X-rays of wavelength 0.8 nm are Compton-scattered, the scattered beam is observed at an angle of 60.0° relative to the incident beam. Calculate the energy of the scattered X-ray photons.
X-rays of wavelength 0.8 nm are Compton-scattered, the scattered beam is observed at an angle of 60.0° relative to the incident beam. Calculate the energy of the scattered X-ray photons.
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![**Problem Statement:**
X-rays of wavelength 0.8 nm are Compton-scattered. The scattered beam is observed at an angle of 60.0° relative to the incident beam. Calculate the energy of the scattered X-ray photons.
**Explanation:**
This problem involves the Compton scattering of X-rays. In Compton scattering, an X-ray photon collides with an electron, resulting in a change in the photon's wavelength and direction. The change in wavelength is given by the Compton wavelength shift formula:
\[ \Delta \lambda = \frac{h}{m_ec} (1 - \cos \theta) \]
where:
- \( \Delta \lambda \) is the change in wavelength,
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \( m_e \) is the electron rest mass (\(9.109 \times 10^{-31} \, \text{kg}\)),
- \( c \) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \( \theta \) is the angle of scattering.
The energy of the scattered photon can be calculated using the relation between energy and wavelength:
\[ E = \frac{hc}{\lambda} \]
**No graphs or diagrams are provided or needed for this problem.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c4a5f83-7aca-4e4e-8516-6de83483f29d%2F838e68c4-c03e-4f73-aea2-7102e176e994%2Fbjwxy2h_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
X-rays of wavelength 0.8 nm are Compton-scattered. The scattered beam is observed at an angle of 60.0° relative to the incident beam. Calculate the energy of the scattered X-ray photons.
**Explanation:**
This problem involves the Compton scattering of X-rays. In Compton scattering, an X-ray photon collides with an electron, resulting in a change in the photon's wavelength and direction. The change in wavelength is given by the Compton wavelength shift formula:
\[ \Delta \lambda = \frac{h}{m_ec} (1 - \cos \theta) \]
where:
- \( \Delta \lambda \) is the change in wavelength,
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \( m_e \) is the electron rest mass (\(9.109 \times 10^{-31} \, \text{kg}\)),
- \( c \) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \( \theta \) is the angle of scattering.
The energy of the scattered photon can be calculated using the relation between energy and wavelength:
\[ E = \frac{hc}{\lambda} \]
**No graphs or diagrams are provided or needed for this problem.**
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