RPR-07

Effective dose E = Σ H wT

E = H1 w1 + H2 w2 + H3 w3. Whole-body stochastic risk from organ doses.

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QuantitiesICRP 103 E

Governing equation

E=\sum_T H_T w_T

$H_1 \in \left[0, 200\right]$

where

H_1: Organ 1 equivalent (mSv)
w_1: wT 1 (—)
H_2: Organ 2 equivalent (mSv)
w_2: wT 2 (—)
H_3: Organ 3 equivalent (mSv)
w_3: wT 3 (—)
E: Effective dose (mSv)

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

E=\sum_T H_T w_T

$H_1 \in \left[0, 200\right]$

$H_1 = 0$ $E = 0.64$

Along the curve

②

Domain of the variable — blue

H_1_{\min} = 0,\quad H_1_{\max} = 200

$H_1 \in \left[0, 200\right]$

$H_1 = 0$ $H_1 = 0$

Along the curve

③

Response curve — green

E=\sum_T H_T w_T

$H_1 \in \left[0, 200\right]$

$H_1 = 0$ $E = 0.64$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}H_1}

$H_1 \in \left[0, 200\right]$

$H_1 = 1.258$ $E^{\prime} = 0.12$

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-07 — Effective dose E = Σ H wT) is the form associated with ICRP 103 E. Working symbols: $H_1$ , $w_1$ , $H_2$ , $w_2$ , $H_3$ , $w_3$ $\rightarrow$ $E$ . Σ wT = 1 over all tissues. E is not a physical dose in an organ; it is a risk-weighted sum.

Purpose

Purpose: compute

E

from

H_1

w_1

H_2

w_2

H_3

w_3

in Radiation protection via

E=\sum_T H_T w_T

E = H1 w1 + H2 w2 + H3 w3. Whole-body stochastic risk from organ doses. 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

H_1 = 8.000\,\mathrm{mSv}

w_1 = 0.120\,\mathrm{—}

H_2 = 4.000\,\mathrm{mSv}

w_2 = 0.120\,\mathrm{—}

H_3 = 2.000\,\mathrm{mSv}

w_3 = 0.080\,\mathrm{—}

, the governing relation

E=\sum_T H_T w_T

yields

E = 1.600\,\mathrm{mSv}

. Three organs, three chips, one effective bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Organ 1 equivalent H_18 mSvwT 1 w_10.12 —Organ 2 equivalent H_24 mSvwT 2 w_20.12 —Organ 3 equivalent H_32 mSvwT 3 w_30.08 —

Outputs

Effective dose E1.600 mSv

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Narration of this film

Three organs, three chips, one effective bar.

Σ wT = 1 over all tissues. E is not a physical dose in an organ; it is a risk-weighted sum.

Reading speed

Watch on YouTube