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Specific activity validation — molar masses and the becquerel per gram

Validation of the specific activity calculator

Specific activity is derived here from the definitions of the mole and the becquerel, and every molar mass the calculator uses is set against the evaluated atomic masses. This report found an error in the calculator, states its size, and records what was changed.

Subject
The specific activity calculator at /calc/specific-activity/, both of its directions, and the functions specificActivity, massFromActivity and activityFromMass in src/engine/decay.ts.
Report date
2026-09-18
Source revision
09c0347
Archived source
10.5281/zenodo.22794265
Nuclides covered
147 of 147
Checks performed
1189
Acceptance criteria
Mathematics: relative difference below 1e-12. Molar masses: identical to the evaluated value within 1e-15. Worked cases: below 1e-9.
Largest found
2.220e-16 on the mathematics (S-ID-01 @Tl-201), 0 on the stored specific activities
Result
All checks pass.

Scope

This report covers the specific activity calculator: the becquerel per gram of a pure nuclide, the conversion of an activity to a mass, and the conversion of a mass to an activity, for all 147 nuclides in the data set. The half-lives those answers rest on are validated separately, in the decay report, and are taken as given here. Isotopic mixtures, chemical compounds and daughter ingrowth are outside the quantity itself and are treated under refusals.

What this report found

Until this report, the calculator used the mass number in place of the molar mass, and four pages of this site described that substitution as accurate to 0.03% for every nuclide. Checked against the evaluated atomic masses, that statement is false. 95 of the 147 nuclides exceed 0.03%, 29 of them exceed 0.1%, and the worst — H-3 — is off by 0.535%, some 18 times the claimed bound. The median nuclide is off by 0.0666%.

The discrepancy is not rounding. An atomic mass is the mass number plus the mass excess divided by c², and the mass excess is the nuclear binding energy — it is most negative near A = 56, where binding per nucleon peaks, and strongly positive for the lightest nuclides. It therefore changes sign across the chart, from 0.535% at H-3 to about −0.11% through the iron region. A quantity that changes sign has no single small bound, and the figure 0.03% has no traceable origin in this repository.

Rather than restate the bound more accurately, the approximation was removed. The molar masses are now the evaluated atomic masses from AME2020, corrected for isomer excitation energy where the nuclide is an isomer, and specific activities were recomputed. Every specific activity on this site changed, by up to 0.53%.

Which of the two is correct is settled by the definition rather than by comparison: the molar mass of a nuclide is its atomic mass expressed in grams per mole, while the mass number is a count of nucleons. No external figure is needed to decide it, and none is claimed here.

It is worth recording nonetheless that this repository carried a regression fence for tritium, 3.56 × 10¹⁴ Bq/g, written before this report and without a citation. The mass-number calculation gave 3.5789 × 10¹⁴; the atomic-mass calculation gives 3.55986×10¹⁴, which matches that fence to 0.004% against 0.53%. An uncited value is not a source and is not used as one. It is mentioned because it was fixed in advance of the change and so could not have been fitted to it.

Why the existing tests could not see it

The engine test suite already checked that each stored specific activity matched ln 2 · NA / (T½ · A) — the same expression, with the same mass number, that had generated the value. A test that recomputes a number the way it was computed will pass forever, whatever the number means. This is the difference between a consistency check and a validation: the error was only visible once an outside evaluation was brought in.

Comparing against something independent, where that is possible

The decay report could set this site's half-lives against a genuinely separate evaluation, because two independent evaluations of half-lives exist. Atomic masses are different. The Atomic Mass Evaluation is a single global least-squares adjustment of essentially all mass measurements, and there is no second evaluation to play against it. Claiming that two sources agree would be dishonest here.

What can be done instead is done, and it is three things.

  1. The derivation is shown in full, so that the formula is not asserted. It rests on the definitions of the mole, the becquerel and the half-life, and on nothing else.
  2. Two independent columns of the evaluation are checked against each other. AME2020 publishes both the atomic mass and the mass excess, which satisfy m = A + Δ/c². Across all 147 nuclides the largest residual is 5.72e-11. This will not catch an error in the evaluation, but it does catch an error in reading it — which is the failure mode actually within reach, and one this project has already hit once, in the decay report.
  3. The source line is reproduced for every nuclide, so a reader can open the published file and compare characters rather than trusting a transcription.

The conversion from the unified atomic mass unit to keV, needed for the isomer correction, is derived from SI definitions rather than quoted: it reproduces the published CODATA value to 3.09e-12, which is the rounding of the printed figure.

The implementation under test

specificActivity  = (LN2 * N_A) / (tHalfS * molarMass)
massFromActivity  = bq / saBqPerG
activityFromMass  = grams * saBqPerG

Three expressions with no iteration and no series, so there is no accumulated error to bound. The questions are whether these are the right expressions, whether the two inputs are right, and whether the functions refuse where no answer exists.

Derivation

S-U-01 — Specific activity from the definition of the mole and of activity

In the code: specificActivity in src/engine/decay.ts · Cited: CODATA 2022, Avogadro constant · 15th CGPM (1975), Resolution 8

  1. A sample of mass m grams of a pure nuclide of molar mass M grams per mole holds m/M moles.
  2. One mole holds N_A atoms, so the sample holds N = (m/M)·N_A atoms.
  3. Activity is the expected number of decays per second: A = λ·N, with λ the decay constant.
  4. The half-life fixes λ: after T½ the surviving fraction is e^(−λT½) = 1/2, so λ = ln 2 / T½.
  5. Substituting, A = (ln 2 / T½)·(m/M)·N_A becquerel.
  6. Specific activity is activity per unit mass, a = A/m = ln 2 · N_A / (T½ · M) becquerel per gram.
  7. The mass m cancels, which is the point: specific activity is a property of the nuclide, not of the sample.
  8. This case carries no arithmetic. It is here so that the formula is derived rather than asserted, and so that the two inputs it needs — the half-life and the molar mass — are named explicitly.

S-U-02 — The molar mass is the atomic mass, not the mass number

In the code: the m_u field of every nuclide in src/data/nuclides.json · Cited: AME2020, file mass_1.mas20, column ATOMIC MASS (micro-u) · AME2020, file mass_1.mas20, carbon-12 line · CODATA 2022, molar mass constant

  1. The mass number A counts nucleons. It is an integer and it is not a mass.
  2. The atomic mass of the neutral atom is A plus the mass excess Δ divided by c², where Δ is negative where the nucleus is tightly bound and positive where it is loosely bound.
  3. Because Δ is largest in magnitude near A = 56, where nuclear binding per nucleon peaks, the difference between the atomic mass and A is not a rounding error with a single bound. It is a physical quantity that changes sign across the chart of nuclides.
  4. Carbon-12 is the one exception by construction: the unified atomic mass unit is defined so that its atomic mass is exactly 12 u, and AME2020 lists it with zero uncertainty.
  5. Converting an atomic mass in u to a molar mass in g/mol uses the molar mass constant M_u = 1.000 000 001 05(31) × 10⁻³ kg/mol. The factor differs from 1 g/mol by 1.05 × 10⁻⁹ relative, which is four orders of magnitude below the six significant figures the calculator prints, so the numerical value in u is used directly as g/mol.
  6. Before 2026-09-18 this calculator used A in place of M and described the substitution as accurate to 0.03%. It is not; see the measured distribution in this report.

