorities, current activities, recollections, and previous experiences can all influence perceived colour.

Phosphorescence

Phosphorescence is a type of photoluminescence where a material absorbs energy from a light source (like sunlight or UV light) and then emits light at a slower rate, even after the light source has been removed. The emitted light often has a longer wavelength than the absorbed light, causing a characteristic glow-in-the-dark effect.

Here is a short explanation of phosphorescence:

  • Excitation: When a phosphorescent material is exposed to light, electrons within the material absorb the photons’ energy and move to a higher energy state (become excited).
  • Trapped State: Unlike fluorescence, where electrons immediately return to their ground state and emit light, in phosphorescence, the excited electrons get “trapped” in a forbidden triplet state. This means they can’t directly transition back to their lower energy state.
  • Gradual Release: Over time, the trapped electrons slowly find their way back to the ground state, releasing the stored energy as light. This process is much slower than fluorescence, which is why phosphorescence produces that lingering afterglow.

Key Points:

  • Duration: Phosphorescence can last for seconds, minutes, or even hours, unlike fluorescence which ends almost immediately after the light source is removed.
  • Excitation Source: Phosphorescent materials typically need light with shorter wavelengths for excitation, such as ultraviolet light.

Examples:

  • Glow-in-the-dark toys: These are coated with phosphorescent materials.
  • Safety signs: Phosphorescent signs stay visible in low light conditions.
  • Watch dials: Some watch dials used to use phosphorescent paint for nighttime visibility (this has been replaced by safer alternatives in modern watches).
Light sources
Emission mechanism DescriptionExamples
LIGHT-EMITTING PROCESS
LuminescenceLight emission due to the excitation of electrons in a material.Electrons within a material gain energy and then release light as they return to a lower energy state.Bioelectroluminescence
Electroluminescence
Photoluminescence
- Fluorescence
- Phosphorescence
Sonoluminescence
Thermoluminescence
Blackbody radiation (Type of thermal radiation)Electromagnetic radiation (including visible light) emitted by any object with a temperature above absolute zero.Electromagnetic radiation (including visible light) emitted by any object with a temperature above absolute zero.All objects above temperature of absolute zero.
ChemiluminescenceLight from natural and artificial chemical reactions.Light from natural and artificial chemical reactions.Bioluminescence
Chemiluminescent reactions:
- Luminol reactions
- Ruthenium chemiluminescence
Nuclear reactionLight emission as a byproduct of nuclear reactions (fusion or fission).Light emitted as a byproduct of nuclear reactions.Nuclear reactors
Stars undergoing fusion
Thermal radiationLight emission due to the thermal excitation of atoms and molecules at high temperatures.Light emission due to the thermal excitation of atoms and molecules.Sun
Stars
Incandescent light bulbs
TriboluminescenceLight emission due to mechanical stress applied to a material.Light emission due to the mechanical stress applied to a material, causing the movement of electric charges and subsequent light emission.Sugar crystals cracking
Adhesive tape peeling
Quartz crystals fracturing.
Natural light source
Fireflies
Deep-sea creatures
Glowing mushrooms
Bioluminescence Light emission from biological organisms.Involves the luciferase enzyme.
Sun
Stars
Nuclear FusionLight emission as a byproduct of nuclear fusion reactions in stars.Electromagnetic spectrum (visible light, infrared, ultraviolet).
Fire
Candles
Thermal radiationLight emission due to the thermal excitation of atoms and molecules during the combustion of a fuel source.Burning of a fuel source, releasing heat and light.
Artificial light source
Fluorescent lights Highlighters
Safety vests
Chemiluminescence Light emission from chemical reactions.Fluorescence (absorption and re-emission of light).
Glow sticks
Emergency signs
ChemiluminescenceLight emission due to phosphorescence - a type of chemiluminescence.A type of chemiluminescence where light emission is delayed after the initial excitation.
Glow sticks
Light sticks
Chemiluminescence Chemiluminescence Light emission from a chemical reaction that does not involve combustion.
Tungsten light bulbs
Toasters
Thermal radiationHeated filament radiates light and heat.Light emission from a hot filament.
Fluorescent lamps
LED lights
ElectroluminescenceExcitation of atoms by electric current.Light emission when electric current excites atoms in a material.
Neon signsElectrical DischargeDischarge of electricity through gas.Light emission when electricity flows through a gas.
Sugar crystals cracking
Pressure-sensitive adhesives
TriboluminescenceLight emission from friction or pressure.Light emission due to mechanical forces.
Fluorescent paint Highlighters
Safety vests
PhotoluminescenceAbsorption and subsequent re-emission of light at a lower energy.Absorption and re-emission of light.

