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Bq/g
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Bq/g
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Bq/mol
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s⁻¹
The Specific Activity Calculator determines the activity per unit mass of a pure radioactive isotope. Specific activity $$SA = \lambda N_A / M$$ is an intrinsic property of each radionuclide, depending only on its half-life and molar mass. It tells you how "hot" a gram of pure isotope is and sets the theoretical maximum activity achievable for any given mass of that substance.
Specific activity is crucial in radiopharmacy for calculating required masses of radioactive drugs, in waste management for classifying materials by activity concentration, and in research for determining the radiochemical purity of labeled compounds. This calculator provides results in both SI (Bq/g) and conventional (Ci/g) units.
Specific activity is defined as the activity per unit mass of a pure radionuclide:
$$SA = \frac{\lambda \cdot N_A}{M} = \frac{\ln(2) \cdot N_A}{t_{1/2} \cdot M}$$
where:
$$\lambda$$ = decay constant (s⁻¹)
$$N_A = 6.022 \times 10^{23}$$ mol⁻¹ (Avogadro's number)
$$M$$ = molar mass (g/mol)
$$t_{1/2}$$ = half-life (seconds)
This formula comes from the activity equation $$A = \lambda N$$ applied to one gram: the number of atoms in one gram is $$N = N_A/M$$, so $$A_{\text{per gram}} = \lambda N_A/M$$. Shorter half-lives and smaller molar masses give higher specific activities because the atoms decay faster and there are more atoms per gram.
Specific Activity (Bq/g) is the number of disintegrations per second in one gram of pure isotope. Specific Activity (Ci/g) expresses the same quantity in curies. For perspective, the specific activity of Ra-226 is exactly 1 Ci/g by the historical definition of the curie. The Specific Activity (Bq/mol) gives the activity of one mole of the pure isotope. Very short-lived isotopes have enormous specific activities, meaning even tiny masses produce intense radiation.
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Pure C-14 has a specific activity of ~4.46 Ci/g. In practice, C-14 labeled compounds have much lower specific activities because only a fraction of carbon atoms are C-14.
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I-131 has an extremely high specific activity of ~124 kCi/g due to its short half-life. Therapeutic doses of ~100 mCi require less than a microgram of material.
Specific activity is the activity per unit mass of a radioactive substance, typically expressed in Bq/g or Ci/g. For a carrier-free (pure) radionuclide, it depends only on the half-life and molar mass: $$SA = \ln(2) \cdot N_A / (t_{1/2} \cdot M)$$. It represents the maximum possible activity concentration for that isotope.
In nuclear medicine, high specific activity ensures that therapeutic or diagnostic effects come from minimal mass of material. This is critical because the chemical mass of the radiopharmaceutical can affect its biological behavior. Carrier-free or high specific activity preparations minimize pharmacological side effects while delivering the required radioactivity.
Carrier-free means a radioactive sample contains no stable isotopes of the same element. The specific activity equals the theoretical maximum. In practice, some stable isotope "carrier" is usually present, reducing the specific activity below the theoretical value.
Among commonly used isotopes, shorter-lived ones have higher specific activities. Fluorine-18 (t½ = 110 min) has SA ≈ 6.3 × 10⁴ Ci/g, while Tc-99m (t½ = 6 hr) has SA ≈ 5.3 × 10 Ci/g. Extremely short-lived nuclear states can have astronomically high specific activities.
Radioactive waste is classified based on activity concentration (specific activity). Low-level waste (LLW) typically contains less than 4 GBq/t of alpha emitters. Intermediate and high-level waste have progressively higher activity concentrations, requiring more stringent containment and longer isolation periods.
For a pure isotope in isolation, the specific activity remains constant because both the activity and mass decrease at the same rate. However, if decay products accumulate and add to the total mass, or if the sample contains mixed isotopes, the effective specific activity of the mixture changes over time.
Natural uranium (99.27% U-238, 0.72% U-235, 0.005% U-234) has a combined specific activity of about 25.4 kBq/g. Despite being mostly long-lived U-238, the trace U-234 contributes significantly due to its much shorter half-life.
Specific activity is determined by measuring the activity of a known mass of material. The activity is measured using calibrated radiation detectors (ionization chambers, scintillation counters, or semiconductor detectors), and the mass is determined by weighing or chemical analysis.
Volumetric activity (or activity concentration) is activity per unit volume, measured in Bq/L or Bq/m³. It is commonly used for liquid and gaseous radioactive materials, such as monitoring radon levels in air (Bq/m³) or tritium in water (Bq/L).
Heavier atoms have fewer atoms per gram ($$N = N_A/M$$). Since activity depends on atom count ($$A = \lambda N$$), heavier isotopes have lower specific activity for the same half-life. This is why tritium (M = 3) has much higher specific activity than C-14 (M = 14) despite having a shorter half-life.
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