30. Light emission

Summary

From the lights we use in our homes, to the lights illuminating our smartphone screens, to the Sun in the sky, light emission is a very big part of our lives. This chapter will explore different types of light-emission processes from incandescence to lasers.

Light emission

Recall from a previous chapter that electrons move about in shells around the nucleus of an atom. These shells, also called orbitals, are characterized by the amount of energy of each electron. Each atom has a unique set of energy levels that each electron can occupy. The lowest energy level is known as the ground state. An electron can be bumped into higher energy levels, in which case the electron is said to be in an excited state.

We can model these different energy levels using an energy-level diagram, similar to that shown in Figure 30.1. An electron can only reside in one of the energy levels of an atom at any given time, and cannot have an energy that is in between levels. The energy levels are therefore discrete: they only have certain allowed values for their energies.

An energy level diagram. On the left is an arrow showing that energy increases vertically. On the right are horizontal lines depicting energy levels. The bottom one is labeled E0 (ground state). The next one up is labeled E1, then E2, then E3, finally E4.
Figure 30.1 – An energy-level diagram depicts all of the different energy levels in which electrons can reside. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

The lowest energy that an electron can occupy is called the ground state, often designated by E_0. The higher available energy levels are called excited states. For example, the energy level diagram in Figure 30.1 shows the first four excited states above the ground state.

Electrons can jump from one energy level to another. When an electron gains energy equal to the exact difference in energy between the (lower) starting level and the (higher) ending level, it can jump up one or more levels. Electrons can gain energy from light waves or from collisions with other electrons or subatomic particles. When electrons gain energy and move up one or more energy levels, this process is known as electron excitation.

Eventually, electrons that are in an excited state will relax back to the ground state. This process is called deexcitation. The deexcitation process can happen either as a result of a collision with another atom or with the emission of light. Either way, energy needs to be conserved. In this chapter, the light emission process is considered. The energy of that light will be equal to the exact difference in energy between the (higher) starting level and the (lower) ending level. The frequency of the emitted light is proportional to the energy of the emitted light. The equation we can use to determine the energy difference between such levels is

    $$E = hf,$$

where E is the energy of the light, f is the frequency, and h is the constant of proportionality known as Planck’s constant. Planck’s constant is equal to

    $$h = 6.626 \times 10^{-34}~\textrm{Js}.$$

Each element has a unique configuration of energy levels. This means that each element has a unique spectrum of light that can be emitted during the deexcitation process. It’s possible for electrons to drop between any two levels, meaning that many different frequencies of light can be generated by this process. An atom with four energy levels (one ground state and three excited states) can represent up to six possible transitions, and six different frequencies of emitted light, as shown in Figure 30.2.

An energy level diagram with four energy levels. Depicted are transitions from E3-E2, E3-E1, E3-E0, E2-E1, E2-E0, and E1-E0. On each transition is a depiction of a light wave containing a label equal to the energy difference between levels.
Figure 30.2 – A substance with four energy levels can support up to six different electron transitions, each with its own wavelength of light that will be emitted during that deexcitation process. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

The collection of frequencies of light emitted by a substance via this deexcitation process is known as its emission spectrum. The measurement and analysis of these spectra is known as spectroscopy. Using spectroscopy, it’s possible to determine the composition of gases (for example, stars, among other things) by examining the frequencies of light they emit. These frequencies can be compared to known emission spectra of different elements, such as hydrogen and helium, to determine the exact elements that are present in stars and other celestial bodies. This is particularly useful as it is not feasible to obtain samples from stars to bring back to Earth to measure using other methods!

A gas discharge lamp is a type of light source that generates light using electron excitation and deexcitation. A gas discharge lamp contains a tube filled with a gas. When a large voltage is applied to that gas, it is given enough energy to ionize the gas. Ionized gas contains many mobile electrons, which can create current. This current causes collisions between electrons and other ions of the gas, which excites electrons. When the electrons deexcite, light is emitted.

The spectra of gas discharge lamps can be measured with a diffraction grating. The spectra for a few different gas discharge lamps, and photographs of the light they produce, are shown in Figure 30.3. The distinct color of each lamp comes from the combination of all of the wavelengths of visible light that they emit.

