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E = mc2 and the weight of energy

The formula E = mc2 is an icon in physics but, in basic education, it tends to be approached just as a prescription for simple numerical conversions of mass into energy. In order to go beyond this narrow scope, in this work one considers some applications of the mass–energy equivalence to microscopic problems, since there it plays an essential role, especially in the description of bound systems. In this realm one may grasp how far-reaching its consequences are. The cases discussed, which range from larger to smaller scales, are carbon monoxide, a hydrogen atom, a deuteron and a proton. One begins by discussing the energy balances of exothermic reactions involving these bound systems so as to produce evidence that their masses are smaller than those of their isolated constituents. One then considers a bound system as an isolated body and moves into a more microscopic description, showing that the entities which effectively contribute to its mass are constituent masses, supplemented by both kinetic and potential energies. The action of the gravitational field of the Earth over these entities gives rise to the observed weight of the bound system. In the case of protons and neutrons, 99% of the weight is given by just internal kinetic and potential energies. One also indicates that this picture holds for the weight of ordinary objects.