RPR-02

Half-value layer

HVL = ln 2 / μ. Thickness that halves a narrow beam.

Reading speed

ShieldingHVL

Governing equation

\mathrm{HVL}=\ln 2/\mu,\quad T=2^{-x/\mathrm{HVL}}

$x \in \left[0, 40\right]$

where

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

The figure, part by part

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①

Governing law — red

\mathrm{HVL}=\ln 2/\mu,\quad T=2^{-x/\mathrm{HVL}}

$x \in \left[0, 40\right]$

$x = 0$ $HVL = 1$

Along the curve

②

Domain of the variable — blue

x_{\min} = 0,\quad x_{\max} = 40

$x \in \left[0, 40\right]$

$x = 0$ $x = 0$

Along the curve

③

Response curve — green

\mathrm{HVL}=\ln 2/\mu,\quad T=2^{-x/\mathrm{HVL}}

$x \in \left[0, 40\right]$

$x = 0$ $HVL = 1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}HVL}{\mathrm{d}x}

$x \in \left[0, 40\right]$

$x = 0.252$ $HVL^{\prime} = -0.362$

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-02 — Half-value layer) is the form associated with HVL. Working symbols: $\mu$ , $x$ $\rightarrow$ $HVL$ , $T$ . n HVLs transmit 2^{−n}. Broad-beam HVL is larger because of scatter build-up.

Purpose

Purpose: compute

HVL

T

from

\mu

x

in Radiation protection via

\mathrm{HVL}=\ln 2/\mu,\quad T=2^{-x/\mathrm{HVL}}

HVL = ln 2 / μ. Thickness that halves a narrow beam. 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 = 2.000\,\mathrm{cm}

, the governing relation

\mathrm{HVL}=\ln 2/\mu,\quad T=2^{-x/\mathrm{HVL}}

yields

HVL = 1.733\,\mathrm{cm}

T = 0.4493\,\mathrm{—}

. Slabs stacking, a beam halved each time. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Attenuation μ \mu0.4 1/cmThickness x2 cm

Outputs

Half-value layer HVL1.733 cm
Narrow-beam transmission T0.4493 —

Reading speed

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Narration of this film

Slabs stacking, a beam halved each time.

n HVLs transmit 2^{−n}. Broad-beam HVL is larger because of scatter build-up.

Reading speed

Watch on YouTube