How does the physical size of a radioactive source relate to its specific activity?

The specific activity of a radioactive source is defined as the radioactivity per unit mass of the material. This means that smaller sources of radioactive material can have a higher concentration of radioactive isotopes in relation to their mass compared to larger sources, which may have more mass but not necessarily a proportionally greater amount of active isotopes.

Radioactive decay is a random process, and the specific activity measures how many decays occur in a given mass. Therefore, a smaller source can yield a higher specific activity, as there may be a more significant number of isotopes present relative to its total mass. This principle highlights the relationship between the size of the source and its ability to produce radioactivity per unit mass, making smaller sources more efficient in terms of specific activity.

It’s also important to consider that larger sources can dilute the concentration of the radioactive isotopes, resulting in a lower specific activity compared to what a smaller source could provide if it has a greater ratio of radionuclide to non-radioactive material.

Thus, the correct understanding of the relationship between physical size and specific activity supports the idea that a smaller radioactive source has a higher activity in terms of the ratio of decay events to mass.