For each of four gases (helium, neon, argone, and krypton) are shown the emission spectra. On the right is a photograph of the gas discharge lamp containing that gas. Helium discharge is red/yellow. Neon discharge is red/orange. Argone discharge is red/pink. Krypton discharge is blue/white.
Figure 30.3 – Helium, neon, argon, and krypton (among other gases) can be used in gas discharge lamps. Each has its own unique spectrum of light emission, which creates light in its own unique color. Helium spectrum and neon spectrum, created by Teravolt, are licensed under Public Domain. Argon spectrum, created by Abilanin, is licensed under CC BY-SA 3.0. Krypton spectrum, created by Mrgoogfan, is licensed under Public Domain. Helium discharge, neon discharge, argone discharge, and krypton discharge, created by Alchemist-hp, are licensed under GFDL 1.2.

Before LED lighting was ubiquitous, many stores would use “neon lights” for their signs. These neon lights could contain neon, a noble gas that emits an reddish orange color, or other gases that emit different colors. “Neon” lights are shown in Figure 30.4. Note that each color is generated with a different gas.

A photograph of a building containing stripes of different colored "neon" lighting.
Figure 30.4 – “Neon” lighting is not just composed of neon gas discharge. Each color “neon” light comes from a different element. Coloful light, by Violetbonmua, is licensed under CC BY-SA 3.0.

Sodium vapor lights were commonly used on highways, as they are a relatively efficient way to generate high intensity lighting, perfect for driving at night. Sodium vapor lamps can be identified by their unique yellow hue, as shown in Figure 30.5. Many of these lamps are being replaced by LEDs, which are capable of generating a more pleasant white color.

A photograph of a sodium vapor street lamp which is on and emitting a yellow colored light.
Figure 30.5 – Sodium vapor lamps, which have a distinct yellow color, were very commonly used on roadsides and highways. Sodium-vapor street light, by Famartin, is licensed under CC BY-SA 4.0.

X-rays

In 1895, a new type of electromagnetic wave was discovered when a beam of electrons emitted from a cathode-ray tube caused a nearby piece of paper to fluoresce (a process that will be described later in this chapter). These electromagnetic waves were called “x-rays” due to the fact that their characteristics were unknown at the time. That name has persisted, and we continue to call this type of electromagnetic radiation x-rays even today. While not much was known about the properties of x-rays at the time of their initial discovery, it was known that the rays did not contain any electric charge, due to the fact that they did not deflect in the presence of electric or magnetic fields.

It is now known that x-rays are a type of high-energy electromagnetic radiation produced when highly energetic electrons are quickly slowed when they strike the positive electrode (called the anode) in a cathode-ray tube. The slowing of the electrons produces x-rays consisting of a continuum of energies over the frequency range of x-rays. Maxwell’s equations (the equations used to determine the properties of electromagnetic waves) state that any time a charged particle accelerates (speeds up, slows down, or changes direction), light will be emitted. A broad range of energies is generated due to the collisions between the electrons and the anode. Some electrons may slow down with a single collision (in which a lot of energy is released at once), and others may slow down with multiple collisions.

In addition to the continuous spectrum generated by collisions with the anode, these collisions can knock the electrons in the anode’s atoms into excited states. As those electrons deexcite, they produce x-rays as well. Because the deexcitation process occurs at only specific wavelengths for different materials, these show up on an emission spectrum as very discrete frequencies or energies. A typical x-ray spectrum is shown in Figure. 30.6. The broad background represents the braking radiation (x-rays generated by collisions with the anode), and the discrete spikes represent the emission lines from electron deexcitation (x-rays generated by the deexcitation of excited anode electrons).

Figure 30.6, described in the caption and text.
Figure 30.6 – The wavelengths of light generated in a cathode-ray tube in the x-ray region of the electromagnetic spectrum consists of braking radiation (continuous background) as well as emission from electron deexcitation (discrete spikes). Tube spectrum, by LinguisticDemographer, is licensed under Public Domain.

Light absorption

While an emission spectrum showcases the light emitted by a material, an absorption spectrum shows the wavelengths of light that are absorbed by a material. If white light is shined upon a sample, the sample can absorb particular frequencies (given by its energy-level diagram) causing excitations in the material. Those frequencies will be subtracted out from the white light, and appear as black lines in the absorption spectrum, as shown in Figure 30.7.

A graphic of an absorption spectrum which appears as a continuous rainbow with 4 distinct black lines where absorption has occurred.
Figure 30.7 – An absorption spectrum appears as black lines at frequencies where light causes excitation in electrons. Spectral lines absorption, by Stkl, is licensed under Public Domain.

