RPR-45

Simple shield e^{-μx}

Narrow-beam attenuation.

Reading speed

GoverningSimple shield e^{-μx}

Governing equation

D=D_0 e^{-\\mu x}

$x \in \left[0.2, 40\right]$

where

D0: D0 (mGy)
mu: mu (1/cm)
x: x (cm)
D: Simple shield e^{-μx} (mGy)

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.

00:0 / 00:08

①

Governing law — red

D=D_0 e^{-\\mu x}

$x \in \left[0.2, 40\right]$

$x = 0.2$ $D = 18.46$

Along the curve

②

Domain of the variable — blue

x_{\min} = 0.2,\quad x_{\max} = 40

$x \in \left[0.2, 40\right]$

$x = 0.2$ $x = 0.2$

Along the curve

③

Response curve — green

D=D_0 e^{-\\mu x}

$x \in \left[0.2, 40\right]$

$x = 0.2$ $D = 18.46$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}D}{\mathrm{d}x}

$x \in \left[0.2, 40\right]$

$x = 0.45$ $D^{\prime} = -6.692$

Along the curve

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-45 — Simple shield e^{-μx}) is the form associated with Simple shield e^{-μx}. Working symbols: $D0$ , $mu$ , $x$ $\rightarrow$ $D$ . Narrow-beam attenuation. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

D

from

D0

mu

x

in Radiation protection via

D=D_0 e^{-\\mu x}

Narrow-beam attenuation. 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

D0 = 20.000\,\mathrm{mGy}

mu = 0.400\,\mathrm{1/cm}

x = 5.000\,\mathrm{cm}

, the governing relation

D=D_0 e^{-\\mu x}

yields

D = 2.707\,\mathrm{mGy}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

D0 D020 mGymu mu0.4 1/cmx x5 cm

Outputs

Simple shield e^{-μx} D2.707 mGy

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Narrow-beam attenuation. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube