Isotope Production Calculator

Saturation activity (N·σ·φ) is the theoretical ceiling reached only if you irradiated the target forever — it's the activity level at which new atoms are being activated at exactly the same rate the existing product atoms are decaying away. Actual produced activity follows A(t) = A_sat·(1 − e^(−λt)), and since (1 − e^(−λt)) can only approach 1 as time grows, produced activity can approach but never reach or exceed saturation activity.

At 3.5 half-lives, (1 − e^(−λt)) works out to roughly 0.91, meaning you've reached about 91% of the maximum possible activity. Beyond that point, each additional half-life of irradiation buys progressively less activity gain — going from 3.5 to 7 half-lives only takes you from ~91% to ~99% — so irradiation time beyond about 3.5 half-lives is generally not worth the added reactor time and cost.

The engine doesn't take a specific target isotope as input, so it uses 100 amu as a representative stand-in to convert your entered target mass into a number of atoms via Avogadro's number. Since real target isotopes range from light elements to heavy actinides, this introduces error proportional to how far your actual target's atomic mass is from 100 — treat the absolute activity figures as order-of-magnitude estimates rather than precise production numbers unless your target happens to be near 100 amu.

Total produced activity (in Bq) tells you the overall radioactivity generated, but specific activity (Bq per gram of target) tells you how concentrated that radioactivity is within the target material. This matters because many applications — medical isotopes especially — require the product to be usable at a minimum concentration, so a large total activity spread across a heavy target may still be too dilute for its intended use even if the raw activity number looks impressive.