An incident photon of 1.7 MeV is scattered via Compton interactions through an angle of 22 degrees. What is the wavelength of the scattered photon and what is the new photon energy?
An incident photon of 1.7 MeV is scattered via Compton interactions through an angle of 22 degrees. What is the wavelength of the scattered photon and what is the new photon energy?
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![**Problem Statement: Compton Scattering in Photons**
An incident photon of 1.7 MeV is scattered via Compton interactions through an angle of 22 degrees. What is the wavelength of the scattered photon and what is the new photon energy?
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**Explanation:**
This problem involves calculating the shift in wavelength and energy of a photon due to Compton scattering. The interaction results in a change in direction and energy of the photon after colliding with an electron.
Compton scattering is described by the following equation:
\[ \Delta \lambda = \lambda' - \lambda = \frac{h}{m_e c} (1 - \cos \theta) \]
Where:
- \( \Delta \lambda \) is the change in wavelength.
- \(\lambda\) and \(\lambda'\) are the initial and final wavelengths, respectively.
- \(h\) is Planck’s constant (\(6.626 \times 10^{-34} \, \text{m}^2\text{kg/s}\)).
- \(m_e\) is the electron rest mass (\(9.109 \times 10^{-31} \, \text{kg}\)).
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)).
- \(\theta\) is the scattering angle (22 degrees).
The energy of the photon changes according to the relationship:
\[ E = \frac{hc}{\lambda} \]
By finding the change in wavelength, \(\lambda'\) can be determined, and subsequently, the new energy of the photon can be calculated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2db4564-83b0-4959-8a89-64f7e3b0b98b%2Fddd6136e-2c53-4668-a488-1e3f546293e8%2Foqtecrh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Compton Scattering in Photons**
An incident photon of 1.7 MeV is scattered via Compton interactions through an angle of 22 degrees. What is the wavelength of the scattered photon and what is the new photon energy?
---
**Explanation:**
This problem involves calculating the shift in wavelength and energy of a photon due to Compton scattering. The interaction results in a change in direction and energy of the photon after colliding with an electron.
Compton scattering is described by the following equation:
\[ \Delta \lambda = \lambda' - \lambda = \frac{h}{m_e c} (1 - \cos \theta) \]
Where:
- \( \Delta \lambda \) is the change in wavelength.
- \(\lambda\) and \(\lambda'\) are the initial and final wavelengths, respectively.
- \(h\) is Planck’s constant (\(6.626 \times 10^{-34} \, \text{m}^2\text{kg/s}\)).
- \(m_e\) is the electron rest mass (\(9.109 \times 10^{-31} \, \text{kg}\)).
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)).
- \(\theta\) is the scattering angle (22 degrees).
The energy of the photon changes according to the relationship:
\[ E = \frac{hc}{\lambda} \]
By finding the change in wavelength, \(\lambda'\) can be determined, and subsequently, the new energy of the photon can be calculated.
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