OpenStax College Physics for AP® Courses, Chapter 31, Problem 82 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. A theoretical physicist is aware that this reaction of a proton turning into a neutron, a positron and a neutrino is possible based on conservation laws because there is no conservation law violated by this reaction and so their concern is well then that's just going to happen and then all the protons are going to turn into neutrons and positrons and matter will be destroyed and well, I mean atoms will be destroyed and life will not go on since you know, all these protons which are necessary for the chemical properties of atoms will not be there anymore. So the question in part (a) what energy is released in the decay? So we need to calculate this mass defect, which is the difference in mass between the products and the original reactant you might say— this is called the daughter nuclide and this is the parent nuclide. And so we have the mass of the proton to begin with and from that we subtract the mass of the neutron and the mass of this positron, which is the same mass as an electron and then multiply that by c squared to get the energy released. So that's 938.27 megaelectron volts per c squared— mass energy for a proton— minus 939.57 megaelectron volts per c squared—for a neutron— minus 0.511 megaelectron volts per c squared—for an electron— and then this works out to negative 1.811 megaelectron volts and this negative sign is the reason why this reaction is not spontaneous. So this is an endothermic reaction that requires additional energy inputs to make it happen. And so the assumption that the reaction will be spontaneous is false since energy input is required.