00 Foundations

Activity from mass

A = λN with N from mass and molar mass. Carrier-free specific activity.

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Simulation

Activity from mass — 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=\lambda N,\quad N=\frac{m}{M}N_A,\quad \lambda=\frac{\ln 2}{T_{1/2}}

Typical values

Variables

m · MassµgM · Molar massg/molT½ · Half-lifeh

Results

A
Activity
1.946e+11Bq
A
Activity
194,554.902MBq
a
Specific activity
194,554.9016GBq/mg

Explanation

A=\lambda N,\quad N=\frac{m}{M}N_A,\quad \lambda=\frac{\ln 2}{T_{1/2}}

What it means

Activity is the number of decays per second: A = λN. For a pure radionuclide the atom count N is mass over molar mass times Avogadro’s number. Specific activity a = A/m is then λ N_A / M. Short half-life nuclides have huge specific activity (F-18, Tc-99m); long-lived ones (C-14, U-238) do not. This is a working relation in Radiation physics.

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. Radiation physics lives at the x-ray target, the linac head, and inside the patient: how a photon is born, how it scatters, and how it dies. Use these relations before you trust a spectrum, a wall, or a kV-versus-MV contrast argument.

Hot lab · Open this machine

How to use it

Enter mass in µg, molar mass g/mol, and half-life in hours. Presets cover common nuclides. Output is Bq, MBq, and GBq/mg. Use it for generator yield checks and ‘no-carrier-added’ calculations — real radiopharmaceuticals are rarely 100% pure. Change one input and watch the curve and the simulation follow.

Symbols

mMass1 µg
MMolar mass99 g/mol
T½Half-life6.02 h

Worked example

A typical case from the default values: m = 1 µg (Mass); M = 99 g/mol (Molar mass); T½ = 6.02 h (Half-life). Substituting into the relation gives A = 1.946e+11 Bq; A = 194,554.902 MBq; a = 194,554.9016 GBq/mg. These are teaching numbers — align them with your machine.

Typical values give

A = 1.946e+11Bq
A = 194,554.902MBq
a = 194,554.9016GBq/mg

Where it comes from

The displayed formula is the working relation. A = λN with N from mass and molar mass. Carrier-free specific activity. Usual reference: Cherry / Podgorsak. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Cherry / Podgorsak

Assumptions & limits

Assumes a single isotope with no carrier, no branching, and SI activity (1 Bq = 1 s⁻¹). Chemical impurities, isotopic dilution, and decay-chain daughters are omitted.

Pitfalls

Do not mix free-electron Compton kinematics with photoelectric-dominated kV imaging. Check keV versus MeV, and never treat a spectrum as one photon. Assumes a single isotope with no carrier, no branching, and SI activity (1 Bq = 1 s⁻¹). Chemical impurities, isotopic dilution, and decay-chain daughters are omitted.

Keep this

Photons do not deposit dose; the electrons they set in motion do. Assumes a single isotope with no carrier, no branching, and SI activity (1 Bq = 1 s⁻¹). Chemical impurities, isotopic dilution, and decay-chain daughters are omitted.

In this specialty

Radiation physics