Incandescence

Incandescence is a form of light emission previously discussed in this textbook in the context of heat transfer. All objects emit electromagnetic radiation with a frequency that corresponds to the temperature of that object. Relatively cool objects such as humans, plants, and animals emit light in the infrared portion of the electromagnetic spectrum. Hotter objects will emit light with higher frequencies. At a high enough temperature, objects will emit visible light.

Unlike an emission spectrum, the incandescence spectra of objects is a continuous spread of frequencies (and therefore energies) as opposed to discrete frequencies as seen in the deexcitation of gas atoms. Furthermore, the incandescent spectrum is the same at a given temperature regardless of the material. The incandescent spectrum for different temperatures is shown in Figure 30.8. Notice that cooler objects emit light at wavelengths longer than visible. Hotter objects overlap with the visible portion of the electromagnetic spectrum, which will appear white if enough colors are emitted by the object. The discovery of the correct mathematical expression for the intensity of the incandescent spectrum as a function of frequency was made by Max Planck in 1900.

A graph of incandescence spectra for objects at 3000K, 4000K, and 5000K. The object at 3000K is mostly infrared. The object at 4000K starts to overlap slightly with red and orange visible light. The object at 5000K overlaps with most of the visible region of electromagnetic radiation.
Figure 30.8 – Cool objects will emit light in the infrared or red region of the electromagnetic spectrum. As objects become hotter, their incandescence spectra will start to overlap more with visible light, eventually appearing white or blue. This figure, created by Izaak Neutelings and modified by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-SA 4.0.

In this manner, we can use the color of an incandescent object to determine its temperature. An incandescent object that appears red or orange is cooler than an incandescent object that appears white or blue.

Incandescent light bulbs use the property of incandescence to generate white light. A very thin filament is heated by passing electric current through it. This heat causes the filament to glow with multiple overlapping wavelengths of visible light (shown in Figure 30.9). The mixture of all frequencies of visible light creates white light.

A photograph of a small bulb. The surroundings are very dark. Visible is a glass bulb containing some wires connecting to a glowing filament. The filament is glowing yellow/white in color.
Figure 30.9 – An incandescent bulb emits light through heating a filament, which glows white when it is hot enough. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

Using a diffraction grating, we can see a continuous rainbow spectrum emanating from an incandescent light bulb, shown in Figure 30.10.

A photograph of an incandescent bulb viewed through a diffraction grating. The bulb itself is barely visible except for a yellow/white glow where the filament is. To each side (left and right) of the bulb can be seen a rainbow of light produced by the diffraction grating.
Figure 30.10 – When viewed through a diffraction grating, an incandescent bulb shows a continuous spectrum (rainbow) of light from red to blue. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

Today, we use incandescent bulbs less and less in our homes and work environments, as the process of incandescence to generate light is very inefficient. (In fact, incandescent light bulbs have been or are being phased out in many countries around the world.) The power consumed by incandescent light bulbs is quite high compared to LED and fluorescent lights. Most of the electrical energy used to light an incandescent bulb is wasted as heat.

In the video below, Dr. Pasquale uses a hand-crank generator to light up different bulbs. First, she cranks the generator to light up an incandescent bulb. This takes rather a lot of energy to do, and the bulb lights dimly. Then, she turns the crank to light the LED bulb. This bulb lights right away, as it is very easy to illuminate. An LED bulb requires much less energy to function. However, note that the LED only illuminates every half cycle when powered by an AC generator. This problem can be fixed in home lighting by converting AC to direct current (DC), as previously discussed in this textbook.

Other examples of incandescence in our daily lives are seen in electric stoves and toasters. Both of these objects contain resistive heating elements. Electric current is sent through the heating elements, which then warm up due to their resistance. At cool temperatures, they will glow red, as seen in Figure 30.11 for a hot toaster. As they warm up, they will glow orange, or possibly even yellow if very hot. Note that when the electric stove or toaster is turned off, both still emit light via incandescence! However, we can no longer see it. As the objects are likely at room temperature, we can expect that light to be in the infrared region of the electromagnetic spectrum, and therefore not visible.

