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Basics of Astronomy28 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Thomas Zesiger*

Thomas has taught electronics and communications engineering, math, and physics and has a master's degree in electrical engineering.

In this lesson, we will learn the definition of a photon. We will also explain Planck's constant and its relationship to the photon energy and wavelength. The calculation of photon energy is also demonstrated.

A **photon** is the quantum of electromagnetic radiation. The term **quantum** is the smallest elemental unit of a quantity, or the smallest discrete amount of something. Thus, one quantum of electromagnetic energy is called a photon. The plural of quantum is quanta.

The concept of photons and quanta comes from **quantum mechanics** and quantum theory. Quantum mechanics is a mathematical model that describes the behavior of particles on an atomic and subatomic scale. It demonstrates that matter and energy are quantized, or come in small discrete bundles, on the smallest scales imaginable. A photon propagates at the speed of light.

A photon describes the particle properties of an electromagnetic wave instead of the overall wave itself. In other words, we can picture an electromagnetic wave as being made up of individual particles called photons. Both representations are correct and reciprocal views of electromagnetic waves. For example, light exhibits wave properties under conditions of refraction or interference. Particle properties are exhibited under conditions of emission or absorption of light.

The idea of quantum mechanics and photons originated from scientists' observations of the photoelectric effect. The photoelectric effect is where light striking a metal surface causes electrons to be ejected from the metal. Scientists were unable to explain this phenomenon, but eventually the explanation came from quantum theory.

What they found was that the energy in each quantum of light depends on the frequency of the light. In particular, the energy of a photon equals **Planck's constant** times the frequency of the radiation. Mathematically, this is given by the equation *E* = *hf*. Planck's constant is the fundamental constant of quantum theory that determines the scale of the small-scale world. Planck's constant = 6.63 * 10-34 joule-second (J-s). The total energy in an electromagnetic wave is the sum of the energies of each photon in the wave.

The energy of a photon is so small that we usually measure it in **electronvolts** (eV). One eV is the potential energy of each electron in a 1-volt battery. One eV is equal to 1.6 * 10-19 joules (J). Therefore, we need to convert Planck's constant to appropriate units, which are electronvolts/hertz (eV/Hz). In eV/Hz, Planck's constant is 4.136 * 1015 eV/Hz.

The wavelength of a photon is the same as the wavelength of the electromagnetic wave of which it is a part. This picture shows the wavelength of the electromagnetic spectrum.

The smaller the wavelength, the more photon energy. Thus, a photon of an x-ray has much more energy than that of visible light. This is why too many x-rays are harmful to the human body. Note that since electromagnetic waves travel at the speed of light, frequency and wavelength for electromagnetic waves are related by wavelength = speed of light/frequency.

We will now explore an example of calculating photon energy using red light. The frequency of red light is 4.3 * 1014 Hz. Therefore, we have *E* = (4.136 * 10-15 eV/Hz)(4.3 * 1014 Hz) = 1.78 eV. We follow similar procedures for calculating photon energy by substituting in the appropriate frequency of radiation of the electromagnetic wave.

A **photon** is the quantum of electromagnetic radiation that describes the particle properties of an electromagnetic wave. The energy of a photon is given by the equation *E* = *hf*, where *E* is energy, *h* is Planck's constant, and *f* is frequency. This equation tells us that as the frequency of radiation increases (wavelength decreases), the photon energy increases. The wavelength of a photon depends on the frequency of radiation of the electromagnetic wave and is given by the relationship wavelength = speed of light/frequency.

This lesson should teach you to:

- Define proton, quantum, Planck's constant, and electronvolt
- Recall the equation for the energy of a photon
- Calculate the energy of a photon
- Recall the relationship between frequency and wavelength for electromagnetic waves

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19 in chapter 8 of the course:

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Basics of Astronomy28 chapters | 325 lessons

- Wave Parameters: Wavelength, Amplitude, Period, Frequency & Speed 6:54
- What is Light? 6:45
- The Speed of Light: Distance & Light-Years 5:29
- The Nature of Light: Origin, Spectrum & Color Frequency 7:41
- Electromagnetic Waves: Definition, Sources & Properties 6:25
- The 7 Major Regions of the Electromagnetic Spectrum 6:26
- Reflection: Angle of Incidence and Curved Surfaces 6:14
- Refraction & Dispersion: Definition, Snell's Law & Index of Refraction 9:08
- Diffraction: Relation to Sound & Light and Effects of Wavelength 6:33
- Resonance: Definition & Transmission of Waves 6:54
- Color: White Light, Reflection & Absorption 7:17
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- What Are Wien's Law & the Stefan-Boltzmann Law? 7:38
- Calculations with Wien's Law & the Stefan-Boltzmann Law 7:15
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