NMD-07

Carrier-free specific activity

a = λ NA / M. Bq per kilogram of a pure radionuclide.

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RadiochemistrySpecific activity

Governing equation

a=\lambda N_A/M

$T_{1/2} \in \left[0.1, 200\right]$

where

T_{1/2}: Half-life (h)
M: Molar mass (g/mol)
a: Specific activity (TBq/mg)

The figure, part by part

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①

Governing law — red

a=\lambda N_A/M

$T_{1/2} \in \left[0.1, 200\right]$

$T_{1/2} = 0.1$ $a = 1.17\times 10^{7}$

Along the curve

②

Domain of the variable — blue

T_{1/2}_{\min} = 0.1,\quad T_{1/2}_{\max} = 200

$T_{1/2} \in \left[0.1, 200\right]$

$T_{1/2} = 0.1$ $T_{1/2} = 0.1$

Along the curve

③

Response curve — green

a=\lambda N_A/M

$T_{1/2} \in \left[0.1, 200\right]$

$T_{1/2} = 0.1$ $a = 1.17\times 10^{7}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}a}{\mathrm{d}T_{1/2}}

$T_{1/2} \in \left[0.1, 200\right]$

$T_{1/2} = 1.357$ $a^{\prime} = -4.48\times 10^{6}$

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-07 — Carrier-free specific activity) is the form associated with Specific activity. Working symbols: $T_{1/2}$ , $M$ $\rightarrow$ $a$ . Real preparations are not carrier-free. Reported SA is A/m of the labelled compound.

Purpose

Purpose: compute

a

from

T_{1/2}

M

in Nuclear medicine via

a=\lambda N_A/M

a = λ NA / M. Bq per kilogram of a pure radionuclide. 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

T_{1/2} = 6.010\,\mathrm{h}

M = 99.000\,\mathrm{g/mol}

, the governing relation

a=\lambda N_A/M

yields

a = 194878.620\,\mathrm{TBq/mg}

. A mole of nuclei ticking at λ. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Half-life T_{1/2}6.01 hMolar mass M99 g/mol

Outputs

Specific activity a194878.620 TBq/mg

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Narration of this film

A mole of nuclei ticking at λ.

Real preparations are not carrier-free. Reported SA is A/m of the labelled compound.

Reading speed

Watch on YouTube