A photograph of a toaster seen from the top. The heating elements are glowing red/orange.
Figure 30.11 – The resistive heating elements in an electric toaster incandesce and emit visible light when hot. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

Fluorescence

Fluorescence is a process of light emission where an object absorbs light at a high frequency, causing electron excitation. During the subsequent deexcitation process, light is then emitted at a lower frequency. During this process, a minor amount of heat is generated, which is what causes that change in frequency between the absorbed and emitted light. Energy is conserved. An energy-level diagram depicting this process is shown in Figure 30.12.

An energy level diagram with four energy levels. Depicted is absorption causing excitation from E0 to E3. An arrow from E3 to E2 is labeled "non-radiative deexcitation" and an arrow from E2 to E0 is labeled "radiative deexcitation."
Figure 30.12 – An energy-level diagram depicting the fluorescence process shows the absorption of high-energy light, followed by a non-radiative deexcitation process and the emission of low-energy light. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

Fluorescence has many applications in the medical field. A fluorescent dye can be attached to certain types of cells or other biological materials. When excited with the high frequency light, the fluorescent dye will emit light at a different frequency. This is particularly useful because the high frequency light is usually bright enough to overwhelm any other light. By filtering that high frequency out, only the fluorescent light can be collected, allowing scientists and doctors to see only the parts of samples that are attached to the fluorescent dye. They emit at a different frequency and would not be blocked by that filtering process. In this manner, particular types of cells can be imaged (endothelial cells imaged by fluorescence are shown in Figure 30.13), biological processes can be viewed, and the presence or volume of cancer or bacteria can be measured.

Figure 30.13, described in the caption.
Figure 30.13 – A fluorescence micrograph of endothelial cells stained with three different fluorescent agents as viewed under UV light. FluorescentCells, by National Institutes of Health, is licensed under Public Domain.

Fluorescence is also present in nature. Some types of animals and fish exhibit fluorescence. Even plants contain a fluorescent molecule: chlorophyll. Some minerals in rocks are fluorescent as well. We can see these colorful fluorescent emissions when shining a UV light on the minerals, as demonstrated in the video below.

Fluorescent components are also used in everyday items such as highlighter pens (to create the bright “neon” colors) and laundry detergents (to act as an optical brightener).

Phosphorescence

Phosphorescence is a light emission phenomenon akin to fluorescence. Similarly to fluorescence, a phosphorescent material will become excited by high frequency light and re-emit lower frequency light. However, in phosphorescence, this process of re-emission is extended for a time period even after the exciting source is removed. Sometimes it is a few seconds, sometimes it can be several minutes or hours. In other words, phosphorescence is essentially the same thing as fluorescence, except that the electrons in the excited state remain there for an extended period of time rather than dropping back down immediately after the source of the excitation is removed.

Many “glow-in-the-dark” paints are phosphorescent. When illuminated during the day with sunlight or room lighting, the electrons in the material gain energy. At night, after the illumination is removed, the glow-in-the-dark paint will slowly re-emit the lower frequency light over the span of several minutes or even hours. This is demonstrated in the video below. Dr. Pasquale has a light shining on a glow-in-the-dark star. After turning off the light, the star continues to glow.

Chemicals known as phosphors may emit light using the process of fluorescence, and some may emit light using the process of phosphorescence. Phosphor coatings are very common when high energy light is used to generate white light. By mixing multiple phosphorescent or fluorescent chemicals together, a mixture of red, green, and blue light can be generated to create white light for use in home lighting.

Fluorescent lights

Fluorescent lights use the properties of light emission and phosphorescence to generate light. A mercury vapor inside of a glass tube is excited into a plasma by the application of high voltage. Mercury plasma emits light in the UV region of the electromagnetic spectrum. On its own, this UV light would be useful for sterilization or other medical uses, but would not be a good light source for our homes due to the presence of ionizing radiation.

The surface of a fluorescent light tube is coated with a phosphor. This phosphor absorbs the high-energy UV light and generates other colors of light. The exact chemicals used in the phosphor coating depend on the color temperature of the light. In what may be considered confusing language from a physics perspective, blue colors are known as “cool” and yellow colors are known as “warm” in color theory. Often, this nomenclature will be used on boxes of indoor lighting. However, “cool” lights from the blue part of the visible spectrum are actually at a higher temperature (typically 5000 K) than “warm” lights from the yellow or red part of the visible spectrum (typically 3000 K). When you go to the hardware store to purchase fluorescent bulbs, you will see different color temperatures available, depending on the lighting effect that you prefer. An image of two light fixtures, one fitted with “warm” (3000 K) and one fitted with “cool” (5000 K) bulbs, is shown in Figure 30.14.

