04 Protection
Thickness from TVL₁ and TVLₑ
First tenth-value layer differs from equilibrium TVL for broad beams.
Listen
Listen · English
Simulation
Thickness from TVL₁ and TVLₑ — 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
n
Number of TVLs
3
x
Thickness
36mm
Explanation
What it means
Broad MV beams harden in the first tenth-value layer, so TVL₁ > TVL_e (equilibrium). Thickness is n×TVL₁ if n≤1, else TVL₁ + (n−1) TVL_e with n = −log₁₀ B. 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
Look up TVL₁ and TVL_e for your energy and material in NCRP 151. Example: 6 MV lead TVL₁ ≈ 5.7 cm, TVL_e ≈ 5.4 cm (order of magnitude — use the table). Change one input and watch the curve and the simulation follow.
Symbols
- BTransmission0.001
- TVL₁First TVL14 mm
- TVLₑEquilibrium TVL11 mm
Worked example
A typical case from the default values: B = 0.001 (Transmission); TVL₁ = 14 mm (First TVL); TVLₑ = 11 mm (Equilibrium TVL). Substituting into the relation gives n = 3; x = 36 mm. These are teaching numbers — align them with your machine.
Typical values give
- n = 3
- x = 36mm
Where it comes from
The displayed formula is the working relation. First tenth-value layer differs from equilibrium TVL for broad beams. Usual reference: NCRP 151. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: NCRP 151
Assumptions & limits
Empirical NCRP fit, not a Monte Carlo of your room (maze, ceiling bounce, skyshine). Obliquity (slant through the wall) increases path length as 1/cos φ.
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. Empirical NCRP fit, not a Monte Carlo of your room (maze, ceiling bounce, skyshine). Obliquity (slant through the wall) increases path length as 1/cos φ.
Keep this
Time, distance, shielding — in that order — then calculate the wall. Empirical NCRP fit, not a Monte Carlo of your room (maze, ceiling bounce, skyshine). Obliquity (slant through the wall) increases path length as 1/cos φ.
In this specialty