Source decay

Radioactive decay is a first-order random process: every nucleus has the same probability of decaying in the next instant, independent of how long it has already existed. That gives the exponential law A = A0 x e^(-lambda x dt), where the decay constant lambda = ln2 / T_half. Substituting gives the form radiographers use, A = A0 x e^(-0.693 x dt / T_half), or equivalently A = A0 x 2^(-dt/T_half).

The practical consequence is that exposure times must be recalculated continuously. An Ir-192 source loses roughly 1 percent of its activity per day, so a chart written on Monday is already optimistic by Friday. Selenium-75 at 119.8 days and cobalt-60 at 1925 days are far more stable, while ytterbium-169 at 32 days decays fast enough that the exposure chart needs updating every shift.

Activity alone does not determine exposure - it determines the emitted photon rate. The dose rate at a distance follows from activity multiplied by the specific gamma-ray constant, and the exposure needed at the film follows from that dose rate attenuated through the part. But because both scale linearly with activity, exposure time is simply inversely proportional to the current activity, which is why a decay calculation is the first thing done at the start of a job.

Regulators and source suppliers state activity in becquerels; most field paperwork and exposure charts still use curies. One curie is exactly 3.7 x 10^10 Bq, so 1 Ci = 37 GBq.

A = A0 x e^(-0.693 x dt / T_half)
equivalently A = A0 x 2^(-dt / T_half)
number of half-lives n = dt / T_half
1 Ci = 37 GBq