**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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