Some Equations Relating to Radioactivity

There are 5 variables to be considered here:

• h: half-life
• m: mean lifetime
• k: decay constant
• A: activity (number of decays per unit time)
• N: number of particles

The normal metric unit for activity (A) is the becquerel (Bq) which in base units is ; however the non-metric unit for activity is still often used: the curie (Ci) which is .

The first three variables are independent of the number of particles or the activity; they are different ways of referring to the same property of a particular type of nuclide. The last two depend on the number of particles in question as well.

While the half-life (h) is usually given, the equations relating activity (A) to number of particles (N) is more simply expressed with the decay constant (k); so one needs to be able to convert the half-life to a decay constant: .

Then, the activity (A) of an object with N particles is simply . This equation, when rearranged, also allows one to calculate the number of particles from the activity: .

Finally, another rearrangement of this equation gives a notion of what one definition of the decay constant (k) is: ; the decay constant can be defined as the decays per unit time per number of particles.