S-U-03 — One unified atomic mass unit in keV, derived from the SI

In the code: U_KEV in scripts/masses.py, used to add isomer excitation energy · Cited: CODATA 2022, molar mass constant · CODATA 2022, Avogadro constant · CODATA 2022, atomic mass constant energy equivalent in MeV

  1. The mass of one atomic mass unit is m_u = M_u / N_A, with M_u the molar mass constant.
  2. Its energy equivalent is m_u·c², and dividing by the elementary charge expresses it in electronvolts.
  3. Both c = 299 792 458 m/s and e = 1.602 176 634 × 10⁻¹⁹ C are exact by definition of the SI, and N_A = 6.022 140 76 × 10²³ /mol is exact as well. Only M_u is measured.
  4. m_u c²/e = (1.000 000 001 05 × 10⁻³ × 299 792 458²) / (6.022 140 76 × 10²³ × 1.602 176 634 × 10⁻¹⁹) eV.
  5. = 9.314 941 037 17 × 10⁸ eV = 931 494.103 717 keV.
  6. CODATA lists 931.494 103 72 MeV. The derivation reproduces the published value to 3.1 × 10⁻¹², which is the rounding of the printed figure, so the chain from the SI definitions is confirmed rather than assumed.

S-U-04 — An isomer is heavier than its ground state

In the code: the isomer branch of scripts/masses.py · Cited: NUBASE2020, file nubase_4.mas20, columns 43-54

  1. AME2020 tabulates the ground-state atomic mass. A nuclear isomer is the same nucleus held in an excited state, and that excitation energy is mass.
  2. NUBASE2020 gives the excitation energy E in keV for each isomer, so the isomer's atomic mass is m = m(ground) + E/c², using the conversion derived in S-U-03.
  3. The effect is small. The largest in this data set is U-238m at 2557.9 keV, which is 1.15 × 10⁻⁵ of the atomic mass — roughly one four-hundredth of the mass-number error this report removed.
  4. It is nevertheless two orders of magnitude larger than the AME2020 uncertainties, so it is carried rather than neglected. 36 of the 147 nuclides are isomers.

Identities

These hold for every nuclide, which is what makes them identities rather than test values. Each is checked at all 147 nuclides; the table shows the value at Co-60 and the worst disagreement seen across the set.

Identity Hand Tool Worst difference
Mass to activity and back returns the starting mass S-ID-01 1×10⁰ 1×10⁰ 2.22e-16
Doubling the half-life halves the specific activity S-ID-02 5×10⁻¹ 5×10⁻¹ 0
Doubling the molar mass halves the specific activity S-ID-03 5×10⁻¹ 5×10⁻¹ 0
Activity is proportional to mass S-ID-04 1×10¹ 1×10¹ 1.78e-16
Carbon-12 has an atomic mass of exactly 12 S-ID-05 1.2×10¹ 1.2×10¹ 0
The specific activity is the activity of exactly one gram S-ID-06 1×10⁰ 1×10⁰ 0
Derivations of the identities

S-ID-01 — Mass to activity and back returns the starting mass

  1. activityFromMass(m, a) = m·a and massFromActivity(A, a) = A/a are inverse maps for any positive a.
  2. The tool offers both directions on one screen, so a user can walk a value through both. If they did not compose to the identity the two answers would quietly disagree.
  3. Checked for every one of the 147 nuclides, in both orders.

S-ID-02 — Doubling the half-life halves the specific activity

  1. a = ln 2 · N_A / (T½ · M) is inversely proportional to T½ with everything else fixed.
  2. So a(2T½)/a(T½) = 1/2 exactly, independent of the nuclide and of the molar mass.
  3. This is the single most useful sanity check on the tool: a nuclide that lives twice as long is half as hot per gram.

S-ID-03 — Doubling the molar mass halves the specific activity

  1. The same inverse proportionality holds in M, because a gram of a heavier nuclide holds proportionally fewer atoms.
  2. This is the identity the mass-number approximation perturbed: an error of 0.5% in M is an error of 0.5% in the answer, in the opposite direction.
  3. Because the relationship is exactly linear in 1/M, no part of the calculation damps a molar-mass error. Whatever fraction M is wrong by, the answer is wrong by, which is why the input had to be fixed rather than bounded.

S-ID-04 — Activity is proportional to mass

  1. activityFromMass is linear, so ten times the mass is ten times the activity exactly.
  2. There is no self-absorption, no geometry and no dead time in this quantity — it is a count of atoms — and the linearity records that.
  3. The check matters because the screen offers mass in milligrams through kilograms: a unit prefix applied in the wrong place would break linearity across decades while looking right at one of them.

S-ID-05 — Carbon-12 has an atomic mass of exactly 12

  1. The unified atomic mass unit is defined as one twelfth of the mass of a free neutral carbon-12 atom at rest in its ground state.
  2. AME2020 therefore lists carbon-12 as 12 000 000.0 micro-u with an uncertainty of zero.
  3. The extraction in scripts/masses.py reads that value back as exactly 12 and stops if it does not. It is the one row in the table whose value is known in advance, so it tests the reader rather than the data.

S-ID-06 — The specific activity is the activity of exactly one gram

  1. activityFromMass(1 g, a) must return a itself, and massFromActivity(a, a) must return 1 g.
  2. Trivial arithmetic, but it pins the unit of the headline figure: the number the screen shows is becquerel per gram, not per kilogram and not per mole.
  3. Per mole would be larger by the molar mass, per kilogram by a thousand. Both are plausible-looking numbers, so the unit is fixed by a case rather than left to the label.

Molar masses against the evaluation

Every nuclide in the data set, with the evaluated atomic mass, the deviation of the mass number from it — the error the calculator used to carry — and the resulting specific activity. The largest uncertainty in the evaluation across this set is 1.4e-7 relative, which is 38,839 times smaller than the approximation it replaces, so the measured uncertainty plays no part in the verdict. 36 of the rows are isomers, whose excitation energy is added to the ground-state mass.

Nuclide A AME2020
[u]		 Excitation
[keV]		 This site
[u]		 (M−A)/A Specific activity
[Bq/g]
Ac-227 227 227.027751 — 227.027751 +0.0122% 2.67611×10¹²
Am-241 241 241.056827 — 241.056827 +0.0236% 1.26846×10¹¹
Am-243 243 243.061380 — 243.061380 +0.0253% 7.39013×10⁹
Ar-39 39 38.964313 — 38.964313 -0.0915% 1.26672×10¹²
Au-198 198 197.968244 — 197.968244 -0.0160% 9.05844×10¹⁵
Au-198m 198 197.968244 312.223 197.968579 -0.0159% 1.07413×10¹⁶
Ba-133 133 132.906007 — 132.906007 -0.0707% 9.43286×10¹²
Ba-133m 133 132.906007 288.252 132.906317 -0.0704% 2.24101×10¹⁶
Ba-137m 137 136.905827 661.659 136.906538 -0.0682% 1.99122×10¹⁹
Bi-210 210 209.984120 — 209.984120 -0.0076% 4.59055×10¹⁵
C-14 14 14.003242 — 14.003242 +0.0232% 1.65721×10¹¹
Ca-41 41 40.962278 — 40.962278 -0.0920% 3.24871×10⁹
Ca-45 45 44.956186 — 44.956186 -0.0974% 6.60885×10¹⁴
Cd-109 109 108.904987 — 108.904987 -0.0872% 9.60433×10¹³
Cd-109m1 109 108.904987 59.600 108.905051 -0.0871% 3.24823×10²⁶
Cd-109m2 109 108.904987 463.100 108.905484 -0.0867% 3.61594×10²⁶
Ce-139 139 138.906647 — 138.906647 -0.0672% 2.52712×10¹⁴
Ce-139m 139 138.906647 754.240 138.907457 -0.0666% 5.2189×10¹⁹
Ce-141 141 140.908286 — 140.908286 -0.0650% 1.05485×10¹⁵
Ce-144 144 143.913653 — 143.913653 -0.0600% 1.17829×10¹⁴
Cf-249 249 249.074850 — 249.074850 +0.0301% 1.51302×10¹¹
Cf-252 252 252.081627 — 252.081627 +0.0324% 1.98238×10¹³
Cl-36 36 35.968307 — 35.968307 -0.0880% 1.22057×10⁹
Cm-242 242 242.058834 — 242.058834 +0.0243% 1.22539×10¹⁴
Cm-243 243 243.061387 — 243.061387 +0.0253% 1.87013×10¹²
Cm-244 244 244.062751 — 244.062751 +0.0257% 2.99269×10¹²
Cm-245 245 245.065491 — 245.065491 +0.0267% 6.40815×10⁹
Cm-246 246 246.067222 — 246.067222 +0.0273% 1.14229×10¹⁰
Co-57 57 56.936290 — 56.936290 -0.1118% 3.12263×10¹⁴
Co-60 60 59.933816 — 59.933816 -0.1103% 4.18694×10¹³
Co-60m 60 59.933816 58.590 59.933878 -0.1102% 1.109×10¹⁹
Cr-51 51 50.944765 — 50.944765 -0.1083% 3.42311×10¹⁵
Cs-134 134 133.906719 — 133.906719 -0.0696% 4.78319×10¹³
Cs-134m 134 133.906719 138.744 133.906867 -0.0695% 2.97358×10¹⁷
Cs-135 135 134.905977 — 134.905977 -0.0696% 4.26307×10⁷
Cs-137 137 136.907089 — 136.907089 -0.0678% 3.21202×10¹²
Eu-152 152 151.921751 — 151.921751 -0.0515% 6.44142×10¹²
Eu-152m1 152 151.921751 45.600 151.921800 -0.0514% 8.19652×10¹⁶
Eu-152m2 152 151.921751 65.297 151.921821 -0.0514% 4.77017×10¹⁷
Eu-154 154 153.922986 — 153.922986 -0.0500% 9.99147×10¹²
Eu-154m 154 153.922986 68.170 153.923059 -0.0500% 9.76204×10¹⁷
F-18 18 18.000937 — 18.000937 +0.0052% 3.52084×10¹⁸
Fe-55 55 54.938291 — 54.938291 -0.1122% 8.7745×10¹³
Fe-59 59 58.934873 — 58.934873 -0.1104% 1.84259×10¹⁵
Ga-67 67 66.928202 — 66.928202 -0.1072% 2.21314×10¹⁶
Ga-68 68 67.927980 — 67.927980 -0.1059% 1.5126×10¹⁸
Gd-148 148 147.918121 — 147.918121 -0.0553% 1.25774×10¹²
Ge-68 68 67.928095 — 67.928095 -0.1057% 2.62516×10¹⁴
H-3 3 3.016049 — 3.016049 +0.5350% 3.55986×10¹⁴
Hg-203 203 202.972872 — 202.972872 -0.0134% 5.10676×10¹⁴
Hg-203m 203 202.972872 933.140 202.973874 -0.0129% 9.30559×10²⁵
Ho-166 166 165.932291 — 165.932291 -0.0408% 2.60507×10¹⁶
I-125 125 124.904631 — 124.904631 -0.0763% 6.51098×10¹⁴
I-129 129 128.904984 — 128.904984 -0.0737% 6.536×10⁶
I-131 131 130.906126 — 130.906126 -0.0717% 4.59882×10¹⁵
In-111 111 110.905107 — 110.905107 -0.0855% 1.55319×10¹⁶
In-111m 111 110.905107 536.990 110.905684 -0.0850% 8.14668×10¹⁸
Ir-192 192 191.962602 — 191.962602 -0.0195% 3.40894×10¹⁴
Ir-192m1 192 191.962602 56.720 191.962663 -0.0194% 2.49943×10¹⁹
Ir-192m2 192 191.962602 168.140 191.962783 -0.0194% 2.85922×10¹¹
K-40 40 39.963998 — 39.963998 -0.0900% 2.65215×10⁵
Kr-85 85 84.912527 — 84.912527 -0.1029% 1.45059×10¹³
Kr-85m 85 84.912527 304.871 84.912855 -0.1025% 3.04805×10¹⁷
Lu-177 177 176.943764 — 176.943764 -0.0318% 4.1094×10¹⁵
Lu-177m 177 176.943764 150.398 176.943925 -0.0317% 1.70225×10¹⁴
Mn-54 54 53.940356 — 53.940356 -0.1105% 2.8689×10¹⁴
Mo-99 99 98.907707 — 98.907707 -0.0932% 1.77828×10¹⁶
Na-22 22 21.994438 — 21.994438 -0.0253% 2.31151×10¹⁴
Na-24 24 23.990963 — 23.990963 -0.0377% 3.23155×10¹⁷
Na-24m 24 23.990963 472.207 23.991470 -0.0355% 8.62181×10²³
Nb-95 95 94.906831 — 94.906831 -0.0981% 1.45482×10¹⁵
Nb-95m 95 94.906831 235.690 94.907084 -0.0978% 1.41012×10¹⁶
Ni-59 59 58.934345 — 58.934345 -0.1113% 2.95325×10⁹
