RAD-10

Tenth-value layer

TVL = ln 10 / μ ≈ 3.32 HVL. Thickness that cuts a narrow beam by ten.

Reading speed

AttenuationTVL

Governing equation

\mathrm{TVL}=\ln 10/\mu

$\mu \in \left[0.01, 8\right]$

where

\mu: Linear attenuation (1/cm)
TVL: Tenth-value layer (cm)
HVL: Half-value layer (cm)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\mathrm{TVL}=\ln 10/\mu

$\mu \in \left[0.01, 8\right]$

$\mu = 0.01$ $TVL = 230.3$

Along the curve

②

Domain of the variable — blue

\mu_{\min} = 0.01,\quad \mu_{\max} = 8

$\mu \in \left[0.01, 8\right]$

$\mu = 0.01$ $\mu = 0.01$

Along the curve

③

Response curve — green

\mathrm{TVL}=\ln 10/\mu

$\mu \in \left[0.01, 8\right]$

$\mu = 0.01$ $TVL = 230.3$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}TVL}{\mathrm{d}\mu}

$\mu \in \left[0.01, 8\right]$

$\mu = 0.06$ $TVL^{\prime} = -2083.7$

Along the curve

Lecture brief

Historical brief

Beer attenuation, Compton (1923), Klein–Nishina, Bragg–Gray cavity and KERMA are the transport of photons and charged particles in matter. The sheets compute fluence, kerma and stopping. This sheet (RAD-10 — Tenth-value layer) is the form associated with TVL. Working symbols: $\mu$ $\rightarrow$ $TVL$ , $HVL$ . Shielding rooms are quoted in TVLs. Broad-beam TVL includes a build-up.

Purpose

Purpose: compute

TVL

HVL

from

\mu

in Radiation physics via

\mathrm{TVL}=\ln 10/\mu

TVL = ln 10 / μ ≈ 3.32 HVL. Thickness that cuts a narrow beam by ten. Use it when a real radiation physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mu = 0.400\,\mathrm{1/cm}

, the governing relation

\mathrm{TVL}=\ln 10/\mu

yields

TVL = 5.756\,\mathrm{cm}

HVL = 1.733\,\mathrm{cm}

. A thick wall, a 10× drop. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Linear attenuation \mu0.4 1/cm

Outputs

Tenth-value layer TVL5.756 cm
Half-value layer HVL1.733 cm

Reading speed

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Narration of this film

A thick wall, a 10× drop.

Shielding rooms are quoted in TVLs. Broad-beam TVL includes a build-up.

Reading speed

Watch on YouTube