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°?

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Chapter1: Units, Trigonometry. And Vectors
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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.
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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