Light Sources: Mechanism, examples, and everyday applications

Footnote: Cerenkov radiation and Synchrotron radiation are not included in the table because they are not conventionally classified as light sources.

Phosphorescence

Phosphorescence is a type of photoluminescence where a material absorbs energy from a light source (such as sunlight or UV light) and then emits light at a slower rate, even after the light source has been removed. The emitted light often has a longer wavelength than the absorbed light, causing a characteristic glow-in-the-dark effect.

  • Here is a short explanation:
    • Excitation: When a phosphorescent material is exposed to light, electrons within the material absorb the photons’ energy and move to a higher energy state (become excited).
    • Trapped State: Unlike fluorescence, where electrons immediately return to their ground state and emit light, in phosphorescence, the excited electrons get “trapped” in a forbidden triplet state. This means they can’t directly transition back to their lower energy state.
    • Gradual Release: Over time, the trapped electrons slowly find their way back to the ground state, releasing the stored energy as light. This process is much slower than fluorescence, which is why phosphorescence produces that lingering afterglow.

Photoluminescence

Photoluminescence is the emission of light from a material after it absorbs light. This process involves exciting the electrons in the material to a higher energy level, followed by their relaxation back to a lower energy level, releasing energy in the form of light.

Photoluminescence in three Steps
  1. Absorption: Light excites electrons in a material, pushing them to higher energy levels.
  2. Relaxation: Excited electrons gradually lose energy.
  3. Light Emission: Lost energy is emitted as light of a different wavelength (usually longer).
Key Points
  • Emitted light often has lower energy (longer wavelength) than absorbed light due to energy loss.
  • Different types of photoluminescence exist based on relaxation mechanisms:
    • Fluorescence: Quick relaxation, emitting light soon after absorption.
    • Phosphorescence: Slower relaxation, emitting light later, creating a “glow” effect.
    • Chemiluminescence: Light emission due to a chemical reaction. The reaction can be initiated by various factors, including but not limited to light absorption.
Applications
  • Fluorescent lamps convert ultraviolet light to visible light.
  • LEDs use electroluminescence (photoluminescence triggered by electricity).
  • Biological markers help visualize structures or processes in cells.
  • Quantum dots have bright, tunable photoluminescence for displays and solar cells.
Light sources
Emission mechanism DescriptionExamples
LIGHT-EMITTING PROCESS
LuminescenceLight emission due to the excitation of electrons in a material.Electrons within a material gain energy and then release light as they return to a lower energy state.Bioelectroluminescence
Electroluminescence
Photoluminescence
- Fluorescence
- Phosphorescence
Sonoluminescence
Thermoluminescence
Blackbody radiation (Type of thermal radiation)Electromagnetic radiation (including visible light) emitted by any object with a temperature above absolute zero.Electromagnetic radiation (including visible light) emitted by any object with a temperature above absolute zero.All objects above temperature of absolute zero.
ChemiluminescenceLight from natural and artificial chemical reactions.Light from natural and artificial chemical reactions.Bioluminescence
Chemiluminescent reactions:
- Luminol reactions
- Ruthenium chemiluminescence
Nuclear reactionLight emission as a byproduct of nuclear reactions (fusion or fission).Light emitted as a byproduct of nuclear reactions.Nuclear reactors
Stars undergoing fusion
Thermal radiationLight emission due to the thermal excitation of atoms and molecules at high temperatures.Light emission due to the thermal excitation of atoms and molecules.Sun
Stars
Incandescent light bulbs
TriboluminescenceLight emission due to mechanical stress applied to a material.Light emission due to the mechanical stress applied to a material, causing the movement of electric charges and subsequent light emission.Sugar crystals cracking
Adhesive tape peeling