Ni-63 63 62.929669 — 62.929669 -0.1116% 2.08529×10¹²
Np-237 237 237.048172 — 237.048172 +0.0203% 2.60268×10⁷
P-32 32 31.973908 — 31.973908 -0.0815% 1.05902×10¹⁶
P-33 33 32.971726 — 32.971726 -0.0857% 5.77337×10¹⁵
Pa-231 231 231.035883 — 231.035883 +0.0155% 1.75786×10⁹
Pb-210 210 209.984188 — 209.984188 -0.0075% 2.83754×10¹²
Pm-147 147 146.915145 — 146.915145 -0.0577% 3.43203×10¹³
Po-210 210 209.982874 — 209.982874 -0.0082% 1.66272×10¹⁴
Pr-144 144 143.913311 — 143.913311 -0.0602% 2.79757×10¹⁸
Pu-238 238 238.049558 — 238.049558 +0.0208% 6.33599×10¹¹
Pu-239 239 239.052162 — 239.052162 +0.0218% 2.29505×10⁹
Pu-240 240 240.053812 — 240.053812 +0.0224% 8.39853×10⁹
Pu-241 241 241.056850 — 241.056850 +0.0236% 3.82954×10¹²
Pu-242 242 242.058741 — 242.058741 +0.0243% 1.46505×10⁸
Pu-244 244 244.064204 — 244.064204 +0.0263% 6.66633×10⁵
Ra-223 223 223.018501 — 223.018501 +0.0083% 1.89529×10¹⁵
Ra-224 224 224.020210 — 224.020210 +0.0090% 5.93851×10¹⁵
Ra-226 226 226.025408 — 226.025408 +0.0112% 3.65767×10¹⁰
Ra-228 228 228.031069 — 228.031069 +0.0136% 1.00883×10¹³
Re-188 188 187.958114 — 187.958114 -0.0223% 3.62774×10¹⁶
Re-188m 188 187.958114 172.085 187.958298 -0.0222% 1.99106×10¹⁸
Rh-106 106 105.907286 — 105.907286 -0.0875% 1.31074×10²⁰
Rh-106m 106 105.907286 132.000 105.907428 -0.0873% 5.0145×10¹⁷
Ru-106 106 105.907328 — 105.907328 -0.0874% 1.22695×10¹⁴
S-35 35 34.969032 — 34.969032 -0.0885% 1.58131×10¹⁵
Sb-124 124 123.905937 — 123.905937 -0.0759% 6.477×10¹⁴
Sb-124m1 124 123.905937 10.863 123.905949 -0.0758% 3.62244×10¹⁹
Sb-124m2 124 123.905937 36.844 123.905977 -0.0758% 2.77959×10¹⁸
Sb-125 125 124.905254 — 124.905254 -0.0758% 3.839×10¹³
Sc-46 46 45.955167 — 45.955167 -0.0975% 1.25469×10¹⁵
Sc-46m 46 45.955167 52.011 45.955223 -0.0973% 4.8444×10²⁰
Se-75 75 74.922523 — 74.922523 -0.1033% 5.38351×10¹⁴
Se-79 79 78.918499 — 78.918499 -0.1032% 5.12572×10⁸
Si-32 32 31.974152 — 31.974152 -0.0808% 2.63501×10¹²
Sm-147 147 146.914904 — 146.914904 -0.0579% 8.39105×10²
Sm-151 151 150.919939 — 150.919939 -0.0530% 9.73851×10¹¹
Sm-153 153 152.922104 — 152.922104 -0.0509% 1.63822×10¹⁶
Sm-153m 153 152.922104 98.390 152.922209 -0.0508% 2.57513×10²³
Sn-113 113 112.905176 — 112.905176 -0.0839% 3.71802×10¹⁴
Sn-113m 113 112.905176 77.389 112.905259 -0.0838% 2.87937×10¹⁸
Sr-85 85 84.912932 — 84.912932 -0.1024% 8.77375×10¹⁴
Sr-85m 85 84.912932 238.790 84.913188 -0.1021% 1.21146×10¹⁸
Sr-89 89 88.907451 — 88.907451 -0.1040% 1.07471×10¹⁵
Sr-90 90 89.907728 — 89.907728 -0.1025% 5.08905×10¹²
Ta-182 182 181.950155 — 181.950155 -0.0274% 2.31417×10¹⁴
Ta-182m1 182 181.950155 16.273 181.950172 -0.0274% 8.10658×10²¹
Ta-182m2 182 181.950155 519.577 181.950712 -0.0271% 2.41388×10¹⁸
Tc-99 99 98.906250 — 98.906250 -0.0947% 6.33534×10⁸
Tc-99m 99 98.906250 142.684 98.906403 -0.0945% 1.95154×10¹⁷
Th-228 228 228.028740 — 228.028740 +0.0126% 3.03456×10¹³
Th-229 229 229.031761 — 229.031761 +0.0139% 7.32925×10⁹
Th-230 230 230.033132 — 230.033132 +0.0144% 7.60784×10⁸
Th-232 232 232.038054 — 232.038054 +0.0164% 4.07187×10³
Tl-201 201 200.970820 — 200.970820 -0.0145% 7.90261×10¹⁵
Tl-201m 201 200.970820 919.160 200.971807 -0.0140% 9.84371×10²³
Tl-204 204 203.973863 — 203.973863 -0.0128% 1.71424×10¹³
U-232 232 232.037155 — 232.037155 +0.0160% 8.2738×10¹¹
U-233 233 233.039634 — 233.039634 +0.0170% 3.56563×10⁸
U-234 234 234.040950 — 234.040950 +0.0175% 2.30217×10⁸
U-235 235 235.043928 — 235.043928 +0.0187% 7.99392×10⁴
U-236 236 236.045566 — 236.045566 +0.0193% 2.39276×10⁶
U-238 238 238.050787 — 238.050787 +0.0213% 1.24365×10⁴
U-238m 238 238.050787 2557.900 238.053533 +0.0225% 6.26244×10²⁷
Xe-133 133 132.905911 — 132.905911 -0.0707% 6.92733×10¹⁵
Xe-133m 133 132.905911 233.221 132.906161 -0.0706% 1.65383×10¹⁶
Y-88 88 87.909501 — 87.909501 -0.1028% 5.15423×10¹⁴
Y-88m1 88 87.909501 392.860 87.909923 -0.1024% 1.57751×10²⁵
Y-88m2 88 87.909501 674.550 87.910225 -0.1020% 3.39649×10²³
Y-90 90 89.907142 — 89.907142 -0.1032% 2.01354×10¹⁶
Y-90m 90 89.907142 682.010 89.907874 -0.1024% 4.04283×10¹⁷
Y-91 91 90.907298 — 90.907298 -0.1019% 9.08309×10¹⁴
Zn-65 65 64.929241 — 64.929241 -0.1089% 3.0504×10¹⁴
Zr-93 93 92.906471 — 92.906471 -0.1006% 8.84321×10⁷
Zr-95 95 94.908040 — 94.908040 -0.0968% 7.94992×10¹⁴

