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Radionuclide Activity, Specific Activity & Half-Life

Calculate activity and specific activity from the mass, molar mass and half-life of a single radionuclide using the exact Avogadro constant.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

For one mole of a radionuclide with a one-second half-life, activity is NA × ln(2), approximately 4.1742 × 10²³ Bq.

A = (m/M) NA ln(2)/t½; specific activity = NA ln(2)/(M t½)

Worked example

Enter these known values and leave the other values blank.

Mass of the radionuclide
1 g
Radionuclide molar mass
1 g /mol
Half-life
1 sec
Activity
4.17422988872912627121233e+23 Bq
Specific activity per kilogram
4.17422988872912627121232541e+26 Bq /kg

Assumptions and limitations

  • Enter the mass of the radioactive isotope itself, not total mixture mass unless it is pure. A single decay constant is assumed; daughter activity and decay chains are excluded.
  • Half-life and molar mass must be positive. Zero isotope mass gives zero total activity; specific activity remains a property of the isotope.
  • Activity is decay rate, not radiation dose, shielding requirement or detector count rate. Specific activity is displayed per kilogram regardless of the mass unit chosen above.
  • The Avogadro constant is exactly 6.02214076 × 10²³ mol⁻¹.

Common questions

What assumptions matter for this calculation?

Enter the mass of the radioactive isotope itself, not total mixture mass unless it is pure. A single decay constant is assumed; daughter activity and decay chains are excluded.

References

Bookify uses the exact SI Avogadro constant and accepts zero isotope mass and total activity.

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