A photograph of two light fixtures affixed to a ceiling in a house. One of the light fixtures contains a "cool" bulb glowing bluish-white, and the other fixture contains a "warm" bulb glowing yellowish-white.
Figure 30.14 – A “cool” bulb appears bluish-white, whereas a “warm” bulb appears yellowish-white. The color temperature comes from the phosphor used in the bulb coating. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

Because the mercury vapor emits light at discrete frequencies, and the phosphor coating also emits light at certain frequencies (although the phosphor emission has a broader spectrum), when using a diffraction grating to look at the spectrum of a fluorescent bulb, the combination of both of these effects can be seen. Each of the lines of the mercury vapor emission spectra can be seen, with some blurring between those lines due to the broad phosphor emission spectrum. This is shown in Figure 30.15.

A photograph of a fluorescent bulb viewed through a diffraction grating. The bulb itself is glowing white. To each side (left and right) of the bulb can be seen the spectral components of light produced by the diffraction grating.
Figure 30.15 – A diffraction grating shows the composition of a fluuorescent lamp. There are discrete colors blurred together by the phosphor coating. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

Light-emitting diodes

Light-emitting diodes (LEDs) use two layers of semiconducting material stacked together to create current when a voltage is applied in a certain direction. A diode, discussed previously in this textbook, acts like a one-way valve that only allows current to flow in one direction, if voltage is applied in the correct orientation. An LED is a special type of diode that emits light when current flows.

Every light-emitting diode will generate light at a particular frequency, given by the exact semiconductor that’s used to create it. Because of this, light-emitting diodes are monochromatic. However, engineers and scientists have created LEDs that can generate frequencies from UV to infrared. A selection of several different colored LEDs are shown in Figure 30.16. These are small LEDs used for electronics and hobbyist projects. (Perhaps you have seen LEDs similar to these that are used as indicator lights in appliances or other electronics.)

A photograph of six LEDs placed in a breadboard, all lit up and emitting light. (They are in a dark room to provide contrast with the background.) The individual LED colors are red, orange, yellow, green, blue, and violet.
Figure 30.16 – Small LEDs used for electronics projects come in many different colors. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

Monochromatic light may be appropriate for indicator lights or for use in specific electronic projects, but how can LEDs be used to generate white light, which is required for home lighting? In fact, LEDs can be used to generate white light using two different methods.

The first method for generating white light from an LED is to package three separate LEDs together: one red, one green, and one blue. This is known as an RGB LED. A close-up photograph of an RGB LED, showing the separate red, green, and blue diodes, is shown in Figure 30.17.

Figure 30.17, described in the caption.
Figure 30.17 – A close-up photograph of an RGB LED shows separate red, green, and blue light-emitting diodes inside the package. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

By combining red, green, and blue light together using the color addition process described earlier in this textbook, white light can be generated. RGB LEDs are also used in tunable light bulbs (whose color can be changed by the user). The addition of red, green, and blue LEDs to generate white light is demonstrated in the video below.

The second method for generating white light is similar to that used in fluorescent bulbs. An ultraviolet LED is packaged in a piece of epoxy that is coated with a phosphor. Depending on the exact phosphorescent chemicals used, different color temperatures of white LED bulbs are achieved.

A household light fixture containing integrated LED lights is shown in Figure 30.18. The light fixture contains electronics in the center to convert the high voltage AC signal to a lower value DC voltage appropriate for lighting the LEDs (which is also adjustable for use with a household dimmer switch). The LEDs themselves are arrayed in a circular pattern around the edge of the fixture. Each individual LED is rather small, so many of them are used to generate bright light for our homes.

Figure 30.18, described in the caption and text.
Figure 30.18 – A household light fixture containing integrated LEDs has electronics for converting AC to DC as well as multiple individual light-emitting diodes. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.

An LED light bulb contains similar circuitry inside the bulb casing. This is why LED light bulbs tend to be heavier than similarly sized incandescent light bulbs. An LED light bulb with the casing broken to display the interior components is shown in Figure 30.19.

