In physics, it often helps to start with a picture.

NOTE: There is a mistake at 2:26! The energy of the electron after collision should include the electron's initial energy. In algebraic terms, E_e^2 = E_0^2 + (p_e⋅c)^2. You should get an (m_0⋅c^2)^2 term on both sides of the equation, which cancels out.

0:00 Intro
0:10 Compton Scattering, a Doodle
0:55 ∆λ and θ
1:35 Conservation of Energy
2:40 Conservation of Momentum
4:45 Final Equation

Sources:
-Carroll, Bradley W., and Ostlie, Dale A.. An Introduction to Modern Astrophysics. United Kingdom, Cambridge University Press, 2017.
-Dr. James E. Parks, The Compton Effect-Compton Scattering and Gamma Ray Spectroscopy ([ Ссылка ])
-University Physics III - Optics and Modern Physics (OpenStax), The Compton Effect

Intro and Outro:
"Astronaut in the Ocean" by Masked Wolf, beats by FaMusic

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