RAD-08

Mass attenuation

I = I₀ exp(−(μ/ρ) ρ x). Density-independent attenuation coefficient.

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AttenuationMass attenuation

Governing equation

I=I_0 e^{-(\mu/\rho)\rho x}

where

I_0: Entrance (—)
\mu/\rho: Mass attenuation (cm²/g)
\rho: Density (g/cm³)
x: Thickness (cm)
I/I_0: Transmission (—)

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-08 — Mass attenuation) is the form associated with Mass attenuation. Working symbols: $I_0$ , $\mu/\rho$ , $\rho$ , $x$ $\rightarrow$ $I/I_0$ . Tables quote μ/ρ. Mixture: Σ w_i (μ/ρ)_i (Bragg additivity).

Purpose

Purpose: compute

I/I_0

from

I_0

\mu/\rho

\rho

x

in Radiation physics via

I=I_0 e^{-(\mu/\rho)\rho x}

I = I₀ exp(−(μ/ρ) ρ x). Density-independent attenuation coefficient. 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{—}

\mu/\rho = 0.150\,\mathrm{cm^{2}/g}

\rho = 2.700\,\mathrm{g/cm^{3}}

x = 2.000\,\mathrm{cm}

, the governing relation

I=I_0 e^{-(\mu/\rho)\rho x}

yields

I/I_0 = 0.4449\,\mathrm{—}

. A slab labelled in g/cm². Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Entrance I_01 —Mass attenuation \mu/\rho0.15 cm²/gDensity \rho2.7 g/cm³Thickness x2 cm

Outputs

Transmission I/I_00.4449 —

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00:0 / 00:08

Narration of this film

A slab labelled in g/cm².

Tables quote μ/ρ. Mixture: Σ w_i (μ/ρ)_i (Bragg additivity).

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