RAD-12

Photoelectric absorption

τ ∝ Z⁴ / E³. Photoelectric cross section sketch between edges.

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AttenuationPhotoelectric

Governing equation

\tau\propto Z^4/E^3

$E \in \left[5, 200\right]$

where

Z: Atomic number (—)
E: Photon energy (keV)
\tau_0: Prefactor at Z=1, 1 keV (b)
\tau: Photoelectric (b)

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

\tau\propto Z^4/E^3

$E \in \left[5, 200\right]$

$E = 5$ $\tau = 3156.2$

Along the curve

②

Domain of the variable — blue

E_{\min} = 5,\quad E_{\max} = 200

$E \in \left[5, 200\right]$

$E = 5$ $E = 5$

Along the curve

③

Response curve — green

\tau\propto Z^4/E^3

$E \in \left[5, 200\right]$

$E = 5$ $\tau = 3156.2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\tau}{\mathrm{d}E}

$E \in \left[5, 200\right]$

$E = 6.226$ $\tau^{\prime} = -898.2$

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-12 — Photoelectric absorption) is the form associated with Photoelectric. Working symbols: $Z$ , $E$ , $\tau_0$ $\rightarrow$ $\tau$ . Jumps at K, L edges. High-Z contrast in kV imaging is this Z⁴.

Purpose

Purpose: compute

\tau

from

Z

E

\tau_0

in Radiation physics via

\tau\propto Z^4/E^3

τ ∝ Z⁴ / E³. Photoelectric cross section sketch between edges. 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

Z = 53.000\,\mathrm{—}

E = 40.000\,\mathrm{keV}

\tau_0 = 0.050\,\mathrm{b}

, the governing relation

\tau\propto Z^4/E^3

yields

\tau = 6.164\,\mathrm{b}

. A photon, a K-shell, a photoelectron. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Atomic number Z53 —Photon energy E40 keVPrefactor at Z=1, 1 keV \tau_00.05 b

Outputs

Photoelectric \tau6.164 b

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Narration of this film

A photon, a K-shell, a photoelectron.

Jumps at K, L edges. High-Z contrast in kV imaging is this Z⁴.

Reading speed

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