Physik Abitur Lernzettel (english) / Physics exam
preparation – Quantum Physics, Photons and Photoelectric
Effect
Table of Contents
Quantum Physics
Wave function and interference
Wave-particle duality
Photons
Properties of photons
Energy, wavelength and frequency (calculations and examples)
Momentum of photons
Photoelectric Effect
Definition and laws
Threshold frequency and work function
Kinetic energy of electrons
Experimental explanations
Experiments and Applications
Hallwachs experiment
Einstein’s explanation
Millikan experiment
Further Quantum Effects
Compton effect
Quantization of charge
1
,1. Quantum physics (mechanics)
Quantum physics (mechanics) is the study of matter and energy at the most fundamental (smallest)
level. Here, it mainly examines how small objects can simultaneously exhibit characteristics of both
particles (tiny pieces of matter) and waves (a disturbance or variation that transfers energy). This is
called the “wave-particle duality.”
1. Quantum wave function:
Description:
In quantum physics, a wave function is a mathematical quantity that describes the position and
quantum state of a particle.
The properties of quantum wave functions:
-The wave function describes both wave-like behaviors (such as interference) and particle-like
behaviors (such as the photoelectric effect)
-When two or more wave functions interact in space, their phases (specific positions within a wave
cycle) leads to a phenomenon called interference. When this happens, the waves interact, either
reinforcing or canceling each other depending on relative phases. Interference can be constructive
or destructive
Constructive interference:
When two waves meet in phase (meaning their peaks and troughs align), they combine to create a
wave with a larger amplitude than either wave alone. This leads to an increase in wave intensity.
Destructive interference:
When two waves meet out of phase (where the peak of one wave aligns with the trough of the
other), they can cancel each other out. This results in in a smaller or even zero amplitude in the
overlapping region.
2. Particle - wave duality:
1. The structure of particle - wave duality:
Definition:
Wave-particle duality is a concept in quantum mechanics in which every particle or quantum entity
may be described as either a particle or a wave. This is because when certain conditions change, the
particle or quantum entity can either exhibit properties of a particle or a wave.
Main properties of particle - wave duality:
-According to the wave-particle theory, light has the properties of both a wave and a particle
-Wave-particle duality refers to the fundamental property of matter (such as light and electrons)
where it exhibits particle or wave properties depending on experimental circumstances
2
,2. Photons
1. The structure of photons:
Definition:
Photons are the smallest possible particles of light. As a result, the photon is also the "quantum," or
fundamental unit, of electromagnetic radiation including radio waves, gamma-rays, and visible light.
This means that they are not made up of smaller components or internal structures. Some other
types of quanta (plural) are electrons, neutrinos, and the Higgs boson. In addition, photons exhibit
wave-particle duality. In certain conditions of light, the photons behave as particles (during the
photoelectric effect) and in others as waves (during diffraction and interference).
Properties of photons:
-Photons have no rest mass, which allows them to travel at the speed of light (approximately 3×108
ms-1) in a vacuum
-Photons exhibit both wave-like and particle-like properties
-> They behave as particles in phenomena like the photoelectric effect and as waves in phenomena
like diffraction and interference
-The energy of a photon is directly proportional to its frequency, expressed by the equation E = h ⋅ f,
where E is energy, h is Planck's constant, and f is frequency
-> Higher frequency photons (e.g., gamma rays) have more energy than lower frequency photons
(e.g., radio waves)
-Photons are electrically neutral, meaning they do not carry any charge. This neutrality allows
photons to interact with electric and magnetic fields without being influenced by them
-Despite being massless, photons carry momentum, calculated as p = E / C, where p is momentum,
E is energy, and c is the speed of light
-Since photons are the smallest particle of light, they make up all forms of electromagnetic radiation,
each differing in frequency and energy
3
, 2. Calculations for photons:
1. Energy of a photon:
The energy (E) of a photon is directly proportional to its frequency (f) and is calculated by the
equation: E = h ⋅ f. This means that higher frequency photons (like gamma rays) have more energy,
while lower frequency photons (like radio waves) have less energy.
-Energy of a photon (E / electronvolt (eV) or joule J): The energy carried by a photon.