Quartz crystals fracturing.
Natural light source
Fireflies
Deep-sea creatures
Glowing mushrooms
Bioluminescence Light emission from biological organisms.Involves the luciferase enzyme.
Sun
Stars
Nuclear FusionLight emission as a byproduct of nuclear fusion reactions in stars.Electromagnetic spectrum (visible light, infrared, ultraviolet).
Fire
Candles
Thermal radiationLight emission due to the thermal excitation of atoms and molecules during the combustion of a fuel source.Burning of a fuel source, releasing heat and light.
Artificial light source
Fluorescent lights Highlighters
Safety vests
Chemiluminescence Light emission from chemical reactions.Fluorescence (absorption and re-emission of light).
Glow sticks
Emergency signs
ChemiluminescenceLight emission due to phosphorescence - a type of chemiluminescence.A type of chemiluminescence where light emission is delayed after the initial excitation.
Glow sticks
Light sticks
Chemiluminescence Chemiluminescence Light emission from a chemical reaction that does not involve combustion.
Tungsten light bulbs
Toasters
Thermal radiationHeated filament radiates light and heat.Light emission from a hot filament.
Fluorescent lamps
LED lights
ElectroluminescenceExcitation of atoms by electric current.Light emission when electric current excites atoms in a material.
Neon signsElectrical DischargeDischarge of electricity through gas.Light emission when electricity flows through a gas.
Sugar crystals cracking
Pressure-sensitive adhesives
TriboluminescenceLight emission from friction or pressure.Light emission due to mechanical forces.
Fluorescent paint Highlighters
Safety vests
PhotoluminescenceAbsorption and subsequent re-emission of light at a lower energy.Absorption and re-emission of light.

Light Sources: Mechanism, examples, and everyday applications

Footnote: Cerenkov radiation and Synchrotron radiation are not included in the table because they are not conventionally classified as light sources.

Photoluminescence

Photoluminescence is the emission of light from a material after it absorbs light.

  • The process involves exciting the electrons in the material to a higher energy level, followed by their relaxation back to a lower energy level, releasing energy in the form of light.
  • Photoluminescence takes place in three steps:
    1. Absorption: Light excites electrons in a material, pushing them to higher energy levels.
    2. Relaxation: Excited electrons gradually lose energy.
    3. Light Emission: Lost energy is emitted as light of a different wavelength (usually longer).

Photometry

Photometry is the science concerned with measuring the human perception of light.

  • Measuring human visual responses to light is not straightforward because the eye is a complex and intricate organ.
  • An internationally recognized system of measurements, known as the CIE system, was established in 1931 by the Commission Internationale de l’Eclairage (CIE).
  • The Commission established the typical spectral responsiveness of the human eye to wavelengths across the visible spectrum and compiled the data into a photopic curve.
  • The CIE’s photopic curve shows that, in bright light, the strongest response of the human eye is to the colour green with less sensitivity towards the spectral extremes, red and violet.
  • A second set of measurements of the typical responsiveness of the human eye to wavelengths across the visible spectrum at low levels of light, (where determining colour differences is difficult), resulted in data compiled into the scotopic curve.
  • Having defined the spectral response of the human eye, the CIE sought a standard light source to measure luminous intensity.
  • Luminous intensity is a measure of how bright a light source appears to the human eye, and it is typically used to describe the brightness of light sources such as light bulbs, lamps, and LEDs.
  • The first source, which led to the development of the terms footcandle and candlepower, was a specific type of candle commonly used in the 18th and 19th centuries before standardised artificial light sources were developed.
  • In 1948, the standard was redefined for better repeatability. It was named the International Candle and defined as the amount of light emitted from a given quantity of melting platinum.

