RPR-08

ALARA reduction snapshot

RF = (t/t0) (r0/r)² 2^{−x/HVL}. Time, distance and shielding versus a reference.

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ALARAICRP ALARA

Governing equation

RF=\dfrac{t}{t_0}\left(\dfrac{r_0}{r}\right)^{2}2^{-x/\mathrm{HVL}}

$r \in \left[0.3, 10\right]$

where

t: Exposure time (min)
t_0: Reference time (min)
r: Distance (m)
r_0: Reference distance (m)
x: Shield thickness (mm)
HVL: HVL (mm)
RF: Dose reduction factor (—)

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

RF=\dfrac{t}{t_0}\left(\dfrac{r_0}{r}\right)^{2}2^{-x/\mathrm{HVL}}

$r \in \left[0.3, 10\right]$

$r = 0.3$ $RF = 0.246$

Along the curve

②

Domain of the variable — blue

r_{\min} = 0.3,\quad r_{\max} = 10

$r \in \left[0.3, 10\right]$

$r = 0.3$ $r = 0.3$

Along the curve

③

Response curve — green

RF=\dfrac{t}{t_0}\left(\dfrac{r_0}{r}\right)^{2}2^{-x/\mathrm{HVL}}

$r \in \left[0.3, 10\right]$

$r = 0.3$ $RF = 0.246$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}RF}{\mathrm{d}r}

$r \in \left[0.3, 10\right]$

$r = 0.361$ $RF^{\prime} = -0.995$

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-08 — ALARA reduction snapshot) is the form associated with ICRP ALARA. Working symbols: $t$ , $t_0$ , $r$ , $r_0$ , $x$ , $HVL$ $\rightarrow$ $RF$ . ALARA is optimisation, not a number. This snapshot shows how the three classical levers multiply.

Purpose

Purpose: compute

RF

from

t

t_0

r

r_0

x

HVL

in Radiation protection via

RF=\dfrac{t}{t_0}\left(\dfrac{r_0}{r}\right)^{2}2^{-x/\mathrm{HVL}}

RF = (t/t0) (r0/r)² 2^{−x/HVL}. Time, distance and shielding versus a reference. 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

t = 5.000\,\mathrm{min}

t_0 = 20.000\,\mathrm{min}

r = 2.000\,\mathrm{m}

r_0 = 0.500\,\mathrm{m}

x = 3.000\,\mathrm{mm}

HVL = 2.000\,\mathrm{mm}

, the governing relation

RF=\dfrac{t}{t_0}\left(\dfrac{r_0}{r}\right)^{2}2^{-x/\mathrm{HVL}}

yields

RF = 0.0055\,\mathrm{—}

. A clock, a tape measure, a slab, a shrinking dose. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Exposure time t5 minReference time t_020 minDistance r2 mReference distance r_00.5 mShield thickness x3 mmHVL HVL2 mm

Outputs

Dose reduction factor RF0.0055 —

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Narration of this film

A clock, a tape measure, a slab, a shrinking dose.

ALARA is optimisation, not a number. This snapshot shows how the three classical levers multiply.

Reading speed

Watch on YouTube