RAD-21

Inverse-square intensity

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

Reading speed

DosimetryInverse square

Governing equation

I(r)=I(r_0)\,(r_0/r)^2

$r \in \left[0.2, 30\right]$

where

I_0: Intensity at r₀ (mGy/h)
r_0: Reference distance (m)
r: Distance (m)
I: Intensity (mGy/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

I(r)=I(r_0)\,(r_0/r)^2

$r \in \left[0.2, 30\right]$

$r = 0.2$ $I = 250$

Along the curve

②

Domain of the variable — blue

r_{\min} = 0.2,\quad r_{\max} = 30

$r \in \left[0.2, 30\right]$

$r = 0.2$ $r = 0.2$

Along the curve

③

Response curve — green

I(r)=I(r_0)\,(r_0/r)^2

$r \in \left[0.2, 30\right]$

$r = 0.2$ $I = 250$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}I}{\mathrm{d}r}

$r \in \left[0.2, 30\right]$

$r = 0.387$ $I^{\prime} = -586.2$

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-21 — Inverse-square intensity) is the form associated with Inverse square. Working symbols: $I_0$ , $r_0$ , $r$ $\rightarrow$ $I$ . Valid in air far from scatter. Distance is the cheapest shield.

Purpose

Purpose: compute

I

from

I_0

r_0

r

in Radiation physics via

I(r)=I(r_0)\,(r_0/r)^2

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

I_0 = 10.000\,\mathrm{mGy/h}

r_0 = 1.000\,\mathrm{m}

r = 3.000\,\mathrm{m}

, the governing relation

I(r)=I(r_0)\,(r_0/r)^2

yields

I = 1.1111\,\mathrm{mGy/h}

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

Calculator

Inputs

Intensity at r₀ I_010 mGy/hReference distance r_01 mDistance r3 m

Outputs

Intensity I1.1111 mGy/h

Reading speed

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Narration of this film

A point, expanding spheres, a fading I.

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

Reading speed

Watch on YouTube