The column marked in the warning colour is every nuclide for which the old claim of 0.03% was untrue: 95 of 147. The stored specific activities were recomputed from the half-life and the evaluated molar mass; the largest disagreement between the stored value and that recomputation is 0, and the largest disagreement between a stored molar mass and the evaluated one is 0.

The source line for every nuclide, as published

Each line is reproduced from the AME2020 data file mass_1.mas20, whitespace collapsed. The fields are, in order: N−Z, N, Z, A, element, origin, mass excess and its uncertainty in keV, binding energy per nucleon and its uncertainty in keV, decay mode, beta-decay energy and its uncertainty, then the atomic mass and its uncertainty in micro-u. Isomers carry a second line from NUBASE2020 giving the excitation energy.

  • Ac-227 49 138 89 227 Ac 25849.515 1.926 7650.7084 0.0085 B- 44.7559 0.8297 227 027750.594 2.068
  • Am-241 51 146 95 241 Am 52934.335 1.113 7543.2795 0.0046 B- -767.4346 1.1685 241 056827.343 1.195
  • Am-243 53 148 95 243 Am 57175.005 1.388 7530.1742 0.0057 B- -6.9302 1.5692 243 061379.889 1.490
  • Ar-39 3 21 18 39 Ar + -33242.195 5.000 8562.5988 0.1282 B- 565.0000 5.0000 38 964313.037 5.367
  • Au-198 40 119 79 198 Au -29580.793 0.540 7908.5675 0.0027 B- 1373.5226 0.4905 197 968243.714 0.579
  • Au-198m 40 119 79 198 Au -29580.793 0.540 7908.5675 0.0027 B- 1373.5226 0.4905 197 968243.714 0.579 198 0791 198Aum -29268.6 0.5 312.2227 0.0020
  • Ba-133 21 77 56 133 Ba -87553.512 0.992 8400.2059 0.0075 B- -2059.1203 27.9624 132 906007.443 1.065
  • Ba-133m 21 77 56 133 Ba -87553.512 0.992 8400.2059 0.0075 B- -2059.1203 27.9624 132 906007.443 1.065 133 0561 133Bam -87265.2 1.0 288.252 0.009
  • Ba-137m 25 81 56 137 Ba -87721.401 0.248 8391.8288 0.0018 B- -580.5356 1.6231 136 905827.207 0.266 137 0561 137Bam -87059.74 0.25 661.659 0.003
  • Bi-210 44 127 83 210 Bi -14791.905 1.364 7832.5424 0.0065 B- 1161.1549 0.7662 209 984120.237 1.463
  • C-14 2 8 6 14 C 3019.89328 0.00375 7520.3198 0.0004 B- 156.4765 0.0037 14 003241.98862 0.00403
  • Ca-41 1 21 20 41 Ca -35137.908 0.138 8546.7075 0.0034 B- -6495.5482 0.1553 40 962277.905 0.147
  • Ca-45 5 25 20 45 Ca -40812.230 0.365 8630.5467 0.0081 B- 260.0910 0.7377 44 956186.270 0.392
  • Cd-109 13 61 48 109 Cd -88504.330 1.536 8538.7646 0.0141 B- -2014.8047 4.0662 108 904986.697 1.649
  • Cd-109m1 13 61 48 109 Cd -88504.330 1.536 8538.7646 0.0141 B- -2014.8047 4.0662 108 904986.697 1.649 109 0481 109Cdm -88444.7 1.5 59.60 0.07
  • Cd-109m2 13 61 48 109 Cd -88504.330 1.536 8538.7646 0.0141 B- -2014.8047 4.0662 108 904986.697 1.649 109 0482 109Cdn -88041.2 1.5 463.10 0.11
  • Ce-139 23 81 58 139 Ce -86957.741 2.089 8370.4664 0.0150 B- -2129.0890 2.9962 138 906647.029 2.242
  • Ce-139m 23 81 58 139 Ce -86957.741 2.089 8370.4664 0.0150 B- -2129.0890 2.9962 138 906647.029 2.242 139 0581 139Cem -86203.5 2.1 754.24 0.08
  • Ce-141 25 83 58 141 Ce -85431.058 1.315 8355.3956 0.0093 B- 583.4758 1.1784 140 908285.991 1.411
  • Ce-144 28 86 58 144 Ce + -80431.942 2.833 8314.7612 0.0197 B- 318.6462 0.8321 143 913652.763 3.041
  • Cf-249 53 151 98 249 Cf 69722.733 1.182 7483.3954 0.0048 B- -1452# 30# 249 074850.428 1.269
  • Cf-252 56 154 98 252 Cf -a 76034.610 2.358 7465.3474 0.0094 B- -1260.0000 50.0000 252 081626.507 2.531
  • Cl-36 2 19 17 36 Cl -29522.008 0.036 8521.9322 0.0010 B- 709.5343 0.0449 35 968306.822 0.038
  • Cm-242 50 146 96 242 Cm 54803.699 1.141 7534.5040 0.0047 B- -2948# 135# 242 058834.187 1.224
  • Cm-243 51 147 96 243 Cm -a 57181.936 1.496 7526.9261 0.0062 B- -1507.6936 4.5065 243 061387.329 1.605
  • Cm-244 52 148 96 244 Cm -a 58451.835 1.106 7523.9527 0.0045 B- -2261.9902 14.3567 244 062750.622 1.187
  • Cm-245 53 149 96 245 Cm 61004.524 1.149 7515.7677 0.0047 B- -809.2519 1.4964 245 065491.047 1.233
  • Cm-246 54 150 96 246 Cm 62616.912 1.525 7511.4716 0.0062 B- -1350.0000 60.0000 246 067222.016 1.637
  • Co-57 3 30 27 57 Co -59345.658 0.516 8741.8845 0.0090 B- -3261.6970 0.6417 56 936289.819 0.553
  • Co-60 6 33 27 60 Co -n -61650.437 0.403 8746.7692 0.0067 B- 2822.8058 0.2124 59 933815.536 0.433
  • Co-60m 6 33 27 60 Co -n -61650.437 0.403 8746.7692 0.0067 B- 2822.8058 0.2124 59 933815.536 0.433 060 0271 60Co m -61591.8 0.4 58.59 0.01
  • Cr-51 3 27 24 51 Cr -51450.715 0.167 8711.9923 0.0033 B- -3207.4893 0.3256 50 944765.388 0.178
  • Cs-134 24 79 55 134 Cs -86891.165 0.016 8398.6470 0.0003 B- 2058.8368 0.2508 133 906718.501 0.017
  • Cs-134m 24 79 55 134 Cs -86891.165 0.016 8398.6470 0.0003 B- 2058.8368 0.2508 133 906718.501 0.017 134 0551 134Csm -86752.421 0.016 138.7441 0.0026
  • Cs-135 25 80 55 135 Cs -87581.956 0.364 8401.3393 0.0027 B- 268.6983 0.2862 134 905976.907 0.390
  • Cs-137 27 82 55 137 Cs + -86545.772 0.302 8388.9581 0.0022 B- 1175.6285 0.1723 136 907089.296 0.324
  • Eu-152 26 89 63 152 Eu -72888.500 1.166 8226.5854 0.0077 B- 1818.8037 0.7002 151 921750.980 1.252
  • Eu-152m1 26 89 63 152 Eu -72888.500 1.166 8226.5854 0.0077 B- 1818.8037 0.7002 151 921750.980 1.252 152 0631 152Eum -72842.9 1.2 45.5998 0.0004
  • Eu-152m2 26 89 63 152 Eu -72888.500 1.166 8226.5854 0.0077 B- 1818.8037 0.7002 151 921750.980 1.252 152 0632 152Eun -72823.2 1.2 65.2969 0.0004
  • Eu-154 28 91 63 154 Eu -71738.367 1.188 8217.1006 0.0077 B- 1967.9913 0.7535 153 922985.699 1.275
  • Eu-154m 28 91 63 154 Eu -71738.367 1.188 8217.1006 0.0077 B- 1967.9913 0.7535 153 922985.699 1.275 154 0631 154Eum -71670.2 1.2 68.1702 0.0004
  • F-18 0 9 9 18 F 873.112 0.463 7631.6383 0.0257 B- -4444.5049 0.5888 18 000937.324 0.497
  • Fe-55 3 29 26 55 Fe -57481.422 0.308 8746.5981 0.0056 B- -3451.4254 0.3241 54 938291.158 0.330
  • Fe-59 7 33 26 59 Fe -60664.957 0.330 8754.7746 0.0056 B- 1564.8804 0.3690 58 934873.492 0.354
