Photons and Energy
Copyright (c) Lant, Montgomery, and Mazziotti 2023 This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Learning Goals:
References
By the end of this lesson, students will be able to:
Define the concept of photons and the relationship between a photon's frequency and its energy
In the realm of quantum physics (or quantum mechanics), electromagnetic radiation is often described in terms of photons. A photon is the smallest discrete unit or "packet" of electromagnetic energy. It can be thought of as a particle-like entity that carries both energy and momentum. Electromagnetic radiation, including visible light, is composed of photons. When a molecule transitions from a higher energy state to a lower energy state, it emits a photon; likewise, when a molecule transitions from a lower energy state to a higher energy state, it absorbs a photon.
The energy of a photon is directly proportional to its frequency (or inversely proportional to its wavelength) according to the equation derived in 1906 by Albert Einstein
E = hν
where E represents the energy, h is Planck's constant, and n is the frequency of the electromagnetic wave. This relationship is known as the wave-particle duality of electromagnetic radiation, which means that photons exhibit both wave-like and particle-like properties.
The energy of photons varies across the electromagnetic spectrum. For instance, photons of visible light have energies that correspond to the colors we perceive. Red light has lower energy photons, while violet light has higher energy photons within the visible spectrum. As we move towards shorter wavelengths, photons become more energetic, such as X-rays and gamma rays, which can have significant health risks.
The concept of photons reveals the discrete nature of electromagnetic radiation and its interaction with matter in quantum mechanics. While electromagnetic radiation can be described as waves propagating through space, photons provide a particle-based explanation of its behavior and the transfer of energy.
The first determination of Planck's constant, denoted by the symbol h, is attributed to Max Planck himself. Planck was a German physicist who introduced in 1900 the concept of quantization and played a foundational role in the development of quantum theory. In 1914 it was measured explicitly by Robert Millikan at The University of Chicago in a confirmation of Einstein's equation above.
Figure 1: Photograph of Robert Millikan (left) with Albert Einstein (right) at Caltech in 1932 (License: Public Domain)
As with the speed of light, we can obtain the modern value of Planck's constant from Maple
ScientificConstants:-GetConstant'h';
Planck_constant,symbol=h,value=6.626070040×10−34,uncertainty=8.1×10−42,units=Js
or
h ≔ ScientificConstants:-Constant'h', units;
h≔ConstantSIhm2kgs
Using evalf that evaluates expressions in Maple to a floating-point number yields its known value in Standard International (SI) units
h ≔ evalfh;
h≔6.626070040×10−34m2kgs
We can use Planck's constant that we just defined as the symbol h in solving problems! For example, consider again the radio wave discussed above with a wavelength of 1000 m. We can use Einstein's equation to compute the energy of a photon with that wavelength. Using the equation relating frequency and wavelength, we can rewrite Einstein's equation as
E = hcλ
As before, we first define λ in Maple with the SI unit of distance (meters or m)
lambda ≔ 1000*Units:-Unit'm';
λ≔1000m
Second, we compute the energy of the photon
E ≔ h*c/lambda;
E≔6.626070040×10−37cmm2kgs
Third, we combine units to obtain the energy in the SI unit of energy known as the Joule
E ≔ combineE, units;
E≔6.626070040×10−37ckgms
(a) What is the energy of red light whose wavelength is 750 nm (nanometers) or 7.5 x 10-7 m. (Hint: Repeat the steps above with the wavelength for red light.)
1. Christie, R. The Physical and Chemical Basis of Colour. In Colour Chemistry. 2nd Ed. Royal Chemical Society: Cambridge. 2001. pp. 12-21. 2. Stockman, A., MacLeod, D. I., & Johnson, N. E. (1993). Spectral sensitivities of the human cones. Journal of the Optical Society of America, A, Optics, Image & Science, 10(12), 2491–2521.
Selection of Additional Readings and Resources
Baumann, U. https://www.colorsystem.com/?page_id=551 (accessed 2023-09-07).
A webpage summarizing and visualizing the evolution of color systems and color spaces from Plato to CIELab and other modern-day models.
Buether, A.; Augsburg, A.; Venn, A. In Colour: Design principles, planning strategies, visual communication; Institut für Internationale Architektur-Dokumentation, 2014; pp 33–37.
A chapter on color systems and color spaces and their importance in art and designer from the perspective of a designer.
Ciechanowski, B. Color Spaces – Bartosz Ciechanowski. https://ciechanow.ski/color-spaces/ (accessed 2023-09-07).
An interactive webpage by Bartosz Ciechanowski that explores the technical aspects of how additive color (colored light) can be mapped onto the RGB colorspace for use in screens.
Coblis - Color Blindness Simulator. https://www.color-blindness.com/coblis-color-blindness-simulator/ (accessed 2023-09-07).
An interactive webpage that simulates various types of colorblindness for those of us with standard color vision. See if you can guess which cone cell type might be affected for each type of vision.
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