3-43. In the Compton scattering of a photon with energy E, from an electron at rest, show that the energy of the scattered photon E₂ is given by E₂ E₁ (E₁/mc)(1-cos) + 1
3-43. In the Compton scattering of a photon with energy E, from an electron at rest, show that the energy of the scattered photon E₂ is given by E₂ E₁ (E₁/mc)(1-cos) + 1
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![**Level II**
**3-43.** In the Compton scattering of a photon with energy \( E_1 \) from an electron at rest, show that the energy of the scattered photon \( E_2 \) is given by
\[
E_2 = \frac{E_1}{\left(\frac{E_1}{mc^2}\right)(1 - \cos \phi) + 1}
\]
**Explanation:**
This problem is about demonstrating a relationship in Compton scattering, a phenomenon where a photon scatters off an electron at rest. The formula provided is used to calculate the energy \( E_2 \) of the photon after scattering, factoring in the initial energy \( E_1 \) of the photon, the rest mass energy of the electron \( mc^2 \), and the scattering angle \( \phi \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09613d8c-4cef-4639-a65c-ee2add319cba%2F7e0c9c84-b22d-4de3-8c17-fef92ed30324%2F4sy4ym4_processed.png&w=3840&q=75)
Transcribed Image Text:**Level II**
**3-43.** In the Compton scattering of a photon with energy \( E_1 \) from an electron at rest, show that the energy of the scattered photon \( E_2 \) is given by
\[
E_2 = \frac{E_1}{\left(\frac{E_1}{mc^2}\right)(1 - \cos \phi) + 1}
\]
**Explanation:**
This problem is about demonstrating a relationship in Compton scattering, a phenomenon where a photon scatters off an electron at rest. The formula provided is used to calculate the energy \( E_2 \) of the photon after scattering, factoring in the initial energy \( E_1 \) of the photon, the rest mass energy of the electron \( mc^2 \), and the scattering angle \( \phi \).
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