The 10 half-life rule of thumb for radioactive materials
Published: Sept 29, 2021
Source: Ionactive Radiation Protection Resources
The 10-half-life reduction rule is an approximation and 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 yield a thousand-fold reduction in activity (\(\frac{1}{1000}\))
For gamma emitters particularly, 10 Half-life will lead to a thousand-fold reduction in measurable dose rate (all other variables being constant such as distance and shielding).
Mathematically, \(0.5^{10}\) is \(\frac{1}{1024}\), but this is an approximation, so \(\frac{1}{1000}\) 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
If you want to investigate radioactive decay and half-life further, then try our Radioactive Decay calculator with Half-Life Analysis (and decay curve plotting).
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. For this scenario we would be looking at about 72 MBq of F-18 and we can show the decay process on the following interactive plot.
If you are curious how we came up with approximately 72 MBq of F-18, then head over to our Dose Rate to Radioactivity Calculator. We used this calculator with inputs of 1000 micro Sv/h at 10 cm from F-18. For simplicity we assumed a point source, but if you really want to dig into this subject you could also use our Dose Rate from a Radioactive Planar Source Calculator which would evaluate dose rates from a spill over an extended area.