  • Ga-67 5 36 31 67 Ga -66879.156 1.176 8707.5330 0.0176 B- -4205.4380 4.4066 66 928202.276 1.262
  • Ga-68 6 37 31 68 Ga - -67086.054 1.430 8701.2195 0.0210 B- -107.2555 2.3594 67 927980.161 1.535
  • Gd-148 20 84 64 148 Gd -76269.419 1.460 8248.3398 0.0099 B- -5732.4723 12.5208 147 918121.414 1.566
  • Ge-68 4 36 32 68 Ge x -66978.799 1.876 8688.1371 0.0276 B- -8084.2715 2.6320 67 928095.305 2.014
  • H-3 0 1 2 1 3 H 14949.81090 0.00008 2827.2654 0.0003 B- 18.59202 0.00006 3 016049.28132 0.00008
  • Hg-203 43 123 80 203 Hg -25269.203 1.630 7887.4828 0.0080 B- 492.1062 1.2247 202 972872.396 1.750
  • Hg-203m 43 123 80 203 Hg -25269.203 1.630 7887.4828 0.0080 B- 492.1062 1.2247 202 972872.396 1.750 203 0801 203Hgm -24336.1 1.6 933.14 0.23
  • Ho-166 32 99 67 166 Ho -63070.339 0.786 8135.4933 0.0047 B- 1853.8057 0.7792 165 932291.209 0.844
  • I-125 19 72 53 125 I - -88836.024 1.353 8450.2911 0.0108 B- -1636.6632 0.4259 124 904630.610 1.452
  • I-129 23 76 53 129 I -88507.176 3.153 8435.9908 0.0244 B- 188.8936 3.1534 128 904983.643 3.385
  • I-131 25 78 53 131 I + -87442.727 0.605 8422.2977 0.0046 B- 970.8477 0.6046 130 906126.375 0.649
  • In-111 13 62 49 111 In -88392.050 3.424 8522.2824 0.0308 B- -2453.4692 6.3368 110 905107.236 3.675
  • In-111m 13 62 49 111 In -88392.050 3.424 8522.2824 0.0308 B- -2453.4692 6.3368 110 905107.236 3.675 111 0491 111Inm -87855 3 536.99 0.07
  • Ir-192 38 115 77 192 Ir -34835.631 1.314 7938.9999 0.0068 B- 1452.8946 2.2739 191 962602.414 1.410
  • Ir-192m1 38 115 77 192 Ir -34835.631 1.314 7938.9999 0.0068 B- 1452.8946 2.2739 191 962602.414 1.410 192 0771 192Irm -34778.9 1.3 56.720 0.005
  • Ir-192m2 38 115 77 192 Ir -34835.631 1.314 7938.9999 0.0068 B- 1452.8946 2.2739 191 962602.414 1.410 192 0772 192Irn -34667.5 1.3 168.14 0.12
  • K-40 2 21 19 40 K -33535.497 0.056 8538.0907 0.0014 B- 1310.9051 0.0596 39 963998.165 0.060
  • Kr-85 13 49 36 85 Kr + -81480.341 2.000 8698.5633 0.0235 B- 687.0000 2.0000 84 912527.260 2.147
  • Kr-85m 13 49 36 85 Kr + -81480.341 2.000 8698.5633 0.0235 B- 687.0000 2.0000 84 912527.260 2.147 085 0361 85Kr m -81175.4 2.0 304.871 0.020
  • Lu-177 35 106 71 177 Lu -52383.903 1.221 8053.4495 0.0069 B- 496.8425 0.7921 176 943763.570 1.310
  • Lu-177m 35 106 71 177 Lu -52383.903 1.221 8053.4495 0.0069 B- 496.8425 0.7921 176 943763.570 1.310 177 0711 177Lum -52233.5 1.2 150.3984 0.0010
  • Mn-54 4 29 25 54 Mn -p -55558.247 1.007 8737.9768 0.0186 B- 696.3688 1.0587 53 940355.772 1.080
  • Mo-99 15 57 42 99 Mo -85970.106 0.229 8607.7982 0.0023 B- 1357.7631 0.8905 98 907707.299 0.245
  • Na-22 0 11 11 22 Na -5181.391 0.132 7915.6624 0.0060 B- -4781.4051 0.1631 21 994437.547 0.141
  • Na-24 2 13 11 24 Na -n -8417.901 0.017 8063.4882 0.0007 B- 5515.6774 0.0210 23 990963.012 0.017
  • Na-24m 2 13 11 24 Na -n -8417.901 0.017 8063.4882 0.0007 B- 5515.6774 0.0210 23 990963.012 0.017 024 0111 24Na m -7945.694 0.017 472.2074 0.0008
  • Nb-95 13 54 41 95 Nb -86786.272 0.508 8647.2133 0.0054 B- 925.6009 0.4938 94 906831.110 0.545
  • Nb-95m 13 54 41 95 Nb -86786.272 0.508 8647.2133 0.0054 B- 925.6009 0.4938 94 906831.110 0.545 095 0411 95Nb m -86550.6 0.5 235.69 0.02
  • Ni-59 3 31 28 59 Ni -61156.833 0.351 8736.5912 0.0060 B- -4798.3786 0.3973 58 934345.442 0.376
  • Ni-63 7 35 28 63 Ni -65512.891 0.426 8763.4955 0.0068 B- 66.9768 0.0149 62 929669.021 0.457
  • Np-237 51 144 93 237 Np 44871.599 1.120 7574.9895 0.0047 B- -220.0630 1.2944 237 048171.640 1.201
  • P-32 2 17 15 32 P -n -24304.876 0.040 8464.1203 0.0013 B- 1710.6608 0.0400 31 973907.643 0.042
  • P-33 3 18 15 33 P + -26337.350 1.090 8513.8073 0.0330 B- 248.5079 1.0900 32 971725.692 1.170
  • Pa-231 49 140 91 231 Pa 33424.338 1.771 7618.4267 0.0077 B- -381.6138 2.0325 231 035882.500 1.901
  • Pb-210 46 128 82 210 Pb -14728.429 1.448 7835.9656 0.0069 B- 63.4758 0.4992 209 984188.381 1.554
  • Pm-147 25 86 61 147 Pm -79041.984 1.288 8284.3712 0.0088 B- 224.0638 0.2940 146 915144.944 1.382
  • Po-210 42 126 84 210 Po -15953.060 1.146 7834.3462 0.0055 B- -3980.9605 7.6101 209 982873.686 1.230
  • Pr-144 26 85 59 144 Pr + -80750.588 2.708 8311.5411 0.0188 B- 2997.4400 2.4000 143 913310.682 2.907
  • Pu-238 50 144 94 238 Pu 46163.148 1.138 7568.3611 0.0048 B- -2258.2731 58.9005 238 049558.175 1.221
  • Pu-239 51 145 94 239 Pu 48588.220 1.112 7560.3187 0.0047 B- -802.1402 1.6635 239 052161.596 1.194
  • Pu-240 52 146 94 240 Pu 50125.319 1.105 7556.0433 0.0046 B- -1384.7902 13.7882 240 053811.740 1.186
  • Pu-241 53 147 94 241 Pu 52955.115 1.105 7546.4395 0.0046 B- 20.7799 0.1658 241 056849.651 1.186
  • Pu-242 54 148 94 242 Pu 54716.876 1.245 7541.3284 0.0052 B- -751.1373 0.7080 242 058740.979 1.336
  • Pu-244 56 150 94 244 Pu 59806.021 2.346 7524.8154 0.0096 B- -73.1143 2.6856 244 064204.401 2.518
  • Ra-223 47 135 88 223 Ra 17233.245 2.090 7685.3101 0.0094 B- -591.8099 6.9657 223 018500.648 2.243
  • Ra-224 48 136 88 224 Ra 18825.832 1.811 7679.9236 0.0081 B- -1408.3152 4.0869 224 020210.361 1.944
  • Ra-226 50 138 88 226 Ra 23667.576 1.927 7661.9636 0.0085 B- -641.6252 3.2730 226 025408.186 2.068
  • Ra-228 52 140 88 228 Ra +a 28940.194 1.995 7642.4289 0.0088 B- 45.5402 0.6344 228 031068.574 2.141
  • Re-188 38 113 75 188 Re -n -39016.880 0.738 7966.7481 0.0039 B- 2120.4209 0.1520 187 958113.658 0.792
  • Re-188m 38 113 75 188 Re -n -39016.880 0.738 7966.7481 0.0039 B- 2120.4209 0.1520 187 958113.658 0.792 188 0751 188Rem -38844.8 0.7 172.0848 0.0024
  • Rh-106 16 61 45 106 Rh -86362.656 5.390 8553.9317 0.0508 B- 3544.8865 5.3348 105 907285.879 5.786
  • Rh-106m 16 61 45 106 Rh -86362.656 5.390 8553.9317 0.0508 B- 3544.8865 5.3348 105 907285.879 5.786 106 0451 106Rhm -86231 10 132 11 BD