An LED light bulb is photographed with the glass bulb broken on purpose to show the circuitry in the container. There are 16 individual LEDs as well as several electronics components.
Figure 30.19 – An LED light bulb contains electronics inside the bulb casing. LED-E27-Light-Bulb-1134, by David R. Tribble, is licensed under CC BY-SA 4.0 .

Photovoltaic panels, or solar panels, function by the reverse process. Light that’s absorbed by a semiconducting material will generate electric current. This is an excellent method of creating energy that does not require fossil fuels, and uses a process totally different from the generators discussed in a previous chapter.

Lasers

The term laser is an acronym for light amplification by stimulated emission of radiation. A laser contains a light source to start this light amplification process. (A laser pointer will likely contain a light-emitting diode as a light source.) This light source shines into an amplifying medium. This can be a gas or even a solid material that amplifies light by means of stimulated emission. Stimulated emission occurs when an electric field is used to provoke deexcitation of many electrons, all of which emit photons that are identical to each other. While this is a very complicated process, in general it means that the material is capable of generating more light from the initial light source. (There is an energy source used; a laser does not violate conservation of energy!)

In addition to the amplifying material, a laser contains two mirrors on each end to cause the light waves to travel back and forth throughout the material. This does two things: first, it causes the light to spend more time in the amplifying material, creating more light by stimulated emission. Second, it causes the light waves to interfere, creating light waves that are all in the same phase and have the same wavelength using the process of constructive interference. Because the output light all has the same wavelength, a laser is a monochromatic light source. Different types of lasers will emit at different frequencies. The output from six different lasers is shown in Figure 30.20.

A photograph of six lasers all emitting light at different colors. The individual laser colors are red, red, green, green, blue, and violet.
Figure 30.20 – A laser is capable of generating very intense monochromatic light. Each type of laser can produce light at different frequencies. Lasers, by 彭嘉傑, is licensed under CC BY 2.5.

The output of a laser contains light waves that are very high-intensity and also completely identical. (Because of the high intensity output, it is extremely important to exercise caution when using lasers, as they can cause vision loss or even blindness if used incorrectly.) This type of light is known as coherent light. Coherent light means that all of the waves have the same frequency and phase.

The properties of laser light make them extremely useful in many scientific, medical, and industrial applications. In communications, lasers are used to send optical data along fiber optic cables (using the property of total internal reflection to remain inside the cable). They are also used to read or write from optical discs such as CDs and DVDs. Industrial uses of the high intensity output generated from lasers include laser welding and cutting. The straight lines projected by lasers have use in construction and surveying. Medical uses of lasers include cancer treatment and laser eye surgery. In addition, scientists and engineers frequently use lasers in scientific and medical research.

Further reading

Practice questions

Conceptual comprehension

  1. If you are able, go outside on a clear day and look at the sky (preferably with a telescope). If you do not have access to an unobstructed sky or telescope, take a look at the January 16, 2024 NASA Astronomy Picture of the Day. What does it mean for some of the stars to appear red and for some of the stars to appear blue?

Numerical analysis

  1. A hydrogen atom requires the absorption of a light wave containing 2.18 \times 10^{-18}~\textrm{J} of energy to ionize its electron. Calculate the wavelength and frequency of a light wave with that value of energy.
  2. Consider the energy-level diagram shown in Figure 30.21. Calculate the…
    1. …total number of electron transitions.
    2. …amount of energy required to jump from the ground state (E0) to E2.
    3. …wavelength of light corresponding to the energy difference between the ground state (E0) and E2.
    4. …largest energy transition.
    5. …wavelength of light corresponding to the largest energy transition.
    6. …smallest energy transition.
    7. …wavelength of light corresponding to the smallest energy transition.
An energy-level diagram consisting of 6 levels. The ground state (E0, 0 J), E1 which has an energy level of 3.48E-19 J, E2 which has an energy level of 5.44E-19 J, E3 which has an energy level of 9.66E-19 J, E4 which has an energy level of 2.18E-18 J, and E5 which has an energy level of 8.70E-18 J.
Figure 30.21 – A simplified energy-level diagram corresponding to an atom of helium. This figure, created by Alyssa J. Pasquale, Ph.D., is licensed under CC BY-NC-SA 4.0.
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Conceptual Physics Copyright © 2024 by Alyssa J. Pasquale, Ph.D.; David R. Fazzini, Ph.D.; and Carley Bennett, Ph.D. is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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