# Half-thickness and safety

Physics Narrative for 14-16

## Thicker is safer, as activity is reduced by a constant fraction for each additional thickness

If you want to be safe from those ionising photons then there is no substitute for plenty of absorber atoms between you and the source. You can increase the number of atoms in two ways: use denser materials (so more particles per cubic metre) or place a greater thickness of absorber between you and the source. So either change the material of which the protective absorber is made or place more slices of material between you and the absorber.

Each slice absorbs a given fraction of the photons. This is a consequence of a fixed probability that each photon is absorbed on its passage through each millimetre of absorber. Averaged over the many photons in a beam, this produces a constant fractional decay. This kind of decay is an important pattern in mathematics, and one that rather commonly occurs in nature. This is an exponential variation, here with the thickness of absorber traversed.

## How the activity varies: exponential variation with distance

The exponential pattern is one that has a signature: each increment in the independent variable produces the same fractional change in the dependent variable. This is always true: for radiations you'll see this where the independent variable is thickness (here) or time (to come in episode 05). One significant fractional change is a halving. So for radiations you'll often see the half-thickness quoted: the thickness of absorber required to reduce the number of photons incident on the front face of the slice by 50 % before they exit through the back face of that slice. For the photons used for medical X-rays, the half thickness for lead is about 0.5 millimetre. However, photons with energy five times as high have a half thickness of 10 millimetre of lead, or 50 mm of concrete.

Start with 1 024 000 high-energy photons.

- After 50 mm of concrete there will be 512 000 photons.
- After 100 mm of concrete there will be 256 000 photons.
- After 150 mm of concrete there will be 128 000 photons.
- After 200 mm of concrete there will be 64 000 photons.

Is this safe? How much more concrete must you use to be safe

? Is there a completely safe

?

The law of diminishing returns ensures that there is no such thing. There is a balance to be struck.