Photometry

Photometry is the science concerned with measuring the human perception of light.

  • Measuring human visual responses to light is not straightforward because the eye is a complex and intricate organ.
  • An internationally recognized system of measurements, known as the CIE system, was established in 1931 by the Commission Internationale de l’Eclairage (CIE).
  • The Commission established the typical spectral responsiveness of the human eye to wavelengths across the visible spectrum and compiled the data into a photopic curve.
  • The CIE’s photopic curve shows that, in bright light, the strongest response of the human eye is to the colour green with less sensitivity towards the spectral extremes, red and violet.
  • A second set of measurements of the typical responsiveness of the human eye to wavelengths across the visible spectrum at low levels of light, (where determining colour differences is difficult), resulted in data compiled into the scotopic curve.

Photon

A photon is a particle that carries electromagnetic radiation. It is the fundamental unit of light.

  • Thinking of photons as particles is useful for understanding the quantum nature of light.
  • In the world of quantum physics, photons are the fundamental constituents of all forms of electromagnetic radiation, including light. They serve as the carriers of the electromagnetic force.
  • Photons are elementary particles that have no mass and no electric charge. They are the quanta of the electromagnetic field, which is the fundamental field that describes electromagnetic interactions. Electromagnetic radiation, including light, is a manifestation of the electromagnetic field.
  • Photons are the carriers of electromagnetic force because they are the only particles that can mediate electromagnetic interactions. When two charged particles interact electromagnetically, they exchange photons. The exchange of photons gives rise to the electromagnetic force.<
  • Photons have no rest mass and always travel at the speed of light in a vacuum.
  • Photons exhibit both wave-like and particle-like properties, a characteristic referred to as wave-particle duality. This duality is inherent to quantum particles, causing light to behave as a wave under certain conditions, as both waves and photons in others, and strictly as particles in yet others.
Photons properties
  • Photons, the elemental particles of electromagnetic radiation, possess distinct properties:
    • Energy: The energy of a photon is contingent upon its frequency or wavelength. Higher frequencies correspond to greater energy levels.
    • Number: Intensity or brightness dictates the number of photons present in electromagnetic radiation. Higher intensities correlate with larger photon counts.
    • Direction and Polarization: Photons travel in straight paths, but interactions with matter can alter their direction. Additionally, photons can exhibit polarization, indicating the orientation of their electric and magnetic fields.
    • Speed: Photons travel at the speed of light, an astounding 299,792,458 meters per second in a vacuum.
Photons and mass
  •  The statement above about zero rest mass can be broken down as follows:
    • According to the theory of relativity, any object that has mass needs energy to accelerate.
    • The amount of energy required to accelerate an object increases as the object’s mass increases.
    • Photons are unique in that they have zero rest mass and this means they do not require any energy to be accelerated.
    • As a result, they always move at the speed of light in a vacuum.
    • So photons always travel at approximately 299,792 kilometres per second and, when undisturbed, they never decelerate or come to a halt.
Energy of photons, wavelength, frequency and colour
  • The energy of a photon (its photon energy) is intrinsically linked to its wavelength and frequency, and in perceptual terms, to its colour.
    • Photon Energy: The energy of a photon, E, is given by the equation E=hf, where h is Planck’s constant and f is the frequency of the photon. So, a photon with a higher frequency has higher energy.
    • Frequency and Wavelength: Frequency (f) and wavelength (λ) are related by the speed of light (c), through the equation c=fλ. So, photons with a higher frequency have a shorter wavelength, and photons with a lower frequency have a longer wavelength.
    • Colour Perception: In terms of colour perception, different frequencies and wavelengths of electromagnetic energy are perceived as different colours.
    • For example, photons with high energy (high frequency, short wavelength) are perceived as blue/violet, while photons with lower energy (low frequency, long wavelength) are perceived as red. The range of frequencies (or wavelengths) that human eyes can detect is known as the visible light spectrum.
Photons and interaction with charged particles
  • Photons can interact with charged particles such as electrons within atoms. In such events, they can either be absorbed, resulting in the elevation of the particle to a higher energy state or be emitted when a particle transitions from a higher energy state to a lower one.
  • A higher energy state refers to a quantum state or level of an atomic or subatomic system in which an electron or particle has absorbed energy and moved to a more excited or elevated position, typically farther from the nucleus or centre of the system.
Photons and interaction with matter
  • Photons can engage with matter through various processes. They can be scattered, absorbed, or emitted during interactions with atoms and molecules. These processes are crucial for a range of phenomena from the heating of surfaces under sunlight to the transmission of information in fibre optic cables.
Photons and polarization
  • Photons can be polarized. This means their electric and magnetic fields can oscillate in a specific orientation. Polarization is used in various applications, from LCD screens to polarized sunglasses, and is also a significant aspect of certain quantum mechanical phenomena.
Photons and their Energy, Frequency, Wavelength and Momentum
  • The energy of a photon determines its frequency, wavelength and momentum. This energy can be transferred during interactions, leading to phenomena like fluorescence and the photoelectric effect. In the visible spectrum, different energies (and therefore frequencies and wavelengths) correspond to different colours of light.
  • The energy of a photon is directly proportional to its frequency. This means that photons with higher frequencies have more energy. The energy of a photon is also inversely proportional to its wavelength. This means that photons with longer wavelengths have less energy. The momentum of a photon is inversely proportional to its wavelength. This means that photons with shorter wavelengths have more momentum.
Photons and wave-particle duality
  • 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.

