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A 19.5 pm x-ray photon scatters off a free electron at A (see the figure below), producing a photon of wavelength A' traveling at an angle 0 = 43.0° relative to the first photon's direction. This second photon scatters off another free electron at B, producing a photon with wavelength " and moving in a direction directly opposite the first photon. Determine the wavelengths à' and λ", both in pm. HINT (a) A' (b) " pm pm Electron 1 Electron 2

A 19.5 pm x-ray photon scatters off a free electron at A (see the figure below), producing a photon of wavelength A' traveling at an angle 0 = 43.0° relative to the first photon's direction. This second photon scatters off another free electron at B, producing a photon with wavelength " and moving in a direction directly opposite the first photon. Determine the wavelengths à' and λ", both in pm. HINT (a) A' (b) " pm pm Electron 1 Electron 2

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**Interactive Compton Scattering Example** A **19.5 pm** x-ray photon scatters off a free electron at point **A** (see the accompanying diagram), producing a photon with a wavelength **λ'** traveling at an angle **θ = 43.0°** relative to the original photon’s direction. Subsequently, this new photon scatters off another free electron at point **B**, producing a photon with a wavelength **λ''** that moves in a direction directly opposite to the first photon. Your task is to determine the wavelengths **λ'** and **λ''**, both measured in picometers (pm). **Diagram Explanation:** - **Initial Photon (λ):** An incoming photon with wavelength **λ** encounters an electron at point **A**. - **Scattered Photon (λ'):** The photon, after interaction, changes direction at an angle **θ = 43.0°**, producing a wavelength **λ'**. - **Electron 1:** The electron at **A** gains momentum and moves in a specific direction marked by the diagram. - **Second Interaction at B:** - The photon with wavelength **λ'** interacts with another electron at point **B**. - A new photon with wavelength **λ''** is produced, moving opposite to the original photon’s direction. - **Electron 2:** The electron at **B** moves in another distinct direction after the interaction. **Parameters:** - Initial angles, **α** and **β**, define electron scatter directions. **Calculations Needed:** - Solve for **(a) λ'** pm - Solve for **(b) λ''** pm **Hint:** Use Compton scattering formulas to find the changes in wavelength.
Transcribed Image Text:**Interactive Compton Scattering Example** A **19.5 pm** x-ray photon scatters off a free electron at point **A** (see the accompanying diagram), producing a photon with a wavelength **λ'** traveling at an angle **θ = 43.0°** relative to the original photon’s direction. Subsequently, this new photon scatters off another free electron at point **B**, producing a photon with a wavelength **λ''** that moves in a direction directly opposite to the first photon. Your task is to determine the wavelengths **λ'** and **λ''**, both measured in picometers (pm). **Diagram Explanation:** - **Initial Photon (λ):** An incoming photon with wavelength **λ** encounters an electron at point **A**. - **Scattered Photon (λ'):** The photon, after interaction, changes direction at an angle **θ = 43.0°**, producing a wavelength **λ'**. - **Electron 1:** The electron at **A** gains momentum and moves in a specific direction marked by the diagram. - **Second Interaction at B:** - The photon with wavelength **λ'** interacts with another electron at point **B**. - A new photon with wavelength **λ''** is produced, moving opposite to the original photon’s direction. - **Electron 2:** The electron at **B** moves in another distinct direction after the interaction. **Parameters:** - Initial angles, **α** and **β**, define electron scatter directions. **Calculations Needed:** - Solve for **(a) λ'** pm - Solve for **(b) λ''** pm **Hint:** Use Compton scattering formulas to find the changes in wavelength.
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