Specific Activity Calculator:
Enter the values of half-life, T1/2(s) and molar mass, M(g/mol) to determine the value of Specific Activity, a(Bq/g).
Specific Activity Formula:
Specific Activity is a measure of the radioactivity of a particular isotope per unit mass of the element or compound in which it is found. It is expressed as the decay rate (disintegrations per second) per gram of a substance.
It is typically used in radiochemistry, nuclear medicine, and radiopharmaceuticals to quantify the purity and intensity of radioactive materials. Specific Activity is defined as the activity of a radionuclide divided by its mass, where activity refers to the number of radioactive decays occurring per unit time.
The higher the specific activity, the greater the number of radioactive atoms per gram, making the substance more potent in terms of radiation emission. It is influenced by the isotope’s half-life, which determines the rate at which it decays over time.
Shorter half-life isotopes have higher specific activity because they undergo decay more rapidly compared to those with longer half-lives. The formula accounts for the inverse relationship between specific activity and half-life, meaning isotopes with shorter half-lives have higher specific activity values.
It is particularly significant in medical applications where radiopharmaceuticals with high specific activity ensure effective treatment with minimal substance quantity. In nuclear physics, it helps in determining the level of radioactivity of various isotopes used in power generation, research, and industrial applications.
It is measured in units such as Becquerels per gram (Bq/g) or Curies per gram (Ci/g), where 1 Becquerel corresponds to one disintegration per second. The value of specific activity helps in comparing different radioactive isotopes and selecting the appropriate isotope for a particular application.
Specific Activity, a(Bq/g) in Becquerel per gram equals 1.32 * 1016 divided by the product of half-life, T1/2(s) in seconds and molar mass, M(g/mol) in grams per mole.
Specific Activity, a(Bq/g) = 1.32 * 1016 / T1/2(s) * M(g/mol)
a(Bq/g) = specific activity in Becquerel per gram, Bq/g.
T1/2(s) = half-life in seconds, s.
M(g/mol) = molar mass in gram per mole, g/mol.
Specific Activity Calculation:
- A radioactive isotope has a half-life of 24 hours and a molar mass of 60 g/mol. Calculate its specific activity.
Given: T1/2(s) = 86400s, M(g/mol) = 60g/mol.
Specific Activity, a(Bq/g) = 1.32 * 1016 / T1/2(s) * M(g/mol)
a(Bq/g) = 1.32 * 1016 / 86400 * 60
a(Bq/g) = 1.32 * 1016 / 51840
a(Bq/g) =2546Bq/g.
- A radioactive element has a specific activity of 4 × 108 Bq/g and a molar mass of 90 g/mol. Calculate its half-life.
Given: a(Bq/g) = 4 * 108Bq/g, M(g/mol) = 90g/mol.
Specific Activity, a(Bq/g) = 1.32 * 1016 / T1/2(s) * M(g/mol)
T1/2(s) = 1.32 * 1016 / a(Bq/g) * M(g/mol)
T1/2(s) = 1.32 * 1016 / 4 * 108 * 90
T1/2(s) = 3.67 * 105s.