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Ch 38: Photons: Light Waves Behaving as Particles
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 38: Photons: Light Waves Behaving as ParticlesProblem 17
Chapter 38, Problem 17

X rays with initial wavelength 0.06650.0665 nm undergo Compton scattering. What is the longest wavelength found in the scattered x rays? At which scattering angle is this wavelength observed?

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Understand the concept of Compton scattering: Compton scattering involves the change in wavelength of X-rays or gamma rays when they are scattered by electrons. The change in wavelength is given by the Compton wavelength shift formula.
Use the Compton wavelength shift formula: Δλ = λ' - λ = (h/mc) * (1 - cos(θ)), where λ is the initial wavelength, λ' is the scattered wavelength, h is Planck's constant, m is the electron mass, c is the speed of light, and θ is the scattering angle.
Identify the longest wavelength: The longest wavelength occurs when the change in wavelength Δλ is maximized. This happens when the scattering angle θ is 180 degrees, because cos(180°) = -1, which maximizes the term (1 - cos(θ)).
Calculate the longest wavelength: Substitute θ = 180° into the Compton wavelength shift formula to find λ'. Use the given initial wavelength λ = 0.0665 nm and the constants h, m, and c to compute λ'.
Determine the scattering angle for the longest wavelength: As calculated, the longest wavelength is observed at a scattering angle of 180 degrees.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Compton Scattering

Compton scattering is a phenomenon where X-rays or gamma rays are scattered by electrons, resulting in a change in wavelength. This effect is significant in quantum physics as it demonstrates the particle-like properties of light. The change in wavelength depends on the angle at which the photon is scattered.
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Wavelength Shift Formula

The wavelength shift in Compton scattering is given by the formula: Δλ = (h/mc)(1 - cos θ), where h is Planck's constant, m is the electron mass, c is the speed of light, and θ is the scattering angle. This formula allows us to calculate the change in wavelength based on the scattering angle, crucial for determining the longest wavelength.
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Scattering Angle

The scattering angle in Compton scattering is the angle between the incident and scattered photon directions. It plays a critical role in determining the extent of the wavelength shift. The longest wavelength occurs at the maximum scattering angle, which is 180 degrees, where the photon is scattered directly backward.
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Related Practice
Textbook Question

X rays with an initial wavelength of 0.900×10−100.900\(\times\)10^{-10} m undergo Compton scattering. For what scattering angle is the wavelength of the scattered x rays greater by 1.0%1.0\% than that of the incident x rays?

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Textbook Question

The photoelectric work function of potassium is 2.32.3 eV. If light that has a wavelength of 190190 nm falls on potassium, find the stopping potential in volts.

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Textbook Question

A photon scatters in the backward direction (ϕ=180\(\phi\)=180°) from a free proton that is initially at rest. What must the wavelength of the incident photon be if it is to undergo a 10.0%10.0\% change in wavelength as a result of the scattering?

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Textbook Question

An electron and a positron are moving toward each other and each has speed 0.500c0.500c in the lab frame. What is the kinetic energy of each particle?

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Textbook Question

The photoelectric work function of potassium is 2.32.3 eV. If light that has a wavelength of 190190 nm falls on potassium, find the kinetic energy, in electron volts, of the most energetic electrons ejected.

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Textbook Question

The cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is 15.015.0 kV, what are the shortest-wavelength x rays produced by the television?

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