RAD-20

Radiation length

E = E₀ e^{−x/X₀}. High-energy electron energy in a radiator.

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AttenuationRadiation length

Governing equation

E=E_0 e^{-x/X_0}

$x \in \left[0.01, 10\right]$

where

E_0: Incident energy (MeV)
x: Thickness (cm)
X_0: Radiation length (cm)
E: Remaining energy (MeV)

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

E=E_0 e^{-x/X_0}

$x \in \left[0.01, 10\right]$

$x = 0.01$ $E = 98.23$

Along the curve

②

Domain of the variable — blue

x_{\min} = 0.01,\quad x_{\max} = 10

$x \in \left[0.01, 10\right]$

$x = 0.01$ $x = 0.01$

Along the curve

③

Response curve — green

E=E_0 e^{-x/X_0}

$x \in \left[0.01, 10\right]$

$x = 0.01$ $E = 98.23$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}x}

$x \in \left[0.01, 10\right]$

$x = 0.073$ $E^{\prime} = -157.1$

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-20 — Radiation length) is the form associated with Radiation length. Working symbols: $E_0$ , $x$ , $X_0$ $\rightarrow$ $E$ . X₀ is the distance for e-fold bremsstrahlung. Lead: 0.56 cm. Pair-production photons similar.

Purpose

Purpose: compute

E

from

E_0

x

X_0

in Radiation physics via

E=E_0 e^{-x/X_0}

E = E₀ e^{−x/X₀}. High-energy electron energy in a radiator. 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

E_0 = 100.000\,\mathrm{MeV}

x = 0.500\,\mathrm{cm}

X_0 = 0.560\,\mathrm{cm}

, the governing relation

E=E_0 e^{-x/X_0}

yields

E = 40.95\,\mathrm{MeV}

. A radiator slab, a fading electron energy. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Incident energy E_0100 MeVThickness x0.5 cmRadiation length X_00.56 cm

Outputs

Remaining energy E40.95 MeV

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Narration of this film

A radiator slab, a fading electron energy.

X₀ is the distance for e-fold bremsstrahlung. Lead: 0.56 cm. Pair-production photons similar.

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