How do you determine isotope stability?

You measure the number of nuclear disintegrations per second and, with some difficulty, figure out the material's half-life.

The gold standard for determining whether radioactivity is present is to use appropriate protocols to measure using an appropriate instrument; the key word here is appropriate.

A "universal" instrument that functions flawlessly in every situation does not exist; instead, different types of radiation are detected by different instruments, and nuclei decay by emitting one or more of the following radiations: protons, neutrons, alpha particles, beta particles, X-rays, or γ rays. Some of these radiations are very hard to detect.

There are 253 isotopes that are stable by definition, with only 90 isotopes predicted to be perfectly stable and another 163 that are energetically unstable but have never been observed to decay.

A radioactive isotope's half-life, or the amount of time it takes for half of its nuclei to break down, indicates how quickly it decays. The half-lives of different radioisotopes range from 10⁻²⁴ s (hydrogen-7) to 10²⁴ years (tellurium-128).

Thus, the half-life of a stable nucleus is longer than 10^^⁴ years.

Isotope stability is determined primarily by the balance between the number of protons and neutrons in the nucleus. Generally, isotopes with a balanced or nearly equal number of protons and neutrons are more stable. However, there are exceptions, such as isotopes with magic numbers of protons or neutrons, which tend to be more stable. Additionally, isotopes with too many or too few neutrons compared to protons are usually unstable and undergo radioactive decay to achieve a more stable configuration.