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Carbon-14 Nitrogen-14 Binding Energies
Name: Abby
Status: educator
Grade: 9-12
Location: WI
Country: USA
Date: Spring 2012
Question:
Carbon-14 decays into nitrogen-14 by beta emission. I have/had the understanding that when a nuclei decays the binding energy of the daughter is greater than the binding energy of the parent. From my research this does not seem to be true for carbon-14 into nitrogen-14. The binding energy per nucleon for carbon-14 is 7.520319 MeV and the binding energy per nucleon for nitrogen-14 is 7.475614 MeV. I understand that carbon-14 had too many neutrons and that it decays by beta because of this. I understand that nitrogen-14 is more stable than carbon-14 but if it is more stable than why isn't the binding energy of nitrogen-14 greater than that of carbon-14. Hope this all makes sense.
Replies:
The difference may be that a proton is simply more stable than a neutron. Multiplied over the 14 nucleons composing them, the difference between the total binding energies you give for C-14 and N-14 is 0.62587 MeV. The rest energy difference between one neutron and one proton is 1.29 MeV. When a neutron beta decays, the beta particle (electron) has a rest energy of about 0.51 MeV. So when a neutron of C-14 changes to a proton of N-14, the binding energy increases by about half an MeV, but the lower energy of the electron + proton products more than compensates for that.
Richard E. Barrans Jr., Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming
Abby,
I think we need to make a distinction between nuclear stability versus spontaneity of a reaction. Normally these two go together and so we tend to think that a nuclear transformation (or chemical reaction) is spontaneous because the products are more stable than the reactants. However, as you've seen, this is not always true - and the two ideas really should be separate.
You are correct that the binding energy of C-14 is higher than that of N-14. This then means that the mechanical energy needed to "disassemble" C-14 is higher than that for N-14. This would indicate that N-14 is more stable against "disassembly". Reaction spontaneity, on the other hand, comes from whether energy is released and entropy increase. So if energy is released (which happens in the C-14 to N-14 transformation), and entropy increases (which it does with the production of two additional particles: the beta-particle and neutrino), then the reaction is spontaneous. The nuance here is that the transformation is spontaneous despite C-14 having a higher stability against disassembly then N-14.
Greg (Roberto Gregorius)
Canisius College
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Update: June 2012
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