04 Protection
Transmission from HVL and TVL
Barrier transmission for thickness x.
Listen
Listen · English
Simulation
Transmission from HVL and TVL — Change the numbers; the scene follows.
Where it works
Treatment vault
Shielded door
At the shielded door — transmission, required thickness, stacked TVLs.
Open this machineFormula
Variables
Results
B
Transmission
0.0625
B
Transmission
6.25%
TVL
Tenth-value layer
8.3048mm
n
Number of HVLs
4
Curve
Explanation
What it means
A slab of HVL halves a narrow beam; a TVL reduces it tenfold. B = 2^{−x/HVL} = 10^{−x/TVL}. TVL = HVL × log₂(10) ≈ 3.32 HVL for a monoenergetic beam. This is a working relation in Radiation protection.
Where it is used
Clinically it sits on the Treatment vault — Shielded door. At the shielded door — transmission, required thickness, stacked TVLs. 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 HVL in the same units (mm Pb, mm Al, cm concrete). Read B and the equivalent number of HVLs. For polyenergetic beams the first HVL is smaller than later ones — use the stacked TVL equation. Change one input and watch the curve and the simulation follow.
Symbols
- xThickness10 mm
- HVLHalf-value layer2.5 mm
Worked example
A typical case from the default values: x = 10 mm (Thickness); HVL = 2.5 mm (Half-value layer). Substituting into the relation gives B = 0.0625; B = 6.25 %; TVL = 8.3048 mm; n = 4. These are teaching numbers — align them with your machine.
Typical values give
- B = 0.0625
- B = 6.25%
- TVL = 8.3048mm
- n = 4
Where it comes from
The displayed formula is the working relation. Barrier transmission for thickness x. 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, constant HVL (no hardening, no buildup). Broad-beam barriers need NCRP TVL tables that already fold in scatter.
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, constant HVL (no hardening, no buildup). Broad-beam barriers need NCRP TVL tables that already fold in scatter.
Keep this
Time, distance, shielding — in that order — then calculate the wall. Narrow beam, constant HVL (no hardening, no buildup). Broad-beam barriers need NCRP TVL tables that already fold in scatter.
In this specialty