Activity of a Radioactive Sample
Imagine you have a jar of fireflies. Each firefly glows at a random moment, and once it glows, it stops forever. You don't care about any single firefly — you care about how many flashes you see per second. That rate of flashing is the activity of your jar.
A radioactive sample is exactly that jar. Inside are unstable nuclei. Each nucleus will "flash" (decay) at some unpredictable instant, and after that it becomes a stable atom. The activity A is simply the number of decays happening each second.
The precise definition
If you have N unstable nuclei at a given moment, and each has a constant probability λ of decaying per second (the decay constant), then the number of decays per second is:
λ is a fixed property of the isotope — it tells you how "eager" each nucleus is to decay. A large λ means each nucleus is very likely to decay soon, so the activity is high even with few nuclei.
Why activity itself decays
As nuclei decay, N drops. Since A is proportional to N, the activity must drop too. The mathematics is straightforward: the rate at which N decreases is exactly the activity (each decay removes one nucleus), so
dtdN=−A=−λN
This differential equation gives the familiar exponential decay:
N(t)=N0e−λt
Multiply both sides by λ and you get the activity:
A(t)=λN0e−λt=A0e−λt
The activity itself decays exponentially with the same decay constant λ.
A common mistake is to think activity is constant. It is not — it falls off exactly like the number of undecayed nuclei, because every decay reduces the remaining stock.
Units
The SI unit is the becquerel (Bq): 1 Bq = 1 decay per second. That is a tiny number. Historically, the curie (Ci) was used: 1 Ci = 3.7×1010 Bq, roughly the activity of one gram of radium-226. …