What is the maximum energy of a scattered photon when a high energy photon strikes an orbital electron and scatters at 180 degrees?

When a high-energy photon scatters off an orbital electron at an angle of 180 degrees, the phenomenon is described by the conservation of energy and momentum. In this scenario, a photon transfers its energy to the electron, causing it to recoil.

The maximum energy of the scattered photon can be derived from the Compton scattering formula. The primary principle involved states that as the photon scatters backwards (at 180 degrees), it transfers the maximum possible energy to the electron. The energy of the incoming photon is directly related to the mass-energy equivalence of the electron, which has a rest mass energy of approximately 0.511 MeV.

At 180-degree scattering, the energy of the scattered photon can be derived using the following relationship: [ E_{photon, \text{scattered}} = \frac{E_{photon, \text{initial}}}{1 + \frac{E_{photon, \text{initial}}}{m_ec^2}(1 - cos(\theta))} ] Substituting ( \theta = 180^\circ ): [ E_{photon, \text{scattered}} = \frac{E_{photon, \text{initial}}}{1 + 2