00 Foundations
HVL, TVL and barrier n-value
HVL = ln 2 / μ, TVL = ln 10 / μ ≈ 3.32 HVL. n = log(1/B) / log 2 HVLs.
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Simulation
HVL, TVL and barrier n-value — 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
HVL
Half-value layer
1.3863cm
TVL
Tenth-value layer
4.6052cm
n_HVL
Number of HVLs
6.6439
n_TVL
Number of TVLs
2
x
Thickness required
9.2103cm
Explanation
What it means
One half-value layer cuts intensity in half; one tenth-value layer cuts it by ten. Narrow-beam μ gives the theoretical HVL; broad-beam (with scatter) needs a larger effective HVL — the first HVL is smaller than the second because the beam hardens. Shielding reports quote TVLs of lead, concrete and steel at the design energy. This is a working relation in Radiation physics.
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. Radiation physics lives at the x-ray target, the linac head, and inside the patient: how a photon is born, how it scatters, and how it dies. Use these relations before you trust a spectrum, a wall, or a kV-versus-MV contrast argument.
Treatment vault · Open this machineHow to use it
Enter linear attenuation μ (cm⁻¹) and the desired transmission B. Read HVL, TVL and how many of each you need. 2 mm Pb at μ = 2.5 cm⁻¹ (≈100 keV) is several HVLs. Change one input and watch the curve and the simulation follow.
Symbols
- μLinear attenuation0.5 cm⁻¹
- BDesired transmission0.01
Worked example
A typical case from the default values: μ = 0.5 cm⁻¹ (Linear attenuation); B = 0.01 (Desired transmission). Substituting into the relation gives HVL = 1.3863 cm; TVL = 4.6052 cm; n_HVL = 6.6439; n_TVL = 2; x = 9.2103 cm. These are teaching numbers — align them with your machine.
Typical values give
- HVL = 1.3863cm
- TVL = 4.6052cm
- n_HVL = 6.6439
- n_TVL = 2
- x = 9.2103cm
Where it comes from
The displayed formula is the working relation. HVL = ln 2 / μ, TVL = ln 10 / μ ≈ 3.32 HVL. n = log(1/B) / log 2 HVLs. Usual reference: NCRP 147 / 151. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: NCRP 147 / 151
Assumptions & limits
Monoenergetic narrow beam. Real barriers use broad-beam TVLs that include Compton scatter buildup. First and equilibrium TVL differ (NCRP 151 tables). μ must match the material and the spectrum.
Pitfalls
Do not mix free-electron Compton kinematics with photoelectric-dominated kV imaging. Check keV versus MeV, and never treat a spectrum as one photon. Monoenergetic narrow beam. Real barriers use broad-beam TVLs that include Compton scatter buildup. First and equilibrium TVL differ (NCRP 151 tables). μ must match the material and the spectrum.
Keep this
Photons do not deposit dose; the electrons they set in motion do. Monoenergetic narrow beam. Real barriers use broad-beam TVLs that include Compton scatter buildup. First and equilibrium TVL differ (NCRP 151 tables). μ must match the material and the spectrum.
In this specialty