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Chapter 5: Problem 17

How is the energy of a photon related to its wavelength? What kind of photons carry the most energy? What kind of photons carry the least energy?

Short Answer

Expert verified
The energy of a photon is inversely related to its wavelength, as described by the formula \( E = hc / λ \). Thus, the photons that carry the most energy are gamma rays, which have the shortest wavelengths. The photons that carry the least energy are radio waves, which have the longest wavelengths.

Step by step solution

01

Understanding The Energy-Wavelength Relationship

The energy \( E \) of a photon is inversely proportional to its wavelength \( λ \). This relationship is described by the equation \( E = hƒ \), where \( h \) is Planck's constant (approximately \( 6.62607004 × 10^{-34} m^2 kg/s \)) and \( ƒ \) is the frequency of the associated electromagnetic wave. The frequency and wavelength of a wave are inversely related by the equation \( λ= c/ƒ \), where \( c \) is the speed of light (~\( 299,792 km/s \)). Combining these equations yields the formula \( E = hc / λ \), which directly describes the energy of a photon in terms of its wavelength.
02

Categorizing Photons By Energy

Photons can take on a range of energies, corresponding to the different types of light in the electromagnetic spectrum. At the low-energy end of the spectrum (long wavelength), we find radio waves, with energies on the order of microelectron volts (μeV). Moving up the energy scale, we encounter microwaves, infrared light, visible light, ultraviolet light, X-rays, and gamma rays. Gamma rays are at the high-energy end of the spectrum (short wavelength), with energies on the order of giga-electron volts (GeV) or more.
03

Identifying the Highest-energy and Lowest-energy Photons

Given the inverse relationship between energy and wavelength, the type of photon that carries the most energy per photon will be the one with the shortest wavelength. This is the gamma ray. Conversely, the type of photon that carries the least energy per photon will be the one with the longest wavelength. This is the radio wave.

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Most popular questions from this chapter

Use the Starry Night Enthusiast \({ }^{\mathrm{TM}}\) program to examine some distant celestial objects. First display the entire celestial sphere (select Guides \(>\) Atlas in the Favourites menu) and ensure that deep space objects are displayed by opening View \(>\) Deep Space and clicking on Messier Objects and Bright NGC Objects. You can now search for objects (i), (ii), and (iii) listed below. Click the Find tab at the left of the main view window to open the Find pane, click on the magnifying glass icon at the left of the edit box at the top of the Find pane and select Search All from the menu, and then type the name of the object in the edit box followed by the Enter (Return) key. The object will be centered in the view. For each object, use the zoom controls at the right-hand end of the Toolbar (at the top of the main window) to adjust your view until you can see the object in detail. For each object, state whether it has a continuous spectrum, an absorption line spectrum, or an emission line spectrum, and explain your reasoning. (i) The Lagoon Nebula in Sagittarius. (Hint: See Figure 5-18.) (With a field of view of about \(6^{\circ} \times 4^{\circ}\), you can compare and contrast the appearance of the Lagoon Nebula with the Trifid Nebula just to the north of it.) (ii) M31, the great galaxy in the constellation Andromeda. (Hint: The light coming from this galaxy is the combined light of hundreds of billions of individual stars.) (ii) The Moon. (Hint: Recall from Section \(3-1\) that moonlight is simply reflected sunlight.)

Explain why astronomers are interested in blackbody radiation.

What is the temperature of the Sun's surface in degrees Fahrenheit?

(a) Describe the spectrum of hydrogen at visible wavelengths. (b) Explain how Bohr's model of the atom accounts for the Balmer lines.

The bright star Bellatrix in the constellation Orion has a surface temperature of \(21,500 \mathrm{~K}\). What is its wavelength of maximum emission in nanometers? What color is this star?
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