03 Nuclear

Carrier-free specific activity

a = λ N_A / M for a pure radionuclide.

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Simulation

Carrier-free specific activity — Change the numbers; the scene follows.

Where it works

Hot lab

Dose calibrator

In the dose calibrator well — assayed activity, decay between two times, Marinelli.

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Formula

a = \frac{\lambda N_A}{M} = \frac{(\ln 2)\,N_A}{T_{1/2}M}

Variables

T½ · Half-lifehM · Molar massg/mol

Results

a
Specific activity
1.946e+17Bq/g
a
Specific activity
194,554.9016GBq/mg
a
Specific activity
5.2582e+6Ci/g

Explanation

a = \frac{\lambda N_A}{M} = \frac{(\ln 2)\,N_A}{T_{1/2}M}

What it means

Carrier-free specific activity is λ N_A / M — the Bq per gram if every atom is the radionuclide. F-18 is enormous (TBq/µg); I-131 is high; U-238 is tiny. Real products are diluted by stable carrier and other isotopes. This is a working relation in Nuclear medicine.

Where it is used

Clinically it sits on the Hot lab — Dose calibrator. In the dose calibrator well — assayed activity, decay between two times, Marinelli. Nuclear-medicine relations sit in the hot lab, on the camera, and in the voxel: decay, SUV, TOF, and counting statistics. They decide whether an uptake is real or a clock error.

Hot lab · Open this machine

How to use it

Enter T½ in hours and molar mass. Compare with the certificate of analysis: if measured a is far below this, carrier is present (which may still be clinically fine). Change one input and watch the curve and the simulation follow.

Symbols

T½Half-life6.02 h
MMolar mass99 g/mol

Worked example

A typical case from the default values: T½ = 6.02 h (Half-life); M = 99 g/mol (Molar mass). Substituting into the relation gives a = 1.946e+17 Bq/g; a = 194,554.9016 GBq/mg; a = 5.2582e+6 Ci/g. These are teaching numbers — align them with your machine.

Typical values give

a = 1.946e+17Bq/g
a = 194,554.9016GBq/mg
a = 5.2582e+6Ci/g

Where it comes from

The displayed formula is the working relation. a = λ N_A / M for a pure radionuclide. Usual reference: Cherry. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Cherry

Assumptions & limits

One isotope, 100% isotopic purity, no decay during labelling. Branching does not change A = λN but may change useful photon/particle yield.

Pitfalls

Activity is not counts. SUV needs the true injected activity, the residual, and the correct decay time — a clock off by 10 min on ¹⁸F is a several-percent error. Do not compare SUVs across reconstructions. One isotope, 100% isotopic purity, no decay during labelling. Branching does not change A = λN but may change useful photon/particle yield.

Keep this

Write the assay time next to every activity. Decay does the rest. One isotope, 100% isotopic purity, no decay during labelling. Branching does not change A = λN but may change useful photon/particle yield.

In this specialty

Nuclear medicine