Example Values Deduced From Experimentally Measured Atom Nuclide Masses
The following table lists some binding energies and mass defect values. Notice also that we use 1 u = 1 a.m.u = 931.494028(±0.000023) MeV. To calculate the "binding energy" we use the formula P*(mp+me) + N * mn - mnuclide where P denotes the number of protons of the nuclides and N its number of neutrons. We take mp = 938.2723 Mev, me = 0.5110 MeV and mn = 939.5656 MeV. The letter A denotes the sum of P and N (number of nucleons in the nuclide). If we assume the reference nucleon has the mass of a neutron (so that all "total" binding energies calculated are maximal) we could define the total binding energy as the difference from the mass of the nucleus, and the mass of a collection of A free neutrons. In other words, it would be - mnuclide. The "total binding energy per nucleon" would be this value divided by A.
| nuclide | P | N | mass excess | total mass | total mass / A | total binding energy / A | mass defect | binding energy | binding energy / A |
|---|---|---|---|---|---|---|---|---|---|
| 56Fe | 26 | 30 | -60.6054 MeV | 55.934937 u | 0.9988382 u | 9.1538 MeV | 0.528479 u | 492.275 MeV | 8.7906 MeV |
| 58Fe | 26 | 32 | -62.1534 MeV | 57.933276 u | 0.9988496 u | 9.1432 MeV | 0.547471 u | 509.966 MeV | 8.7925 MeV |
| 60Ni | 28 | 32 | -64.4721 MeV | 59.930786 u | 0.9988464 u | 9.1462 MeV | 0.565612 u | 526.864 MeV | 8.7811 MeV |
| 62Ni | 28 | 34 | -66.7461 MeV | 61.928345 u | 0.9988443 u | 9.1481 MeV | 0.585383 u | 545.281 MeV | 8.7948 MeV |
56Fe has the lowest nucleon-specific mass of the four nuclides listed in this table, but this does not imply it is the strongest bound atom per hadron, unless the choice of beginning hadrons is completely free. Iron releases the largest energy if any 56 nucleons are allowed to build a nuclide—changing one to another if necessary, The highest binding energy per hadron, with the hadrons starting as the same number of protons Z and total nucleons A as in the bound nucleus, is 62Ni. Thus, the true absolute value of the total binding energy of a nucleus depends on what we are allowed to construct the nucleus out of. If all nuclei of mass number A were to be allowed to be constructed of A neutrons, then Fe-56 would release the most energy per nucleon, since it has a larger fraction of protons than Ni-62. However, if nucleons are required to be constructed of only the same number of protons and neutrons that they contain, then nickel-62 is the most tightly bound nucleus, per nucleon.
| nuclide | P | N | mass excess | total mass | total mass / A | total binding energy / A | mass defect | binding energy | binding energy / A |
|---|---|---|---|---|---|---|---|---|---|
| n | 0 | 1 | 8.0716 MeV | 1.008665 u | 1.008665 u | 0.0000 MeV | 0 u | 0 MeV | 0 MeV |
| 1H | 1 | 0 | 7.2890 MeV | 1.007825 u | 1.007825 u | 0.7826 MeV | 0.0000000146 u | 0.0000136 MeV | 13.6 eV |
| 2H | 1 | 1 | 13.13572 MeV | 2.014102 u | 1.007051 u | 1.50346 MeV | 0.002388 u | 2.22452 MeV | 1.11226 MeV |
| 3H | 1 | 2 | 14.9498 MeV | 3.016049 u | 1.005350 u | 3.08815 MeV | 0.0091058 u | 8.4820 MeV | 2.8273 MeV |
| 3He | 2 | 1 | 14.9312 MeV | 3.016029 u | 1.005343 u | 3.09433 MeV | 0.0082857 u | 7.7181 MeV | 2.5727 MeV |
In the table above it can be seen that the decay of a neutron, as well as the transformation of tritium into helium-3, releases energy; hence, it manifests a stronger bound new state when measured against the mass of an equal number of neutrons (and also a lighter state per number of total hadrons). Such reactions are not driven by changes in binding energies as calculated from previously fixed N and Z numbers of neutrons and protons, but rather in decreases in the total mass of the nuclide/per nucleon, with the reaction.
Read more about this topic: Nuclear Binding Energy
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