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In studying the periodic table, I noticed that calcium (with atomic number 20) is the heaviest element with stable isotopes with a 1:1 ratio of protons to neutrons. For elements heavier than calcium, the number of neutrons exceeds the number of protons in stable isotopes. What causes this trend, and why do elements beyond calcium need an increasing neutron-to-proton ratio for stability? How does this relate to nuclear forces or the binding energy in atomic nuclei? Any insights or explanations regarding the physics behind this would be appreciated.

Qmechanic
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mcodesmart
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1 Answers1

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The protons in the nucleus can only be packed in there as densely as they are by using neutrons as glue to overcome the gigantic electrostatic force of repulsion that they exert on each other.

The protons and neutrons in the nucleus strive to occupy certain well-defined energy levels inside the nucleus, much as how the electrons get grouped into orbitals. But unlike electrons, the nucleons have well-defined diameters which means their natural tendency is to "pack down" into the densest glob possible, called hexagonal close-packing. That tendency does not always accommodate the nuclear energy levels, with the result that some "misfit" nuclei are less-tightly bound than other, similar ones- and certain packing schemes "fit in" with certain energy levels to result in specific nuclei which are especially stable. These are the so-called magic nuclear number elements that user Mass is referring to.

Note also that the electrostatic repulsion between protons is a long-ranged force, so every proton within the nucleus experiences the repulsive force from every other proton. However, the residual strong force holding nucleons together is extremely short-ranged: only the nucleons close enough to be "touching" (i.e., nearest neighbors) feel the attractive nuclear force. This difference in range, coupled with packing irregularities and the nuclear energy levels, further complicates the establishment of magic numbers and all of this stuff biases the composition of stable nuclei heavier than calcium to have more neutrons than protons in them.

niels nielsen
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