A radiography source is retired not when it becomes safe but when it becomes uneconomic. Exposure time is inversely proportional to activity, so as the source decays every shot takes longer, and at some point the crew spends more time waiting than working. That threshold is a commercial decision, typically somewhere between a quarter and a fifth of the original activity, and it defines the working life of the source.

Setting A = A0 x 2^(-t/T_half) equal to the threshold and solving for time gives t = T_half x log2(A0 / A_min). Each halving of the threshold buys exactly one more half-life, which is why the working life of an iridium source is so short – dropping from 100 Ci to 20 Ci is 2.32 half-lives, about 171 days, and no amount of careful handling extends it.

The isotope’s half-life dominates the planning. An Ir-192 source is a quarterly consumable; a Se-75 source at 119.8 days lasts roughly 1.6 times as long for the same activity ratio; Co-60 at 5.27 years is effectively permanent within a project. Ordering lead time, the transport licence and the source exchange outage all have to be worked back from the date this calculation gives.

The exposure-time multiplier at the threshold is the number that makes the case. At 100 Ci down to 20 Ci every shot takes five times as long as it did on day one, which usually costs far more in crew time than the replacement source.

Worked example

Isotope	ir192
Activity at assay	100 Ci
Minimum working activity	20 Ci
Days since assay	60 d
Half-life	73.83 d
Activity today	56.93 Ci
Working life from assay	171.43 d
Days until replacement	111.43 d
Half-lives of working life	2.322
Exposure multiplier at replacement	5

Falling from 100 Ci to 20 Ci is log2(5) = 2.322 half-lives, so the working life is 73.83 x 2.322 = 171.43 days from assay. With 60 days elapsed, 111.43 days remain. Today the source holds 100 x 2^(-60/73.83) = 56.93 Ci, and at the 20 Ci threshold every exposure will take five times the assay-date chart time.