Molar activity or specific activity?

The 2017 consensus nomenclature and the 2021 EANM guideline reserve molar activity (Am) for activity per amount of substance, in GBq/µmol or Ci/µmol, and specific activity (As) for activity per mass, in GBq/mg. Older papers use “specific activity” for both. The calculator prints both; they differ only by the molecular weight.

Why does molar activity matter for peptide radioligands?

Receptors are finite. Every molecule of ligand, labeled or not, competes for them, and the total peptide amount, not the activity, sets the occupancy. For somatostatin analogues, tumor uptake was shown to depend on the injected peptide amount, and labeling protocols were developed to reach high molar activities so that a given activity carries little cold peptide. The molar activity therefore decides how much of the receptor pool a dose blocks before it images or treats.

What is the carrier-free maximum?

The molar activity a compound would have if every molecule carried a radioactive atom: N_A · λ, which depends only on the half-life. A shorter half-life means a higher ceiling, ⁶⁸Ga about 1.03 × 10⁵ GBq/µmol against ¹⁷⁷Lu about 727 GBq/µmol. Real preparations fall short because of stable isotopes of the same element, the excess of precursor used in labeling and any unlabeled ligand.

What does the share of the maximum tell me?

With no other carrier present it is the fraction of molecules that carry a radioactive atom. At 74 GBq/µmol of ¹⁷⁷Lu that is about 10 %: nine of ten peptide molecules in the vial are cold, and it is those that occupy receptors without delivering decay. It is a way of reading a molar activity, not a quality target.

Molar and specific activity calculator

Molar activity (Am) is the activity per amount of substance of a labeled compound; specific activity (As) is the activity per mass. In receptor-targeted radiopharmaceuticals the two decide how much unlabeled ligand accompanies each becquerel, and so how much of a finite receptor population the cold ligand occupies. This calculator returns both in the units the literature uses and compares the molar activity with the theoretical carrier-free maximum, N_A · λ, for the chosen nuclide. It is for radiochemists, radiopharmacists and anyone developing peptide or small-molecule radioligands.

Calculator

ActivityA

Of the labeled compound, at the reference time.

RadionuclideT½ 6.6443 d

Sets the carrier-free maximum, N_A · ln 2 / T½. Choose none to skip the comparison.

Amount given as

MolesMass and molecular weight

Amount of substancen

Total compound, labeled and unlabeled.

Molecular weight (optional)g/mol

g/mol; adds the specific activity per mass.

Results

Molar activity · GBq/µmol (= MBq/nmol): 74GBq/µmol
In Ci/µmol: 2Ci/µmol
Specific activity: add a molecular weight
In Ci/mg: add a molecular weight
Amount of substance: 100 nmol
Mass: add a molecular weight
Carrier-free maximum · ¹⁷⁷Lu: 727.1GBq/µmol
Share of the maximum: 10.18%
Molecules carrying the nuclide: about 1 in 9.83

Of ten molecules in the preparation, about one carries the nuclide.

For reference and education. Nothing on this page is clinical guidance, a dose recommendation or an Epitorix performance figure; check every number against your own validated procedures.

The formulas

N_A = 6.022 140 76 × 10²³ mol⁻¹

Activity per mole, per gram, and the ceiling

Am: Am = A / n; Molar activity: activity divided by the amount of substance of the compound, labeled and unlabeled together. 1 GBq/µmol = 1 MBq/nmol = 27.03 mCi/µmol.
As: As = A / m = Am / M; Specific activity: activity per mass; the molar activity divided by the molecular weight M. Printed in GBq/mg and Ci/mg.
Am,max: Am,max = N_A · λ = N_A · ln 2 / T½; The carrier-free (theoretical maximum) molar activity, reached when every molecule carries a radioactive atom. N_A = 6.022 140 76 × 10²³ mol⁻¹ (exact). ¹⁷⁷Lu 727 GBq/µmol; ⁶⁸Ga 1.03 × 10⁵; ¹⁸F 6.34 × 10⁴.
Share: Am / Am,max × 100 %; How close the preparation is to carrier-free. With no other carrier present it is also the fraction of molecules that carry a radioactive atom.