Photon

A photon is a particle that carries electromagnetic radiation. It is the fundamental unit of light.

  • Thinking of photons as particles is useful for understanding the quantum nature of light.
  • In the world of quantum physics, photons are the fundamental constituents of all forms of electromagnetic radiation, including light. They serve as the carriers of the electromagnetic force.
  • Photons are elementary particles that have no mass and no electric charge. They are the quanta of the electromagnetic field, which is the fundamental field that describes electromagnetic interactions. Electromagnetic radiation, including light, is a manifestation of the electromagnetic field.
  • Photons are the carriers of electromagnetic force because they are the only particles that can mediate electromagnetic interactions. When two charged particles interact electromagnetically, they exchange photons. The exchange of photons gives rise to the electromagnetic force.<
  • Photons have no rest mass and always travel at the speed of light in a vacuum.
  • Photons exhibit both wave-like and particle-like properties, a characteristic referred to as wave-particle duality. This duality is inherent to quantum particles, causing light to behave as a wave under certain conditions, as both waves and photons in others, and strictly as particles in yet others.

Photon energy

Photon energy is the energy carried by a single photon. The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength.

  • The higher the photon’s frequency, the higher its energy. Equivalently, the shorter the photon’s wavelength, the higher its energy.
  • Photon energy is determined solely by the photon’s frequency and wavelength.
  • Other factors, such as the intensity of the radiation, do not affect the energy of individual photons. In other words, two photons of light with the same frequency have the same energy, regardless of their source. even if one was emitted from a wax candle and the other from the Sun.
  • The electronvolt (eV) and the joule are the units commonly used to express the energy of photons.
  • The energy of a photon can also be expressed:
    • In terms of its wavelength or frequency using Planck’s constant (h). E = hν = hc/λ, where E is the energy, ν is the frequency, λ is the wavelength, and c is the speed of light.
    • As a quantum of electromagnetic radiation.

