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Notice in Table 33.2 that the neutron has a half-life of 882 seconds. This is only for a free neutron, not bound with other neutrons and protons in a nucleus. Given the other particles in the table, and using both their charge and masses, what do you think the most likely decay products for a neutron are? Justify your answer.
Question by OpenStax is licensed under CC BY 4.0.
$n \rightarrow p + e^-$

  • Charge is conserved
  • Energy is released, making the reaction spontaneous.
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OpenStax College Physics for AP® Courses Solution, Chapter 33, Problem 16 (Test Prep for AP® Courses) (1:20)

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Video Transcript
This is College Physics Answers with Shaun Dychko. A free neutron will probably decay into a proton, electron and an electron anti-neutrino; this is possible because charge is conserved, we can see that the zero net charge to begin with is the same as the zero net charge we have in the end because we have plus 1 charge on the proton and a negative one charge from the electron for a total of 0 the electron anti-neutrino has no charge. And we can also say that this reaction could be spontaneous since there is a net energy released. So we can find that net energy released by finding the change in mass between the reactants and the products times c squared so this is also known as the mass defect. So we have the mass of the neutron minus the total mass of the proton and electron times c squared and we assume there is no mass for the electron anti-neutrino. So that's 939.57 megaelectron volts per c squared minus 938.27 plus 0.511 and this works out to 0.789 megaelectron volts. So because this energy released is going to be greater than zero— this is exothermic in other words— it could be spontaneous.