19.3
Nuclear Stability
Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite…
A nucleus contains most of an atom's mass and is tiny compared with the entire atom. The average nuclear density is nine trillion times greater than the density of osmium: the densest element!
The earth would be 30,000 times smaller if it had the density of the nucleus. Why does the nucleus have such a high density?
The nucleons are held together by the close-range strong nuclear force. The balance between the proton–proton repulsions and the nucleon–nucleon attractions determines the stability of the nucleus. When the proton–proton repulsions outweigh the attractive nuclear forces, the nucleus disintegrates.
Plotting nuclides by the numbers of protons and neutrons illustrates that the stable nuclei occupy a central region, indicated in blue, which is called the belt or valley of stability.
Lighter nuclides with neutron-to-proton ratios of one, like carbon-12, enjoy great stability. As the atomic number increases beyond 20, more neutrons are required to counterbalance the proton–proton repulsions.
Neutrons are attracted to each other by nuclear forces, whereas there are no repulsive interactions amongst them. Thus, an increase in the number of neutrons fortifies the nuclear force significantly. All stable heavier nuclides have neutron-to-proton ratios of greater than one.
Radionuclides with higher neutron-to-proton ratios typically undergo beta-minus decay, which converts a neutron into a proton. Thus, the neutron-to-proton ratio decreases to yield a daughter nuclide that is closer to the stability belt on the chart.
Radionuclides with lower neutron-to-proton ratios emit positrons or undergo electron capture to convert protons into neutrons and thereby move closer to the stability belt.
Interestingly, just like electron pairs residing in the orbitals, proton–proton and neutron–neutron pairing is observed in the nucleus. When the numbers of protons and neutrons are both even, nuclei are remarkably stable, as pairing is possible for all nucleons. Only five nuclides with odd numbers of neutrons and protons are stable.
Nuclei with certain numbers of protons or neutrons are more stable than expected, leading these numbers to be called magic numbers. Nuclei with magic numbers of both protons and neutrons are called doubly magic.
All nuclei with atomic numbers higher than 82 are radioactive. However, bismuth-209, atomic number 83, has an exceptionally long half-life among radionuclides.
For a radionuclide far from the stability belt, its decay chain is the series of decay processes by which it ultimately reaches a stable nuclide.
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Q1: What is the strong nuclear force and why is it necessary in the nucleus?
The strong nuclear force is the attractive force holding protons and neutrons together in the nucleus. Over distances less than 10−15 meters, this force is much stronger than electrostatic repulsions between protons. Without it, positively charged protons would repel each other and the nucleus would disintegrate immediately.
Q2: Why do heavier stable nuclei have more neutrons than protons?
Heavier nuclei have more proton-proton repulsions, requiring additional neutrons to provide compensating strong nuclear forces. Neutrons attract each other and protons through nuclear forces without experiencing repulsive interactions among themselves. This increased neutron count stabilizes larger nuclei against electrostatic repulsion and keeps them within the stability band.
Q3: What is the band of stability and where do stable nuclei fall on a neutron-proton plot?
The band of stability is a narrow region on a plot of neutrons versus protons where stable nuclei are located. Lighter stable nuclei have neutron-to-proton ratios near one, while heavier stable nuclei have increasingly higher ratios. Nuclei outside this band are unstable and undergo radioactive decay and decay series to reach stability.
Q4: How do radionuclides move toward the band of stability?
Radionuclides with higher neutron-to-proton ratios undergo beta-minus decay, converting neutrons into protons. Those with lower ratios emit positrons or undergo electron capture, converting protons into neutrons. Both processes shift the nucleus closer to the stability band until reaching a stable nuclide.
Q5: What are magic numbers and why do they affect nuclear stability?
Magic numbers are specific numbers of protons or neutrons (2, 8, 20, 28, 50, 82, 126) that form complete nuclear shells, making nuclei remarkably stable. Nuclei with magic numbers of both protons and neutrons, called doubly magic nuclei, are particularly stable. This concept parallels the stability of noble gases with complete electron shells.
Q6: How does nucleon pairing contribute to nuclear stability?
Proton-proton and neutron-neutron pairing occurs in nuclei, similar to electron pairing in orbitals. Nuclei with even numbers of both protons and neutrons are remarkably stable because all nucleons can pair. Only five nuclides with odd numbers of both protons and neutrons are stable, demonstrating pairing's importance.
Q7: Why are all nuclei with atomic numbers higher than 82 radioactive?
Nuclei with atomic numbers above 82 have excessive proton-proton repulsions that overwhelm the strong nuclear force, making them inherently unstable. Even bismuth-209, with atomic number 83, is radioactive despite its exceptionally long half-life. These unstable nuclei undergo decay series to reach stable configurations.