RPR-03

Tenth-value layer

TVL = ln 10 / μ. Thickness that cuts a narrow beam to 10 %.

Reading speed

ShieldingTVLNCRP 147

Governing equation

\mathrm{TVL}=\ln 10/\mu,\quad T=10^{-x/\mathrm{TVL}}

$x \in \left[0, 60\right]$

where

\mu: Attenuation μ (1/cm)
x: Thickness (cm)
TVL: Tenth-value layer (cm)
T: Narrow-beam transmission (—)

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,\quad T=10^{-x/\mathrm{TVL}}

$x \in \left[0, 60\right]$

$x = 0$ $TVL = 1$

Along the curve

②

Domain of the variable — blue

x_{\min} = 0,\quad x_{\max} = 60

$x \in \left[0, 60\right]$

$x = 0$ $x = 0$

Along the curve

③

Response curve — green

\mathrm{TVL}=\ln 10/\mu,\quad T=10^{-x/\mathrm{TVL}}

$x \in \left[0, 60\right]$

$x = 0$ $TVL = 1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}TVL}{\mathrm{d}x}

$x \in \left[0, 60\right]$

$x = 0.377$ $TVL^{\prime} = -0.345$

Along the curve

Lecture brief

Historical brief

Inverse-square, half-value layer, ICRP weighting and ALARA are the protection craft since the 1920s commissions. The lab computes transmission, equivalent dose and a shielding snapshot. This sheet (RPR-03 — Tenth-value layer) is the form associated with TVL · NCRP 147. Working symbols: $\mu$ , $x$ $\rightarrow$ $TVL$ , $T$ . TVL ≈ 3.32 HVL. Equilibrium TVL (TVLe) is used after the first TVL in broad beams.

Purpose

Purpose: compute

TVL

T

from

\mu

x

in Radiation protection via

\mathrm{TVL}=\ln 10/\mu,\quad T=10^{-x/\mathrm{TVL}}

TVL = ln 10 / μ. Thickness that cuts a narrow beam to 10 %. Use it when a real radiation protection question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

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

x = 5.000\,\mathrm{cm}

, the governing relation

\mathrm{TVL}=\ln 10/\mu,\quad T=10^{-x/\mathrm{TVL}}

yields

TVL = 5.756\,\mathrm{cm}

T = 0.13534\,\mathrm{—}

. A thicker slab and a beam at one tenth. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Attenuation μ \mu0.4 1/cmThickness x5 cm

Outputs

Tenth-value layer TVL5.756 cm
Narrow-beam transmission T0.13534 —

Reading speed

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Narration of this film

A thicker slab and a beam at one tenth.

TVL ≈ 3.32 HVL. Equilibrium TVL (TVLe) is used after the first TVL in broad beams.

Reading speed

Watch on YouTube