RPR-43

Inverse-square dose

Point-source air kerma.

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GoverningInverse-square dose

Governing equation

D=D_0 (r_0/r)^2

$r \in \left[0.3, 10\right]$

where

D0: D0 (mGy)
r0: r0 (m)
r: r (m)
D: Inverse-square dose (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.

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①

Governing law — red

D=D_0 (r_0/r)^2

$r \in \left[0.3, 10\right]$

$r = 0.3$ $D = 133.3$

Along the curve

②

Domain of the variable — blue

r_{\min} = 0.3,\quad r_{\max} = 10

$r \in \left[0.3, 10\right]$

$r = 0.3$ $r = 0.3$

Along the curve

③

Response curve — green

D=D_0 (r_0/r)^2

$r \in \left[0.3, 10\right]$

$r = 0.3$ $D = 133.3$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}D}{\mathrm{d}r}

$r \in \left[0.3, 10\right]$

$r = 0.361$ $D^{\prime} = -540.5$

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-43 — Inverse-square dose) is the form associated with Inverse-square dose. Working symbols: $D0$ , $r0$ , $r$ $\rightarrow$ $D$ . Point-source air kerma. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

D

from

D0

r0

r

in Radiation protection via

D=D_0 (r_0/r)^2

Point-source air kerma. 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 = 12.000\,\mathrm{mGy}

r0 = 1.000\,\mathrm{m}

r = 2.000\,\mathrm{m}

, the governing relation

D=D_0 (r_0/r)^2

yields

D = 3.000\,\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 D012 mGyr0 r01 mr r2 m

Outputs

Inverse-square dose D3.000 mGy

Reading speed

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Narration of this film

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

Point-source air kerma. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube