n incident X-ray photon is scattered from a free electron that is initially at rest. The photon is scattered straight back at an angle of 180∘ from its initial direction. The wavelength of the scattered photon is 0.0770 nm. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Wavelength shift in Compton scattering. Part A Part complete What is the wavelength of the incident photon? Express your answer with the appropriate units. λ = 7.21×10−11 m Previous Answers Correct Set Up: The change in wavelength of the scattered photon is λ′−λ=hmc(1−cosϕ) . The momentum of a photon is given by p=hλ . Solve: Solving for λ we obtain λ=λ′−hmc(1−cosϕ) . Thus, we have λ=(0.0770nm)−(6.626×10−34J⋅s)(9.109×10−31kg)(2.998×108m/s)(1+1)=7.21×10−11m . Part B What is the magnitude of the momentum of the electron after the collision? Express your answer with the appropriate units. pe = Previous AnswersRequest Answer Incorrect; Try Again; One attempt remaining Part C Part complete What is the kinetic energy of the electron after the collision? Express your answer in joules. Ke = 1.74×10−16 J Previous Answers Correct Since the electron is non-relativistic ( v/c<0.1 ), Ke=p2e/(2m)=1.74×10−16J . Reflect: Note that the wavelength of the incident photon is less than the wavelength of the scattered photon. To conserve momentum and energy, the wavelength of the photon cannot decrease after collision with a stationary electron. Provide Feedback
