Radioactive Activity Calculator (from Mass and Half-Life)
Activity in becquerels and curies of a given mass of a radioactive isotope, its specific activity, and how the activity falls over time.
Results
The dashed line marks the value you entered.
What this tool does
Activity — decays per second, measured in becquerels — is the number of atoms times the decay constant ln 2 ÷ T½. That inverse dependence on half-life is the counter-intuitive part: a gram of a short-lived isotope is ferociously active, while a gram of uranium-238, with a half-life of 4.5 billion years, manages only about 12 000 decays per second. The curie was first defined from a gram of radium-226, and with today's half-life of 1600 years the formula gives 0.99 Ci, very close. Years here are Julian years of 365.25 days; enter the mass of the isotope itself, not of the compound.
Formula
A = λN = (ln 2 ÷ T½) × (m ÷ M) × N_A · A(t) = A₀ × 2^(−t ÷ T½)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
m | Mass | g |
mm | Molar mass | g/mol |
hl | Half-life | a |
t | Time elapsed | a |
AB | Activity | GBq |
AC | Activity in curies | Ci |
SA | Specific activity | Bq/g |
AN | Number of atoms | — |
AT | Activity after that time | GBq |
MR | Mass of the isotope left | g |
Worked example
- Mass1 g
- Molar mass226.025 g/mol
- Half-life1600 a
- Time elapsed100 a
- Activity36.576 GBq
- Activity in curies0.98854 Ci
- Specific activity36,575,977,013 Bq/g
- Number of atoms2.66437e+21
- Activity after that time35.0253 GBq
- Mass of the isotope left0.957603 g
Limitations
- Activity counts decays per second. It does not say how dangerous a source is: that depends on the type and energy of the radiation, distance, shielding and exposure time, and is a question for a radiation protection professional.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.