-Planck's constant (h /6.626×10−34 J⋅s): Planck's constant connects the energy of electromagnetic
waves to their frequency
-Frequency of the photon (f / Hertz Hz): The number of waves (cycles) that pass a fixed point in one
second (measured in Hz) (Hz (1000) kHz (1000) MHz (1000) GHz (1000) THz (1000).
2. Wavelength and frequency relationship:
The frequency (f) and wavelength (λ) of a photon are inversely related and connected by the speed
of light (c): f = c / λ . The formula shows that frequency (f) and wavelength (λ) are inversely
proportional. As the wavelength of a photon increases, its frequency decreases, and vice versa.
-Speed of light (c / 3×108 ms-1): This is the constant speed at which light and all electromagnetic
radiation travel in a vacuum.
-Wavelength of the photon (λ / meters): Measured in meters m, the wavelength is the distance
between two consecutive peaks of the electromagnetic wave.
This relationship can be combined with Planck’s formula (E = h ⋅ f) -> E = h ⋅ c / λ. Accordingly, energy
is inversely proportional to wavelength. Shorter-wavelength photons have higher energy, while
longer-wavelength photons have lower energy.
3. Momentum of a photon:
Even though photons are massless, they still carry momentum (p), which is given by: p = E / c. This
equation shows how momentum is directly proportional to a photon´s energy. Since c (the speed of
light) is constant, an increase in momentum (p) results in a proportional increase in energy (E).
-Momentum (p / kg⋅m/s): Momentum is defined as the product of an object's mass and velocity. The
formula to calculate momentum is: Momentum (p) = Mass (m) × Velocity (v).
-Energy of a photon (E / electronvolt eV or joule J): The energy carried by a photon.
-Speed of light (c / 3×108 ms-1): This is the constant speed at which light and all electromagnetic
radiation travel in a vacuum.
The energy E of a photon is also related to its frequency f and wavelength λ by E = h⋅ c / λ. Thus the
momentum of a photon can also be expressed in terms of of wavelength as: p = λ / h
This equation shows that a photon’s momentum is inversely proportional to its wavelength. Shorter
wavelengths correspond to higher momentum while longer wavelengths correspond to lower
momentum.
4
preparation – Quantum Physics, Photons and Photoelectric
Effect
Table of Contents
Quantum Physics
Wave function and interference
Wave-particle duality
Photons
Properties of photons
Energy, wavelength and frequency (calculations and examples)
Momentum of photons
Photoelectric Effect
Definition and laws
Threshold frequency and work function
Kinetic energy of electrons
Experimental explanations
Experiments and Applications
Hallwachs experiment
Einstein’s explanation
Millikan experiment
Further Quantum Effects
Compton effect
Quantization of charge
1
,1. Quantum physics (mechanics)
Quantum physics (mechanics) is the study of matter and energy at the most fundamental (smallest)
level. Here, it mainly examines how small objects can simultaneously exhibit characteristics of both
particles (tiny pieces of matter) and waves (a disturbance or variation that transfers energy). This is
called the “wave-particle duality.”
1. Quantum wave function:
Description:
In quantum physics, a wave function is a mathematical quantity that describes the position and
quantum state of a particle.
The properties of quantum wave functions:
-The wave function describes both wave-like behaviors (such as interference) and particle-like
behaviors (such as the photoelectric effect)
-When two or more wave functions interact in space, their phases (specific positions within a wave
cycle) leads to a phenomenon called interference. When this happens, the waves interact, either
reinforcing or canceling each other depending on relative phases. Interference can be constructive
or destructive
Constructive interference:
When two waves meet in phase (meaning their peaks and troughs align), they combine to create a
wave with a larger amplitude than either wave alone. This leads to an increase in wave intensity.
Destructive interference:
When two waves meet out of phase (where the peak of one wave aligns with the trough of the
other), they can cancel each other out. This results in in a smaller or even zero amplitude in the
overlapping region.
2. Particle - wave duality:
1. The structure of particle - wave duality:
Definition:
Wave-particle duality is a concept in quantum mechanics in which every particle or quantum entity
may be described as either a particle or a wave. This is because when certain conditions change, the
particle or quantum entity can either exhibit properties of a particle or a wave.
