04 Protection
Lead equivalence
x_Pb = x_mat × (μ_mat / μ_Pb). Teaching conversion between concrete, steel and lead.
Listen
Listen · English
Simulation
Lead equivalence — Change the numbers; the scene follows.
Where it works
Treatment vault
Primary barrier
In the bunker maze and barriers — time, distance, TVL, WUT, and weekly controlled-area dose.
Open this machineFormula
Variables
Results
x_Pb
Lead equivalence
1.6mm
x_Pb
Lead equivalence
0.16cm
Explanation
What it means
Lead equivalence is how many millimetres of lead would match a given slab of concrete, steel, glass or gypsum at a stated kV. It is energy-dependent: 1 mm Pb ≈ 80–100 mm concrete at 100 kV, but the ratio shrinks at MV because Compton (∝ electron density) takes over from photoelectric (∝ Z³). Aprons are specified in mm Pb-eq at 80–100 kV. This is a working relation in Radiation protection.
Where it is used
Clinically it sits on the Treatment vault — Primary barrier. In the bunker maze and barriers — time, distance, TVL, WUT, and weekly controlled-area dose. Protection equations are the wall, the occupancy factor, and the badge: time, distance, shielding, and WUT. They turn a room into a legal design.
Treatment vault · Open this machineHow to use it
Enter thickness and μ of the material, and μ of lead at the same quality. Typical 100 kV: μ_Pb ≈ 25 cm⁻¹, μ_concrete ≈ 0.4 cm⁻¹. A 1.5 mm Pb apron at that quality is ~0.15 cm × 25 ≈ 3.8 mean-free-paths. Change one input and watch the curve and the simulation follow.
Symbols
- xMaterial thickness10 cm
- μMaterial μ0.4 cm⁻¹
- μ_PbLead μ25 cm⁻¹
Worked example
A typical case from the default values: x = 10 cm (Material thickness); μ = 0.4 cm⁻¹ (Material μ); μ_Pb = 25 cm⁻¹ (Lead μ). Substituting into the relation gives x_Pb = 1.6 mm; x_Pb = 0.16 cm. These are teaching numbers — align them with your machine.
Typical values give
- x_Pb = 1.6mm
- x_Pb = 0.16cm
Where it comes from
The displayed formula is the working relation. x_Pb = x_mat × (μ_mat / μ_Pb). Teaching conversion between concrete, steel and lead. Usual reference: NCRP 147 / 151. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: NCRP 147 / 151
Assumptions & limits
Narrow-beam μ ratio, not a broad-beam TVL ratio. Real Pb-eq of concrete is tabulated versus kV in NCRP 147. K-edge of lead (88 keV) makes the ratio non-monotone around 80–100 kV.
Pitfalls
Tenth-value layers are for the broad beam in that material and that energy — not a photocopy from another bunker. Occupancy T is not a guess; it is a use pattern. Inverse-square fails against a large scatter source. Narrow-beam μ ratio, not a broad-beam TVL ratio. Real Pb-eq of concrete is tabulated versus kV in NCRP 147. K-edge of lead (88 keV) makes the ratio non-monotone around 80–100 kV.
Keep this
Time, distance, shielding — in that order — then calculate the wall. Narrow-beam μ ratio, not a broad-beam TVL ratio. Real Pb-eq of concrete is tabulated versus kV in NCRP 147. K-edge of lead (88 keV) makes the ratio non-monotone around 80–100 kV.
In this specialty