Photon energy

Photon energy is the energy carried by a single photon.

  • The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength.
  • The higher the photon’s frequency, the higher its energy. Equivalently, the shorter the photon’s wavelength, the higher its energy.
  • Photon energy is determined solely by the photon’s frequency and wavelength.
  • Other factors, such as the intensity of the radiation, do not affect the energy of individual photons. In other words, two photons of light with the same frequency have the same energy, regardless of their source. even if one was emitted from a wax candle and the other from the Sun.

Photon-electron interaction

In photon-electron interactions, a photon can either be absorbed by an electron or scattered by it. During the interaction, the photon transfers some or all of its energy and momentum to the electron.

  • One of the most common interactions used to explain the link between electromagnetism and light (including visible light and other parts of the spectrum) is the photon-electron interaction.
  • The specific outcome of a photon-electron interaction depends on the photon’s energy and the electron’s state. For example, if the photon has enough energy, it can free a bound electron from the atom. This is known as the photoelectric effect.
  • If the photon does not have enough energy to eject the electron, it can be scattered by the electron. Compton scattering involves high-energy photons, like X-rays or gamma rays, where the photon transfers part of its energy to the electron. The photon loses energy (shifts to a longer wavelength) and changes direction, while the electron gains kinetic energy.
  • On absorption of a photon by an electron, the electron gains energy and transitions to a higher energy level – a higher orbital around the nucleus of the atom.
  • When an electron scatters a photon elastically, such as in Rayleigh scattering, the photon alters its trajectory but retains its energy, and the electron’s energy level remains unaffected. In Compton scattering, however, the electron gains energy.
  • A photon can transfer all of its energy to an electron if it has more energy than the electron’s binding energy. In this case, the electron will be ejected from the atom with excess kinetic energy.
  • The amount of energy a photon can transfer to an electron is capped by the photon’s own energy. A photon cannot impart more energy to an electron than it possesses.
  • The likelihood of a photon being absorbed by an electron depends on both the photon’s energy and the electron’s energy level. Absorption occurs when the photon’s energy exactly matches the difference between two energy levels (resonant absorption). Generally, higher photon energy increases the absorption likelihood, while higher electron energy levels tend to decrease the absorption probability due to fewer available transitions.
  • The likelihood of photon scattering is influenced by the photon’s energy and the electron’s energy state. In Compton scattering, the angle of photon-electron collision affects the energy loss of the photon. Polarization of the photon and electron spin can also influence specific types of scattering, but spin is less central in general scattering processes.
  • Examples of a photons-electron interaction include:
    • Photoelectric Effect: When a photon with adequate energy impacts an electron, the electron can be expelled from the atom. Called the photoelectric effect, the photon’s energy must exceed the electron’s binding energy within the atom.
    • Compton Scattering: In a collision between a photon and an electron, the photon can scatter. The photon might relinquish energy during the collision, and the electron can acquire a portion of the photon’s energy.
    • Chromophore excitation: The photon-chromophore interaction accounts for the observable colour of objects.
      • The interaction between photons and chromophores is more intricate than photon-electron interaction. It encompasses energy redistribution among all electrons in a molecule and can result in various outcomes such as fluorescence, phosphorescence, and energy transfer.
      • The interaction between photons and chromophores is generally referred to as molecular excitation or chromophore excitation, distinct from photon-electron interaction but can still be considered a type of photon-electron interaction since it involves the interaction of photons with the electrons in chromophore molecules.
References
  • 1
  • 2

Photon-electron interaction

In photon-electron interactions, a photon can either be absorbed by an electron or scattered by it. During the interaction, the photon transfers some or all of its energy and momentum to the electron.