  • Ru-106 18 62 44 106 Ru -86323.253 5.391 8560.9406 0.0509 B- 39.4038 0.2121 105 907328.181 5.787
  • S-35 3 19 16 35 S -28846.210 0.040 8537.8511 0.0012 B- 167.3218 0.0257 34 969032.321 0.043
  • Sb-124 22 73 51 124 Sb -n -87619.069 1.358 8456.1517 0.0110 B- 2905.0730 0.1317 123 905937.065 1.457
  • Sb-124m1 22 73 51 124 Sb -n -87619.069 1.358 8456.1517 0.0110 B- 2905.0730 0.1317 123 905937.065 1.457 124 0511 124Sbm -87608.2 1.4 10.8627 0.0008
  • Sb-124m2 22 73 51 124 Sb -n -87619.069 1.358 8456.1517 0.0110 B- 2905.0730 0.1317 123 905937.065 1.457 124 0512 124Sbn -87582.3 1.4 36.8440 0.0014
  • Sb-125 23 74 51 125 Sb + -88255.094 2.515 8458.1612 0.0201 B- 766.7000 2.1213 124 905254.264 2.700
  • Sc-46 4 25 21 46 Sc -n -41761.643 0.671 8622.0215 0.0146 B- 2366.6260 0.6666 45 955167.034 0.720
  • Sc-46m 4 25 21 46 Sc -n -41761.643 0.671 8622.0215 0.0146 B- 2366.6260 0.6666 45 955167.034 0.720 046 0211 46Sc m -41709.6 0.7 52.011 0.001
  • Se-75 7 41 34 75 Se -72169.489 0.073 8678.9139 0.0010 B- -3062.4694 4.2855 74 922522.870 0.078
  • Se-79 11 45 34 79 Se -n -75917.466 0.223 8695.5923 0.0028 B- 150.6016 1.0186 78 918499.252 0.238
  • Si-32 4 18 14 32 Si x -24077.689 0.298 8481.4690 0.0093 B- 227.1872 0.3008 31 974151.538 0.320
  • Sm-147 23 85 62 147 Sm -79266.048 1.262 8280.5734 0.0086 B- -1721.4367 2.2832 146 914904.401 1.354
  • Sm-151 27 89 62 151 Sm -74576.480 1.110 8243.9735 0.0074 B- 76.6182 0.5375 150 919938.859 1.191
  • Sm-153 29 91 62 153 Sm -n -72560.059 1.025 8228.5373 0.0067 B- 807.4073 0.7063 152 922103.576 1.100
  • Sm-153m 29 91 62 153 Sm -n -72560.059 1.025 8228.5373 0.0067 B- 807.4073 0.7063 152 922103.576 1.100 153 0621 153Smm -72461.7 1.0 98.39 0.10
  • Sn-113 13 63 50 113 Sn -88328.129 1.575 8506.8117 0.0139 B- -3911.1637 17.1206 112 905175.857 1.690
  • Sn-113m 13 63 50 113 Sn -88328.129 1.575 8506.8117 0.0139 B- -3911.1637 17.1206 112 905175.857 1.690 113 0501 113Snm -88250.7 1.6 77.389 0.019
  • Sr-85 9 47 38 85 Sr -81103.290 2.813 8675.7193 0.0331 B- -3261.1584 19.1729 84 912932.041 3.020
  • Sr-85m 9 47 38 85 Sr -81103.290 2.813 8675.7193 0.0331 B- -3261.1584 19.1729 84 912932.041 3.020 085 0381 85Sr m -80864.5 2.8 238.79 0.05
  • Sr-89 13 51 38 89 Sr -86209.026 0.092 8705.9230 0.0011 B- 1502.1757 0.3510 88 907450.808 0.098
  • Sr-90 14 52 38 90 Sr -85950.945 1.449 8696.0043 0.0161 B- 545.9674 1.4060 89 907727.870 1.555
  • Ta-182 36 109 73 182 Ta -46430.685 1.578 8012.6332 0.0087 B- 1815.4592 1.5276 181 950154.612 1.693
  • Ta-182m1 36 109 73 182 Ta -46430.685 1.578 8012.6332 0.0087 B- 1815.4592 1.5276 181 950154.612 1.693 182 0731 182Tam -46414.4 1.6 16.273 0.004
  • Ta-182m2 36 109 73 182 Ta -46430.685 1.578 8012.6332 0.0087 B- 1815.4592 1.5276 181 950154.612 1.693 182 0732 182Tan -45911.1 1.6 519.577 0.016
  • Tc-99 13 56 43 99 Tc -87327.869 0.908 8613.6105 0.0092 B- 297.5156 0.9453 98 906249.681 0.974
  • Tc-99m 13 56 43 99 Tc -87327.869 0.908 8613.6105 0.0092 B- 297.5156 0.9453 98 906249.681 0.974 099 0431 99Tc m -87185.2 0.9 142.6836 0.0011
  • Th-228 48 138 90 228 Th 26770.899 1.806 7645.0807 0.0079 B- -2152.6993 4.3399 228 028739.741 1.938
  • Th-229 49 139 90 229 Th 29585.517 2.404 7634.6510 0.0105 B- -311.3310 3.7152 229 031761.357 2.581
  • Th-230 50 140 90 230 Th 30862.512 1.209 7630.9974 0.0053 B- -1311.0313 2.8334 230 033132.267 1.297
  • Th-232 52 142 90 232 Th 35446.710 1.421 7615.0338 0.0061 B- -499.8388 7.7338 232 038053.606 1.525
  • Tl-201 39 120 81 201 Tl -27180.778 14.185 7891.2717 0.0706 B- -1909.7458 18.5299 200 970820.235 15.228
  • Tl-201m 39 120 81 201 Tl -27180.778 14.185 7891.2717 0.0706 B- -1909.7458 18.5299 200 970820.235 15.228 201 0811 201Tlm -26262 14 919.16 0.21
  • Tl-204 42 123 81 204 Tl -24346.070 1.154 7880.0238 0.0057 B- 763.7453 0.1768 203 973863.420 1.238
  • U-232 48 140 92 232 U 34609.445 1.808 7611.8984 0.0078 B- -2750# 100# 232 037154.765 1.941
  • U-233 49 141 92 233 U 36919.111 2.254 7603.9574 0.0097 B- -1029.4197 51.0050 233 039634.294 2.420
  • U-234 50 142 92 234 U 38144.959 1.129 7600.7160 0.0048 B- -1809.8462 8.3205 234 040950.296 1.212
  • U-235 51 143 92 235 U 40918.782 1.116 7590.9151 0.0048 B- -124.2619 0.8524 235 043928.117 1.198
  • U-236 52 144 92 236 U 42444.582 1.112 7586.4854 0.0047 B- -933.5116 50.4152 236 045566.130 1.193
  • U-238 54 146 92 238 U 47307.732 1.492 7570.1262 0.0063 B- -146.8652 1.2006 238 050786.936 1.601
  • U-238m 54 146 92 238 U 47307.732 1.492 7570.1262 0.0063 B- -146.8652 1.2006 238 050786.936 1.601 238 0921 238U m 49865.6 1.6 2557.9 0.5
  • Xe-133 25 79 54 133 Xe + -87643.583 2.400 8412.6477 0.0180 B- 427.3600 2.4000 132 905910.748 2.576
  • Xe-133m 25 79 54 133 Xe + -87643.583 2.400 8412.6477 0.0180 B- 427.3600 2.4000 132 905910.748 2.576 133 0541 133Xem -87410.4 2.4 233.221 0.015
  • Y-88 10 49 39 88 Y - -84299.029 1.500 8682.5396 0.0170 B- -670.1549 5.6076 87 909501.274 1.610
  • Y-88m1 10 49 39 88 Y - -84299.029 1.500 8682.5396 0.0170 B- -670.1549 5.6076 87 909501.274 1.610 088 0391 88Y m -83906.1 1.5 392.86 0.09
  • Y-88m2 10 49 39 88 Y - -84299.029 1.500 8682.5396 0.0170 B- -670.1549 5.6076 87 909501.274 1.610 088 0392 88Y n -83624.5 1.5 674.55 0.04
  • Y-90 12 51 39 90 Y -86496.912 0.354 8693.3778 0.0039 B- 2275.6350 0.3726 89 907141.749 0.379
  • Y-90m 12 51 39 90 Y -86496.912 0.354 8693.3778 0.0039 B- 2275.6350 0.3726 89 907141.749 0.379 090 0391 90Y m -85814.9 0.4 682.01 0.05
  • Y-91 13 52 39 91 Y -86351.321 1.843 8684.9421 0.0203 B- 1544.2710 1.8403 90 907298.048 1.978
  • Zn-65 5 35 30 65 Zn -65912.024 0.646 8724.2660 0.0099 B- -3254.5380 0.6305 64 929240.534 0.693
  • Zr-93 13 53 40 93 Zr -87122.028 0.456 8671.6207 0.0049 B- 90.8123 1.4838 92 906470.661 0.489
  • Zr-95 15 55 40 95 Zr -85659.940 0.869 8643.5924 0.0092 B- 1126.3312 0.9854 94 908040.276 0.933