Worked examples

ENSDF half-lives

By hand

Each row is computed from the formulas above; the calculator reproduces every value.

Worked examples of molar and specific activity against the carrier-free maximum.
Activity	Amount	Am, GBq/µmol	Am, Ci/µmol	As, GBq/mg	Share of maximum
7.4 GBq ¹⁷⁷Lu	100 nmol	74.00	2.000	—	10.18 % of 727.1
1 GBq ¹⁷⁷Lu	20 µg at 1 000 g/mol = 20 nmol	50.00	1.351	50.00	6.876 %
200 MBq ¹⁸F	2 nmol	100.0	2.703	—	0.158 % of 63 380
1 GBq ⁶⁸Ga	40 µg at 947.0 g/mol = 42.24 nmol	23.68	0.6399	25.00	0.023 % of 102 750

Questions

What the numbers mean

Molar activity or specific activity?: The 2017 consensus nomenclature and the 2021 EANM guideline reserve molar activity (Am) for activity per amount of substance, in GBq/µmol or Ci/µmol, and specific activity (As) for activity per mass, in GBq/mg. Older papers use “specific activity” for both. The calculator prints both; they differ only by the molecular weight.
Why does molar activity matter for peptide radioligands?: Receptors are finite. Every molecule of ligand, labeled or not, competes for them, and the total peptide amount, not the activity, sets the occupancy. For somatostatin analogues, tumor uptake was shown to depend on the injected peptide amount, and labeling protocols were developed to reach high molar activities so that a given activity carries little cold peptide. The molar activity therefore decides how much of the receptor pool a dose blocks before it images or treats.
What is the carrier-free maximum?: The molar activity a compound would have if every molecule carried a radioactive atom: N_A · λ, which depends only on the half-life. A shorter half-life means a higher ceiling, ⁶⁸Ga about 1.03 × 10⁵ GBq/µmol against ¹⁷⁷Lu about 727 GBq/µmol. Real preparations fall short because of stable isotopes of the same element, the excess of precursor used in labeling and any unlabeled ligand.
What does the share of the maximum tell me?: With no other carrier present it is the fraction of molecules that carry a radioactive atom. At 74 GBq/µmol of ¹⁷⁷Lu that is about 10 %: nine of ten peptide molecules in the vial are cold, and it is those that occupy receptors without delivering decay. It is a way of reading a molar activity, not a quality target.

Sources

Coenen HH et al. Consensus nomenclature rules for radiopharmaceutical chemistry — setting the record straight. Nucl Med Biol 2017;55:v–xi (opens in a new tab) — molar activity (Am) and specific activity (As) defined
Luurtsema G et al. EANM guideline for harmonisation on molar activity or specific activity of radiopharmaceuticals. EJNMMI Radiopharm Chem 2021;6:34 (opens in a new tab) — conventions, terminology, the carrier-free maximum
de Jong M et al. Tumour uptake of the radiolabelled somatostatin analogue [DOTA⁰,Tyr³]octreotide is dependent on the peptide amount. Eur J Nucl Med 1999;26:693–698 (opens in a new tab) — receptor saturation by the peptide amount
Breeman WAP et al. Optimising conditions for radiolabelling of DOTA-peptides with ⁹⁰Y, ¹¹¹In and ¹⁷⁷Lu at high specific activities. Eur J Nucl Med Mol Imaging 2003;30:917–920 (opens in a new tab) — why and how high molar activities are reached
CODATA 2018 — Avogadro constant N_A (NIST) (opens in a new tab) — 6.022 140 76 × 10²³ mol⁻¹, exact
ENSDF — Evaluated Nuclear Structure Data File, via NuDat 3 (opens in a new tab) — the half-lives behind each maximum

A reference tool. It divides an activity by an amount and compares it with N_A · λ; it does not measure, predict or judge a preparation, and nothing here is an Epitorix performance figure.

Calculator

Results

Activity per mole, per gram, and the ceiling

By hand

What the numbers mean

The other six, open in the browser.