A half-value layer is the thickness of a material that halves a gamma beam, and every extra layer halves what remains, so the fraction transmitted is 2 raised to minus the number of layers. A tenth needs 3.32 layers, a hundredth 6.64 and a thousandth 9.97, which with the parent article’s figures is about 40 cm of concrete or 60 cm of packed earth for a hundredth; the figures are minimums because the energy and geometry are not stated.
Part of Radiation Safety
The half-value layer (HVL) is the practical measure of gamma shielding: it turns a required reduction into a thickness of a chosen material.
The Formula And Where It Comes From
Fraction transmitted = (1/2)^n, where n = thickness / HVL. To find the layers needed for a target fraction f, n = log2(1 / f):
- Reduce to 1/10: n = log2(10) = 3.32.
- Reduce to 1/100: n = log2(100) = 6.64.
- Reduce to 1/1,000: n = log2(1,000) = 9.97.
The parent article, Nuclear Safety, rounds 1 percent to 7 layers, which gives 2^-7 = 0.78 percent.
Thickness For Each Target
Using the parent’s HVL for each material, thickness = n x HVL, to the nearest tenth of a centimetre:
| Material | HVL, cm | To 1/10 | To 1/100 | To 1/1,000 |
|---|---|---|---|---|
| Lead | 1.3 | 4.3 | 8.6 | 13.0 |
| Steel | 2.5 | 8.3 | 16.6 | 24.9 |
| Concrete | 6 | 19.9 | 39.9 | 59.8 |
| Packed earth | 9 | 29.9 | 59.8 | 89.7 |
| Water | 18 | 59.8 | 119.6 | 179.4 |
| Wood | 29 | 96.3 | 192.7 | 289.0 |
Check two rows: concrete to 1/100 is 6.64 x 6 = 39.9 cm, about 40 cm, and earth to 1/100 is 6.64 x 9 = 59.8 cm. That agrees with the parent’s advice to pile at least 60 cm of packed earth around a shelter: 60 / 9 = 6.67 layers and 2^-6.67 = 0.0098, about a hundredth. The parent also says a basement reduces exposure by 90 percent or more; a reduction to 1/10 is 3.32 layers, 29.9 cm of earth or 19.9 cm of concrete.
Equivalent Thickness In Another Material
Convert by HVLs: layers = thickness / HVL, then multiply by the other HVL. 42 cm of concrete is 42 / 6 = 7 layers; 7 x 9 = 63 cm of earth and 7 x 18 = 126 cm of water, the parent’s figures. For mass per square metre, see Shielding Materials, where each layer is shown to hold about 135-232 kg/m².
Why The Table Is A Minimum
- Energy. HVLs depend on the gamma energy. The parent does not state what energy its table assumes. Fallout contains a mix, and a lower-energy source is stopped more easily while a higher-energy one is stopped less easily.
- Geometry. The simple formula describes a narrow beam. In a thick shield, scattered radiation adds to what gets through, so the real thickness needed is larger (recalled general knowledge, not from the corpus).
- Gaps and the roof. A shield is as good as its thinnest side, and radiation can arrive from above and be scattered in around openings. See Shelter Design.
- Source type. The table does not apply to alpha, beta or neutron radiation; see Penetration & Shielding.
Worked Example: A Dugout Roof
A group wants a reduction to 1/100 above a dugout. Earth needs 59.8 cm by the table. Allow a margin for the uncertainties above and build thicker rather than thinner. Load: 0.6 m of earth at 1,500-2,000 kg/m³ over 25 m² is 22.5-30 t (from Earth Load Calculations), which the roof must carry. If it cannot, you have the answer to a different question: use a smaller room or more depth, not thinner cover.
Common Mistakes
- Reading 7 layers as exactly 1 percent. It is 0.78 percent; 1 percent is 6.64.
- Using one HVL table for water, earth and concrete as if all were the same energy.
- Not reducing the opening. A door or hatch lets in what the walls keep out.
- Calling the result a safe dose. It is a reduction of an unknown rate.
Safety
A large reduction of an unknown dose rate is still unknown
If the field outside is strong, 1/100 of it may still be significant over days. Stay inside as long as practical, and keep going outside to short, planned trips.
What’s Next
- Learn next: Shelter Design — applying the arithmetic
- Combine with: Shielding Materials — mass per square metre