The 10 half-life rule of thumb for radioactive materials

The 10-half-life reduction rule is an approximation but useful for evaluating contingency plans. It applies to all radioactive materials but is most useful for beta / gamma emitters with reasonably short half-life. The rule of thumb is as follows:

10 Half-Life will lead to a thousand-fold reduction in activity (1/1000)

For gamma emitters particularly, 10 Half-life will lead to a thousand-fold reduction in dose rate (all other variables being constant such as distance and shielding).

Mathematically, 1 / 210 is 1/1024, but this is an approximation, so 1/1000 is good enough.

Now consider the following (after 10 half life).

  • TBq becomes GBq
  • GBq becomes MBq
  • Sv/h becomes mSv/h
  • mSv/h becomes micro Sv/h

Practical example (F-18)

A small vial of F-18 (positron emitter) is spilt on the floor of a laboratory. Dose rates taken 10 cm above the spill indicate 1000 micro Sv/h. Should you clean the spill up now, or leave it to decay first? For the purpose of this rule we are only going to consider decay / dose rate, in real world situations there would be other things to think about (e.g. can the lab wait for the decay if it is preparing F-18 doses for patients required in a few hours time).

The half life of F-18 is near enough 110 minutes. So 10 half life would take 1100 minutes or about 18 hours and 20 minutes. After this time, all other things being equal, the dose rate at 10 cm above the spill would have reduced to 1 micro Sv/h (something much more manageable when considering occupational exposure). Even if 18 hours is not reasonably practicable, good dose saving can be achieved for every half life you are able to leave the spill before cleaning it up.

The ultimate paradox, of course, is that even though we're all going to die, we've all got to live in the meantime…

– Brian Cox -