Radioactive decay is a nuclear process, meaning it occurs at the level of the atomic nucleus. This distinguishes it from chemical reactions, which involve the electrons surrounding the nucleus and are often influenced by temperature. The rate of radioactive decay is largely unaffected by external factors such as temperature, pressure, or chemical state. This constancy is because the process is governed by the fundamental forces operating within the nucleus itself, which are not influenced by external environmental conditions. For instance, heating or cooling a radioactive material does not change the rate at which its nuclei decay. This inherent stability of decay rates is what makes radioactive isotopes reliable as 'clocks' for methods like radiocarbon dating, where the decay rate of carbon-14 remains constant over time regardless of environmental changes.

The decay constant of a radioactive isotope is a fundamental property that is determined by the forces within the atomic nucleus and is specific to each isotope. As such, it cannot be altered by external factors. The decay constant is dictated by the strength of the nuclear force holding the protons and neutrons together in the nucleus and the balance between this force and the repulsive electromagnetic force between protons. These forces are intrinsic properties of the particles themselves and are not influenced by external conditions like temperature, pressure, or chemical state. This immutable nature of the decay constant is crucial in applications like radiometric dating, where the consistent decay rate provides a reliable measure of time. The inability to alter the decay constant assures the reliability and predictability of the decay process over time.

Different isotopes have different half-lives primarily due to variations in their nuclear structure. The stability of a nucleus, which directly influences its likelihood to undergo radioactive decay, is affected by the balance of forces within the nucleus. The strong nuclear force, responsible for holding the nucleus together, competes with the electromagnetic repulsion between protons. Isotopes with a favourable balance of neutrons and protons tend to be more stable and have longer half-lives. Conversely, isotopes with an imbalance in this ratio are less stable and decay more quickly, resulting in shorter half-lives. Additionally, the specific types of decay processes available to an isotope (such as alpha, beta, or gamma decay) also play a role in determining its half-life. Each decay mode is associated with a particular set of nuclear rearrangements and energy changes, which contribute to the overall stability and decay rate of the isotope.

The decay constant of a radioactive isotope is a measure of its stability. A higher decay constant indicates a less stable isotope that decays more rapidly, whereas a lower decay constant suggests a more stable isotope with a slower decay rate. The stability of a radioactive isotope is determined by the balance of forces within its nucleus, specifically the strong nuclear force that binds the nucleus together and the electromagnetic force that causes repulsion between protons. Isotopes with an optimal neutron-to-proton ratio are more stable and exhibit lower decay constants. In contrast, isotopes with an excess or deficiency of neutrons are less stable, leading to higher decay constants. The decay constant is a fundamental property of each isotope, reflecting the intrinsic likelihood of its nucleus to undergo radioactive decay.

Radioactive decay plays a significant role in medical diagnostics, particularly in the field of nuclear medicine. One of the primary applications is in diagnostic imaging techniques, such as Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT). In these methods, radioactive isotopes (known as radiotracers) are introduced into the body. These isotopes decay by emitting gamma rays or positrons, which are detected by specialized scanners to create detailed images of internal body structures. For instance, PET scans utilize isotopes like fluorine-18, which decay by positron emission. The emitted positrons annihilate with electrons in the body, producing gamma rays that are detected to form images. This technique is particularly useful in oncology for detecting and monitoring tumors, as cancerous tissues often absorb more of the radiotracer than normal tissues. Additionally, the decay of radioactive isotopes is used in radiotherapy for treating cancer. Isotopes like iodine-131 are used to deliver targeted radiation to destroy cancerous cells, particularly in cases like thyroid cancer. The precision and effectiveness of radioactive isotopes in these applications stem from their predictable decay rates and the energy released during decay.