Worked cases

Each is computed from the definitions with the arithmetic shown, and compared against what the tool returns. They are chosen to span the range: the nuclide the old approximation missed by the most, one at the opposite sign of the mass excess, an isomer where the excitation energy enters, and both directions of the mass–activity conversion.

Case By hand Tool Difference
Tritium — the nuclide the old approximation missed by the most S-W-01 · H-3 3.5598568228×10¹⁴ Bq/g 3.5598568228×10¹⁴ Bq/g 8.47e-12
Cobalt-60 — the mass of one gigabecquerel S-W-02 · Co-60 2.3883787871×10⁻⁵ g 2.3883787871×10⁻⁵ g 9.38e-12
Caesium-137 — the activity of one gram S-W-03 · Cs-137 3.2120175029×10¹² Bq 3.2120175029×10¹² Bq 3.28e-12
Uranium-238 — the other end of the range S-W-04 · U-238 1.2436520396×10⁴ Bq/g 1.2436520396×10⁴ Bq/g 3.86e-11
Barium-137m — an isomer, where the excitation energy enters S-W-05 · Ba-137m 1.9912246323×10¹⁹ Bq/g 1.9912246323×10¹⁹ Bq/g 8.01e-12
Plutonium-239 — one milligram S-W-06 · Pu-239 2.295048073×10⁶ Bq 2.295048073×10⁶ Bq 1.35e-11

S-W-01 — Tritium — the nuclide the old approximation missed by the most

  1. T½ = 388 781 328.006 973 s (12.32 a, from the data set; the half-life itself is checked in the decay report).
  2. M = 3.016 049 281 32 g/mol (AME2020). The mass number is 3, so the substitution M = A would be 0.535% low.
  3. λ = ln 2 / T½ = 0.693 147 180 6 / 388 781 328.007 = 1.782 871 580 1 × 10⁻⁹ /s.
  4. N_A / M = 6.022 140 76 × 10²³ / 3.016 049 281 32 = 1.996 698 × 10²³ atoms per gram.
  5. a = λ · N_A/M = 1.782 871 580 1 × 10⁻⁹ × 1.996 698 × 10²³ = 3.559 856 822 8 × 10¹⁴ Bq/g.
  6. With M = 3 the same arithmetic gives 3.578 9 × 10¹⁴ Bq/g — a 0.53% difference, which is visible at three significant figures.
  7. Which of the two is correct is settled by the definition, not by comparison: the molar mass of a nuclide is its atomic mass expressed in grams per mole, and the mass number is an atom count. No published figure is needed to decide it.
  8. It is nevertheless worth recording that the value this repository carried as a regression fence before this report, 3.56 × 10¹⁴ Bq/g, matches the atomic-mass result to 0.004% and the mass-number result only to 0.53%. That fence was written without a citation and is not treated here as a source; it is noted because it was fixed before the change and therefore could not have been fitted to it.

S-W-02 — Cobalt-60 — the mass of one gigabecquerel

  1. T½ = 166 344 192 s (1925.28 d), M = 59.933 815 536 g/mol.
  2. λ = 0.693 147 180 6 / 166 344 192 = 4.166 945 489 5 × 10⁻⁹ /s.
  3. a = λ · N_A / M = 4.166 945 489 5 × 10⁻⁹ × 6.022 140 76 × 10²³ / 59.933 815 536 = 4.186 940 553 1 × 10¹³ Bq/g.
  4. m = A / a = 1 × 10⁹ / 4.186 940 553 1 × 10¹³ = 2.388 378 787 1 × 10⁻⁵ g, that is 23.9 micrograms.
  5. Cobalt-60 sits near A = 56, where the mass excess is most negative, so here the old approximation erred the other way: M = 60 would have made the source lighter by 0.11%.

S-W-03 — Caesium-137 — the activity of one gram

  1. T½ = 949 232 333.315 727 s (30.08 a), M = 136.907 089 296 g/mol.
  2. λ = 0.693 147 180 6 / 949 232 333.316 = 7.302 186 790 7 × 10⁻¹⁰ /s.
  3. a = 7.302 186 790 7 × 10⁻¹⁰ × 6.022 140 76 × 10²³ / 136.907 089 296 = 3.212 017 502 9 × 10¹² Bq/g.
  4. One gram therefore holds 3.212 × 10¹² Bq, or 86.81 Ci.
  5. This figure is for the caesium alone. Its daughter Ba-137m is in secular equilibrium in a real source and adds its own activity, which this tool does not include — see the refusals below.

S-W-04 — Uranium-238 — the other end of the range

  1. T½ = 1.409 963 452 544 77 × 10¹⁷ s (4.468 × 10⁹ a), M = 238.050 786 936 g/mol.
  2. λ = 0.693 147 180 6 / 1.409 963 452 5 × 10¹⁷ = 4.916 064 876 1 × 10⁻¹⁸ /s.
  3. a = 4.916 064 876 1 × 10⁻¹⁸ × 6.022 140 76 × 10²³ / 238.050 786 936 = 1.243 652 039 6 × 10⁴ Bq/g.
  4. Twelve thousand becquerel per gram against tritium's 3.6 × 10¹⁴ — eleven orders of magnitude, from the half-life alone.
  5. This case exercises the far end of the floating-point range in the same expression as S-W-01, which is where an arithmetic ordering mistake would show itself.

S-W-05 — Barium-137m — an isomer, where the excitation energy enters

  1. T½ = 153.12 s. The ground-state atomic mass from AME2020 is 136.905 827 207 u, and NUBASE2020 gives the isomer 661.659 keV of excitation.
  2. 661.659 keV / 931 494.103 717 keV·u⁻¹ = 7.103 × 10⁻⁴ u, so M = 136.906 537 527 1 g/mol.
  3. λ = 0.693 147 180 6 / 153.12 = 4.526 823 279 5 × 10⁻³ /s.
  4. a = 4.526 823 279 5 × 10⁻³ × 6.022 140 76 × 10²³ / 136.906 537 527 1 = 1.991 224 632 3 × 10¹⁹ Bq/g.
  5. The excitation shifts the answer by 5 × 10⁻⁶ relative — invisible at six figures, and carried anyway because it is known exactly and costs nothing.

S-W-06 — Plutonium-239 — one milligram

  1. T½ = 760 837 485 247.413 s (24 110 a), M = 239.052 161 596 g/mol.
  2. λ = 0.693 147 180 6 / 7.608 374 852 474 × 10¹¹ = 9.110 318 5 × 10⁻¹³ /s.
  3. a = 9.110 318 5 × 10⁻¹³ × 6.022 140 76 × 10²³ / 239.052 161 596 = 2.295 048 073 0 × 10⁹ Bq/g.
  4. One milligram is therefore 2.295 × 10⁶ Bq, about 62 µCi.
  5. This is the isotope alone. Weapons- or reactor-grade plutonium is a mixture in which Pu-241 dominates the activity while contributing little of the mass, so the mass of real material holding a given activity is not this number.

Where the calculator must refuse

A validation that only asks whether right answers are right will never find these. All five were open when this report was written: the engine returned infinity for a half-life or a molar mass of zero, and a negative mass for a negative activity. Each now returns a not-a-number, which the screen renders as no answer rather than as a plausible one.

InputWhy there is no answerRefused
A half-life of zero S-R-01 Nothing has a half-life of zero, and the formula divides by it. Returning infinity would print as a number on the screen and would be the largest specific activity in the table. yes
A negative half-life S-R-02 The arithmetic happily returns a negative specific activity, which is meaningless and would flow through to a negative mass. yes
A molar mass of zero S-R-03 A gram of a substance with no molar mass would hold infinitely many atoms. The guard belongs in the engine because the data file is not the only caller. yes
A negative activity converted to a mass S-R-04 Activity counts decays, so it cannot be negative. Before the guard this returned a negative mass, which is the kind of answer that survives a screenshot. yes
A specific activity of zero S-R-05 A stable nuclide has no specific activity and no finite mass carries a given activity. Infinity is not the answer; there is no answer. yes

What this report does not establish

Primary sources