RPR-32

Inverse square with air attenuation

Ḣ(r) = Ḣ0 (r0/r)² e^{−μ(r−r0)}. Distance plus a thin air slab.

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GeometryISL + air attenuation

Governing equation

\dot H(r)=\dot H_0(r_0/r)^{2}e^{-\mu(r-r_0)}

$r \in \left[0.5, 200\right]$

where

\dot H_0: Rate at r0 (µSv/h)
r_0: Reference distance (m)
r: Distance (m)
\mu: Air attenuation μ (1/m)
\dot H: 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 H(r)=\dot H_0(r_0/r)^{2}e^{-\mu(r-r_0)}

$r \in \left[0.5, 200\right]$

$r = 0.5$ $\dot H = 401.6$

Along the curve

②

Domain of the variable — blue

r_{\min} = 0.5,\quad r_{\max} = 200

$r \in \left[0.5, 200\right]$

$r = 0.5$ $r = 0.5$

Along the curve

③

Response curve — green

\dot H(r)=\dot H_0(r_0/r)^{2}e^{-\mu(r-r_0)}

$r \in \left[0.5, 200\right]$

$r = 0.5$ $\dot H = 401.6$

Along the curve

④

Rate of change — amber

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

$r \in \left[0.5, 200\right]$

$r = 1.755$ $\dot H^{\prime} = -155.7$

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-32 — Inverse square with air attenuation) is the form associated with ISL + air attenuation. Working symbols: $\dot H_0$ , $r_0$ , $r$ , $\mu$ $\rightarrow$ $\dot H$ . Air μ ≈ 0.005–0.01 m⁻¹ for diagnostic x-rays and much smaller for MV / ⁶⁰Co. Scatter in air (skyshine) is a separate term.

Purpose

Purpose: compute

\dot H

from

\dot H_0

r_0

r

\mu

in Radiation protection via

\dot H(r)=\dot H_0(r_0/r)^{2}e^{-\mu(r-r_0)}

Ḣ(r) = Ḣ0 (r0/r)² e^{−μ(r−r0)}. Distance plus a thin air slab. 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 H_0 = 100.000\,\mathrm{\mu Sv/h}

r_0 = 1.000\,\mathrm{m}

r = 10.000\,\mathrm{m}

\mu = 0.008\,\mathrm{1/m}

, the governing relation

\dot H(r)=\dot H_0(r_0/r)^{2}e^{-\mu(r-r_0)}

yields

\dot H = 0.931\,\mathrm{\mu Sv/h}

. Expanding spheres with a slow exponential skin. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Rate at r0 \dot H_0100 µSv/hReference distance r_01 mDistance r10 mAir attenuation μ \mu0.008 1/m

Outputs

Dose rate \dot H0.931 µSv/h

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Narration of this film

Expanding spheres with a slow exponential skin.

Air μ ≈ 0.005–0.01 m⁻¹ for diagnostic x-rays and much smaller for MV / ⁶⁰Co. Scatter in air (skyshine) is a separate term.

Reading speed

Watch on YouTube