Main properties of particle - wave duality:
-According to the wave-particle theory, light has the properties of both a wave and a particle
-Wave-particle duality refers to the fundamental property of matter (such as light and electrons)
where it exhibits particle or wave properties depending on experimental circumstances
2
,2. Photons
1. The structure of photons:
Definition:
Photons are the smallest possible particles of light. As a result, the photon is also the "quantum," or
fundamental unit, of electromagnetic radiation including radio waves, gamma-rays, and visible light.
This means that they are not made up of smaller components or internal structures. Some other
types of quanta (plural) are electrons, neutrinos, and the Higgs boson. In addition, photons exhibit
wave-particle duality. In certain conditions of light, the photons behave as particles (during the
photoelectric effect) and in others as waves (during diffraction and interference).
Properties of photons:
-Photons have no rest mass, which allows them to travel at the speed of light (approximately 3×108
ms-1) in a vacuum
-Photons exhibit both wave-like and particle-like properties
-> They behave as particles in phenomena like the photoelectric effect and as waves in phenomena
like diffraction and interference
-The energy of a photon is directly proportional to its frequency, expressed by the equation E = h ⋅ f,
where E is energy, h is Planck's constant, and f is frequency
-> Higher frequency photons (e.g., gamma rays) have more energy than lower frequency photons
(e.g., radio waves)
-Photons are electrically neutral, meaning they do not carry any charge. This neutrality allows
photons to interact with electric and magnetic fields without being influenced by them
-Despite being massless, photons carry momentum, calculated as p = E / C, where p is momentum,
E is energy, and c is the speed of light
-Since photons are the smallest particle of light, they make up all forms of electromagnetic radiation,
each differing in frequency and energy
3
, 2. Calculations for photons:
1. Energy of a photon:
The energy (E) of a photon is directly proportional to its frequency (f) and is calculated by the
equation: E = h ⋅ f. This means that higher frequency photons (like gamma rays) have more energy,
while lower frequency photons (like radio waves) have less energy.
-Energy of a photon (E / electronvolt (eV) or joule J): The energy carried by a photon.
-Planck's constant (h /6.626×10−34 J⋅s): Planck's constant connects the energy of electromagnetic
waves to their frequency
-Frequency of the photon (f / Hertz Hz): The number of waves (cycles) that pass a fixed point in one
second (measured in Hz) (Hz (1000) kHz (1000) MHz (1000) GHz (1000) THz (1000).
2. Wavelength and frequency relationship:
The frequency (f) and wavelength (λ) of a photon are inversely related and connected by the speed
of light (c): f = c / λ . The formula shows that frequency (f) and wavelength (λ) are inversely
proportional. As the wavelength of a photon increases, its frequency decreases, and vice versa.
-Speed of light (c / 3×108 ms-1): This is the constant speed at which light and all electromagnetic
radiation travel in a vacuum.
-Wavelength of the photon (λ / meters): Measured in meters m, the wavelength is the distance
between two consecutive peaks of the electromagnetic wave.
This relationship can be combined with Planck’s formula (E = h ⋅ f) -> E = h ⋅ c / λ. Accordingly, energy
is inversely proportional to wavelength. Shorter-wavelength photons have higher energy, while
longer-wavelength photons have lower energy.
3. Momentum of a photon:
Even though photons are massless, they still carry momentum (p), which is given by: p = E / c. This
equation shows how momentum is directly proportional to a photon´s energy. Since c (the speed of
light) is constant, an increase in momentum (p) results in a proportional increase in energy (E).
-Momentum (p / kg⋅m/s): Momentum is defined as the product of an object's mass and velocity. The
formula to calculate momentum is: Momentum (p) = Mass (m) × Velocity (v).
-Energy of a photon (E / electronvolt eV or joule J): The energy carried by a photon.
-Speed of light (c / 3×108 ms-1): This is the constant speed at which light and all electromagnetic
radiation travel in a vacuum.
The energy E of a photon is also related to its frequency f and wavelength λ by E = h⋅ c / λ. Thus the
momentum of a photon can also be expressed in terms of of wavelength as: p = λ / h
This equation shows that a photon’s momentum is inversely proportional to its wavelength. Shorter
wavelengths correspond to higher momentum while longer wavelengths correspond to lower
momentum.
4
