Isotopes are variants of a chemical element, sharing the same number of protons but containing different numbers of neutrons. While some are stable, others possess an unstable combination of these particles. An unstable atomic nucleus is called a radioisotope, and it spontaneously loses energy by emitting radiation in a process known as radioactive decay. This decay transforms the unstable parent atom into a more stable daughter atom, often a different element.
The Role of the Neutron-to-Proton Ratio
The primary factor determining whether an isotope is radioactive is the balance between the neutrons and protons within its nucleus. Protons, being positively charged, repel each other through the electrostatic force, and it is the strong nuclear force that holds the nucleus together. For stability in light elements, the number of neutrons must be approximately equal to the number of protons, maintaining a ratio near 1:1.
As the number of protons increases in heavier elements, the total repulsive force grows significantly over the larger nuclear volume. To counteract this increasing repulsion, the nucleus requires a disproportionately higher number of neutrons to provide enough strong nuclear force to bind the nucleus. The stable ratio of neutrons to protons gradually increases, reaching about 1.5:1 for the heaviest stable elements, such as lead.
When plotted on a graph, the stable isotopes form a narrow region known as the “Band of Stability.” Isotopes that fall outside this band are unstable and will undergo radioactive decay to adjust their composition toward the stable ratio. Isotopes with too many neutrons relative to protons lie above this band, making them neutron-rich and unstable.
Conversely, isotopes with too few neutrons relative to protons fall below the band. Both neutron-rich and proton-rich isotopes change their composition to achieve a lower-energy, more stable configuration. This adjustment of the neutron-to-proton ratio is one of the two main reasons an isotope undergoes decay.
Instability Due to Nuclear Size
The second reason for instability is the sheer size of the atomic nucleus, which places a hard limit on the number of particles that can be bound together. The short-range strong nuclear force only acts effectively between neighboring protons and neutrons. In contrast, the repulsive electrostatic force between protons acts over the entire nuclear volume, regardless of distance.
Once an atom’s nucleus exceeds a certain size, the cumulative long-range repulsion between all the protons inevitably overwhelms the localized attraction of the strong nuclear force. This makes the nucleus unstable, regardless of the neutron-to-proton ratio. This threshold is crossed at atomic number 83, the element Bismuth.
All isotopes of elements with 83 protons or more, starting with Bismuth-209 and extending through elements like Uranium and Plutonium, are radioactive. No combination of neutrons can stabilize a nucleus this large against the internal repulsive forces. Consequently, these heavy isotopes primarily decay by shedding mass to reduce their size.
How Unstable Isotopes Transform
Unstable isotopes transform their nuclei through specific decay mechanisms tailored to correct their imbalance. Neutron-rich isotopes, which lie above the Band of Stability, undergo Beta-minus (\(\beta^-\)) decay. This process involves a neutron transforming into a proton, emitting a high-energy electron and an antineutrino. This conversion increases the atomic number by one while decreasing the neutron count, effectively moving the atom closer to the stable band.
Proton-rich isotopes, found below the Band of Stability, have two main ways to convert a proton into a neutron to achieve stability. Positron Emission (\(\beta^+\) decay) occurs when a proton converts into a neutron, expelling a positron—the anti-particle of an electron—and a neutrino. This decreases the atomic number by one, correcting the proton excess.
Alternatively, proton-rich nuclei use Electron Capture, where the nucleus draws in an electron from the atom’s innermost electron shell. This captured electron combines with a proton to form a neutron, decreasing the atomic number by one. Positron emission and electron capture are competing processes, with electron capture occurring when the energetic requirements for positron emission are not met.
Finally, the large nuclei of elements with 83 or more protons primarily use Alpha (\(\alpha\)) decay to reduce their size. An alpha particle is a cluster of two protons and two neutrons, identical to the nucleus of a Helium-4 atom. By ejecting this particle, the parent nucleus decreases its atomic number by two and its mass number by four, shedding the excess mass and charge that caused the instability.