NMD-29

Specific gamma-ray constant

Ẋ = Γ A / r². Exposure (or air-kerma) rate from a point source.

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ExposureSpecific gamma constant

Governing equation

\dot X=\Gamma A/r^{2}

$r \in \left[0.1, 5\right]$

where

\Gamma: Specific gamma constant (µSv m²/MBq/h)
A: Activity (MBq)
r: Distance (m)
\dot X: Air-kerma 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 X=\Gamma A/r^{2}

$r \in \left[0.1, 5\right]$

$r = 0.1$ $\dot X = 2234.8$

Along the curve

②

Domain of the variable — blue

r_{\min} = 0.1,\quad r_{\max} = 5

$r \in \left[0.1, 5\right]$

$r = 0.1$ $r = 0.1$

Along the curve

③

Response curve — green

\dot X=\Gamma A/r^{2}

$r \in \left[0.1, 5\right]$

$r = 0.1$ $\dot X = 2234.8$

Along the curve

④

Rate of change — amber

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

$r \in \left[0.1, 5\right]$

$r = 0.131$ $\dot X^{\prime} = -22380.1$

Along the curve

Lecture brief

Historical brief

MIRD schema, in-vivo decay, uptake fractions and PET coincidence turned unsealed sources into organ dose. The sheets compute activity, residence and well-counter geometry. This sheet (NMD-29 — Specific gamma-ray constant) is the form associated with Specific gamma constant. Working symbols: $\Gamma$ , $A$ , $r$ $\rightarrow$ $\dot X$ . Γ_Tc-99m ≈ 0.0604 mSv m² GBq⁻¹ h⁻¹. Γ_I-131 ≈ 0.059. Distance is still the cheapest shield.

Purpose

Purpose: compute

\dot X

from

\Gamma

A

r

in Nuclear medicine via

\dot X=\Gamma A/r^{2}

Ẋ = Γ A / r². Exposure (or air-kerma) rate from a point source. Use it when a real nuclear medicine question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\Gamma = 0.060\,\mathrm{\mu Sv m^{2}/MBq/h}

A = 370.000\,\mathrm{MBq}

r = 0.500\,\mathrm{m}

, the governing relation

\dot X=\Gamma A/r^{2}

yields

\dot X = 89.39\,\mathrm{\mu Sv/h}

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

Calculator

Inputs

Specific gamma constant \Gamma0.0604 µSv m²/MBq/hActivity A370 MBqDistance r0.5 m

Outputs

Air-kerma rate \dot X89.39 µSv/h

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Narration of this film

A vial, expanding spheres, a rate.

Γ_Tc-99m ≈ 0.0604 mSv m² GBq⁻¹ h⁻¹. Γ_I-131 ≈ 0.059. Distance is still the cheapest shield.

Reading speed

Watch on YouTube