Final answer:
The wavelength and energy of an incident photon whose wavelength doubles after scattering at a 90° angle can be found by using Compton scattering formula and then calculating the energy based on the found wavelength.
Step-by-step explanation:
The phenomenon of an X-ray photon having its wavelength doubled upon being scattered through 90° can be described by the Compton scattering formula:
Δλ = λ' - λ = h / (m_ec) · (1 - · cosθ)
Where Δλ is the change in wavelength, λ' is the wavelength after scattering, λ is the initial wavelength, h is Planck's constant, m_e is the mass of the electron, c is the speed of light, and θ is the scattering angle.
Given that the wavelength is doubled and the scattering angle is 90°, the initial wavelength can be found using the following steps:
- Identify that cos(90°) = 0, which simplifies the equation to Δλ = h / (m_ec).
- Since the wavelength is doubled, Δλ = λ.
- The initial wavelength λ can be found by rearranging the equation to λ = h / (m_ec).
- Insert the values for h, m_e, and c, and calculate λ.
Once the initial wavelength is known, the energy of the photon can be calculated using the relationship E = hc / λ, where E is the energy.