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Calculate the binding energy per nucleon of , the particle.
Strategy
To find , we first find BE using the Equation and then divide by . This is straightforward once we have looked up the appropriate atomic masses in Appendix A .
Solution
The binding energy for a nucleus is given by the equation
For , we have ; thus,
Appendix A gives these masses as , , and . Thus,
Noting that , we find
Since , we see that is this number divided by 4, or
Discussion
This is a large binding energy per nucleon compared with those for other low-mass nuclei, which have . This indicates that is tightly bound compared with its neighbors on the chart of the nuclides. You can see the spike representing this value of for on the graph in [link] . This is why is stable. Since is tightly bound, it has less mass than other nuclei and, therefore, cannot spontaneously decay into them. The large binding energy also helps to explain why some nuclei undergo decay. Smaller mass in the decay products can mean energy release, and such decays can be spontaneous. Further, it can happen that two protons and two neutrons in a nucleus can randomly find themselves together, experience the exceptionally large nuclear force that binds this combination, and act as a unit within the nucleus, at least for a while. In some cases, the escapes, and decay has then taken place.
There is more to be learned from nuclear binding energies. The general trend in is fundamental to energy production in stars, and to fusion and fission energy sources on Earth, for example. This is one of the applications of nuclear physics covered in Medical Applications of Nuclear Physics . The abundance of elements on Earth, in stars, and in the universe as a whole is related to the binding energy of nuclei and has implications for the continued expansion of the universe.
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