  • One of the most common interactions used to explain the link between electromagnetism and light (including visible light and other parts of the spectrum) is the photon-electron interaction.
  • The specific outcome of a photon-electron interaction depends on the photon’s energy and the electron’s state. For example, if the photon has enough energy, it can free a bound electron from the atom. This is known as the photoelectric effect.
  • If the photon does not have enough energy to eject the electron, it can be scattered by the electron. Compton scattering involves high-energy photons, like X-rays or gamma rays, where the photon transfers part of its energy to the electron. The photon loses energy (shifts to a longer wavelength) and changes direction, while the electron gains kinetic energy.
  • On absorption of a photon by an electron, the electron gains energy and transitions to a higher energy level – a higher orbital around the nucleus of the atom.
  • When an electron scatters a photon elastically, such as in Rayleigh scattering, the photon alters its trajectory but retains its energy, and the electron’s energy level remains unaffected. In Compton scattering, however, the electron gains energy.
  • A photon can transfer all of its energy to an electron if it has more energy than the electron’s binding energy. In this case, the electron will be ejected from the atom with excess kinetic energy.
  • The amount of energy a photon can transfer to an electron is capped by the photon’s own energy. A photon cannot impart more energy to an electron than it possesses.
  • The likelihood of a photon being absorbed by an electron depends on both the photon’s energy and the electron’s energy level. Absorption occurs when the photon’s energy exactly matches the difference between two energy levels (resonant absorption). Generally, higher photon energy increases the absorption likelihood, while higher electron energy levels tend to decrease the absorption probability due to fewer available transitions.
  • The likelihood of photon scattering is influenced by the photon’s energy and the electron’s energy state. In Compton scattering, the angle of photon-electron collision affects the energy loss of the photon. Polarization of the photon and electron spin can also influence specific types of scattering, but spin is less central in general scattering processes.

Photopic curve

A photopic curve is a graphical representation of the sensitivity of the human eye to light under normal, bright lighting conditions. It indicates that the human eye has the strongest response to green light, with less sensitivity to the red and violet ends of the visible spectrum.

  • The standard photopic curve used in the CIE 1931 colour space is based on the photopic luminosity function, which describes the average sensitivity of the human eye to different wavelengths of light under normal, bright lighting conditions.
  • A photopic luminosity function is a mathematical function used to derive the photopic curve from the CIE 1931 colour space.
  • The CIE 1931 colour space is a standardized system for describing colours based on human colour perception. It was developed by the International Commission on Illumination (CIE) in 1931 and is still widely used today.
  • In low light conditions, the sensitivity of the human eye to light changes, and the scotopic curve is used to describe the response of the eye to light.
  • Scotopic and photopic curves have different units of measurement.
    • A photopic curve uses units of luminous flux, which is a measure of the total amount of visible light emitted by a source.
    • A scotopic curve, on the other hand, uses units of luminous intensity, which is a measure of the brightness of a light source per unit of solid angle.

Photopic Curve

A photopic curve is a graphical representation of the sensitivity of the human eye to light under well-lit conditions, such as during the day or in brightly lit environments.

  • The photopic curve appears as a line graph that illustrates how sensitive the human eye is to different wavelengths (colours) of light in these bright conditions. This curve is essential for understanding colour perception and visual acuity in bright light. It shows the minimum amount of light required for the eye to detect various wavelengths.
  • This information is derived from the response of our cone cells, which are responsible for colour vision and function optimally in bright light.
  • Closely related to a photopic curve is a scotopic curve is a graphical representation of the sensitivity of the human eye to light under low-light conditions, such as at night or in very dimly lit environments.
  • The scotopic curve also resembles a line graph that shows how sensitive the eye is to light in these low-light conditions. It is an important tool for understanding night vision. The curve illustrates the minimum amount of light needed for the eye to detect different wavelengths (colours) of light.
  • This information comes from the response of our rod cells, which are more active in low light compared to the cone cells that dominate in bright conditions.
  • It is interesting to note that the scotopic and photopic curves use different units to measure light. The scotopic curve uses units related to light intensity per unit area (such as brightness per square degree), whereas the photopic curve uses units similar to overall brightness.