RAD-07

Build-up factor

I = B I₀ e^{−μ x}. Broad-beam transmission with scatter build-up B ≥ 1.

Reading speed

AttenuationBuild-up

Governing equation

I=B I_0 e^{-\mu x}

$x \in \left[0.1, 40\right]$

where

I_0: Entrance (Gy/s)
B: Build-up (—)
\mu: Attenuation (1/cm)
x: Thickness (cm)
I: Transmitted (Gy/s)

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

I=B I_0 e^{-\mu x}

$x \in \left[0.1, 40\right]$

$x = 0.1$ $I = 2.463$

Along the curve

②

Domain of the variable — blue

x_{\min} = 0.1,\quad x_{\max} = 40

$x \in \left[0.1, 40\right]$

$x = 0.1$ $x = 0.1$

Along the curve

③

Response curve — green

I=B I_0 e^{-\mu x}

$x \in \left[0.1, 40\right]$

$x = 0.1$ $I = 2.463$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}I}{\mathrm{d}x}

$x \in \left[0.1, 40\right]$

$x = 0.351$ $I^{\prime} = -0.356$

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-07 — Build-up factor) is the form associated with Build-up. Working symbols: $I_0$ , $B$ , $\mu$ , $x$ $\rightarrow$ $I$ . B grows with μx and scatter angle. Taylor and geometric-progression fits tabulate B.

Purpose

Purpose: compute

I

from

I_0

B

\mu

x

in Radiation physics via

I=B I_0 e^{-\mu x}

I = B I₀ e^{−μ x}. Broad-beam transmission with scatter build-up B ≥ 1. 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

I_0 = 1.000\,\mathrm{Gy/s}

B = 2.500\,\mathrm{—}

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

x = 5.000\,\mathrm{cm}

, the governing relation

I=B I_0 e^{-\mu x}

yields

I = 1.1809\,\mathrm{Gy/s}

. A slab, a narrow exponential, a broader B-boosted beam. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Entrance I_01 Gy/sBuild-up B2.5 —Attenuation \mu0.15 1/cmThickness x5 cm

Outputs

Transmitted I1.1809 Gy/s

Reading speed

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Narration of this film

A slab, a narrow exponential, a broader B-boosted beam.

B grows with μx and scatter angle. Taylor and geometric-progression fits tabulate B.

Reading speed

Watch on YouTube