RPR-01

Inverse-square dose rate

Ḋ(r) = Ḋ(r0) (r0/r)². Point-source geometric dilution.

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GeometryInverse square

Governing equation

\dot D(r)=\dot D(r_0)\,(r_0/r)^{2}

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

where

\dot D_0: Rate at r0 (µSv/h)
r_0: Reference distance (m)
r: Distance (m)
\dot D: Dose rate (µSv/h)

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

\dot D(r)=\dot D(r_0)\,(r_0/r)^{2}

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

$r = 0.2$ $\dot D = 2500$

Along the curve

②

Domain of the variable — blue

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

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

$r = 0.2$ $r = 0.2$

Along the curve

③

Response curve — green

\dot D(r)=\dot D(r_0)\,(r_0/r)^{2}

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

$r = 0.2$ $\dot D = 2500$

Along the curve

④

Rate of change — amber

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

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

$r = 0.45$ $\dot D^{\prime} = -4586.8$

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-01 — Inverse-square dose rate) is the form associated with Inverse square. Working symbols: $\dot D_0$ , $r_0$ , $r$ $\rightarrow$ $\dot D$ . Valid in air far from scatter and air attenuation. Distance is the cheapest shield.

Purpose

Purpose: compute

\dot D

from

\dot D_0

r_0

r

in Radiation protection via

\dot D(r)=\dot D(r_0)\,(r_0/r)^{2}

Ḋ(r) = Ḋ(r0) (r0/r)². Point-source geometric dilution. 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

\dot D_0 = 100.000\,\mathrm{\mu Sv/h}

r_0 = 1.000\,\mathrm{m}

r = 3.000\,\mathrm{m}

, the governing relation

\dot D(r)=\dot D(r_0)\,(r_0/r)^{2}

yields

\dot D = 11.111\,\mathrm{\mu Sv/h}

. A point, expanding spheres, a fading rate. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Rate at r0 \dot D_0100 µSv/hReference distance r_01 mDistance r3 m

Outputs

Dose rate \dot D11.111 µSv/h

Reading speed

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Narration of this film

A point, expanding spheres, a fading rate.

Valid in air far from scatter and air attenuation. Distance is the cheapest shield.

Reading speed

Watch on YouTube