College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Question:**
If a 7.0-keV photon scatters from a free proton at rest, what is the change in the photon’s wavelength if the photon recoils at 90°?
**Explanation:**
This problem pertains to the field of quantum mechanics and involves the concept of Compton scattering. Compton scattering describes the phenomenon where a photon scatters off a target particle, resulting in a change in the photon's wavelength. The change in wavelength is given by the Compton equation:
\[ \Delta \lambda = \frac{h}{m_pc} \left(1 - \cos \theta\right) \]
where:
- \( \Delta \lambda \) is the change in the wavelength of the photon,
- \( h \) is the Planck constant (\( 6.626 \times 10^{-34} \, \text{Js} \)),
- \( m_p \) is the mass of the proton (\( 1.672 \times 10^{-27} \, \text{kg} \)),
- \( c \) is the speed of light (\( 3.0 \times 10^8 \, \text{m/s} \)),
- \( \theta \) is the scattering angle of the photon, which is 90° in this case.
To find the solution, one would need to substitute these values into the Compton equation and perform the necessary calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F093e7116-3e01-49ad-9157-7a22a5caeb16%2Fe8abe912-10bf-4296-b2ff-7205dd9f4749%2F1kiwxej_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
If a 7.0-keV photon scatters from a free proton at rest, what is the change in the photon’s wavelength if the photon recoils at 90°?
**Explanation:**
This problem pertains to the field of quantum mechanics and involves the concept of Compton scattering. Compton scattering describes the phenomenon where a photon scatters off a target particle, resulting in a change in the photon's wavelength. The change in wavelength is given by the Compton equation:
\[ \Delta \lambda = \frac{h}{m_pc} \left(1 - \cos \theta\right) \]
where:
- \( \Delta \lambda \) is the change in the wavelength of the photon,
- \( h \) is the Planck constant (\( 6.626 \times 10^{-34} \, \text{Js} \)),
- \( m_p \) is the mass of the proton (\( 1.672 \times 10^{-27} \, \text{kg} \)),
- \( c \) is the speed of light (\( 3.0 \times 10^8 \, \text{m/s} \)),
- \( \theta \) is the scattering angle of the photon, which is 90° in this case.
To find the solution, one would need to substitute these values into the Compton equation and perform the necessary calculations.
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