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There are several ways to derive Einstein's celebrated formula for the energyof a massive particle at rest, $E=mc^2$. Noether's theorem applied to therelativistic Lagrange function provides an unambiguous and straightforwardaccess to energy and momentum conservation laws but those tools were notavailable at the beginning of the twentieth century and are not at hand fornewcomers even nowadays. In a pedestrian approach, we start from relativistickinematics and analyze elastic and inelastic scattering processes in differentreference frames to derive the relativistic energy-mass relation. We extend theanalysis to Compton scattering between a massive particle and a photon, and amassive particle emitting two photons. Using the Doppler formula, it followsthat $E=\hbar \omega$ for photons at angular frequency $\omega$ where $\hbar$is the reduced Planck constant. We relate our work to other derivations ofEinstein's formula in the literature.

A pedestrian approach to Einstein's formula $E=mc^2$ with an application to photon dynamics