RPR-27

Broad-beam buildup B

I = I0 B e^{−μx}, B = 1 + a μx e^{b μx}. Scatter recovered in a broad beam.

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ShieldingBuild-up BTaylor

Governing equation

I=I_0 B e^{-\mu x},\quad B=1+a\mu x\,e^{b\mu x}

where

I_0: Unattenuated rate (µSv/h)
\mu: Attenuation μ (1/cm)
x: Thickness (cm)
a: Taylor a (—)
b: Taylor b (—)
B: Buildup factor (—)
I: Broad-beam rate (µSv/h)

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-27 — Broad-beam buildup B) is the form associated with Build-up B · Taylor. Working symbols: $I_0$ , $\mu$ , $x$ , $a$ , $b$ $\rightarrow$ $B$ , $I$ . Narrow-beam μ over-predicts shielding. Berger and Taylor B(μx, E, Z) put the scatter back. B grows with μx and falls with Z.

Purpose

Purpose: compute

B

I

from

I_0

\mu

x

a

b

in Radiation protection via

I=I_0 B e^{-\mu x},\quad B=1+a\mu x\,e^{b\mu x}

I = I0 B e^{−μx}, B = 1 + a μx e^{b μx}. Scatter recovered in a broad 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

I_0 = 100.000\,\mathrm{\mu Sv/h}

\mu = 0.150\,\mathrm{1/cm}

x = 20.000\,\mathrm{cm}

a = 1.200\,\mathrm{—}

b = 0.050\,\mathrm{—}

, the governing relation

I=I_0 B e^{-\mu x},\quad B=1+a\mu x\,e^{b\mu x}

yields

B = 5.183\,\mathrm{—}

I = 25.803\,\mathrm{\mu Sv/h}

. A wide beam, a slab, a detector in scatter. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Unattenuated rate I_0100 µSv/hAttenuation μ \mu0.15 1/cmThickness x20 cmTaylor a a1.2 —Taylor b b0.05 —

Outputs

Buildup factor B5.183 —
Broad-beam rate I25.803 µSv/h

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Narration of this film

A wide beam, a slab, a detector in scatter.

Narrow-beam μ over-predicts shielding. Berger and Taylor B(μx, E, Z) put the scatter back. B grows with μx and falls with Z.

Reading speed

Watch on YouTube