Final answer:
To determine the energy of the scattered photon after a 250 keV photon collides with a free electron at a 120° angle, we use the Compton scattering formula, taking the change in wavelength to calculate the change in energy.
Step-by-step explanation:
The question concerns a photon of energy ℓω = 250 keV that is scattered by a free electron at an angle θ = 120°. To find the energy of the scattered photon, we can use the Compton scattering formula:
λ' - λ = (h/m_ec)(1 - cosθ)
where λ is the initial wavelength, λ' is the wavelength after scattering, h is Planck's constant, m_e is the electron rest mass, c is the speed of light, and θ is the scattering angle. The change in wavelength (λ' - λ) will correspond to a change in photon energy, which can be calculated using the energy-wavelength relation E = hc/λ. Since the energy of the electron after scattering can be ignored (as it is a free, stationary electron before the collision), the energy of the scattered photon purely depends on the change in wavelength due to the scattering process.
It's important to notice that the provided reference information does not directly answer the student's question, but the process for calculating the kinetic energy of an ejected electron (KEe = hf - BE) is somewhat analogous to determining the final energy of a scattered photon, albeit the processes are different (photoelectric effect vs. Compton scattering).