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Bq/g
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Ci/g
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TBq/g
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s⁻¹
4.5969e+21
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Bq/g
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Ci/g
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TBq/g
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s⁻¹
4.5969e+21
The Specific Activity Calculator computes the radioactive activity per unit mass of a pure radioactive isotope, using the decay constant, Avogadro's number, and the molar mass. Specific activity is a fundamental property that depends only on the isotope's half-life and atomic mass—it is the maximum possible activity per gram for a carrier-free (isotopically pure) sample.
The formula is \(SA = \frac{\lambda N_A}{M}\), where \(\lambda = \ln 2 / t_{1/2}\) is the decay constant, \(N_A = 6.022 \times 10^{23}\) is Avogadro's number, and \(M\) is the molar mass in g/mol. The result is typically expressed in Bq/g, Ci/g, or TBq/g.
Specific activity varies enormously between isotopes. Short-lived isotopes have extremely high specific activity: technetium-99m (\(t_{1/2} = 6\) hours) has \(SA \approx 5.3 \times 10^{18}\) Bq/g, meaning a tiny fraction of a microgram produces billions of becquerels. In contrast, long-lived isotopes have low specific activity: uranium-238 (\(t_{1/2} = 4.47 \times 10^9\) years) has only \(SA \approx 1.24 \times 10^4\) Bq/g, which is why natural uranium can be handled with minimal shielding.
This quantity is essential in nuclear medicine for preparing radiopharmaceutical doses: knowing the specific activity tells you how much mass corresponds to the prescribed activity. In radiation safety, specific activity determines the classification and handling requirements of radioactive materials. In environmental science, specific activity helps quantify contamination levels.
Specific activity is also the key to understanding why some isotopes are practical for certain applications and others are not. A medical imaging isotope needs high specific activity (small mass = high activity) so the chemical dose is negligible. A geological dating isotope needs low specific activity (long half-life) so it persists for the timescale being measured.
The concept of specific activity also applies to mixtures and labeled compounds, where the actual specific activity may be lower than the carrier-free maximum due to the presence of stable isotopes of the same element ("carrier").
The specific activity formula combines the decay constant with Avogadro's number:
$$SA = \frac{\lambda \cdot N_A}{M} = \frac{\ln 2}{t_{1/2}} \cdot \frac{N_A}{M}$$
where:
Unit conversions:
$$SA_{Ci/g} = \frac{SA_{Bq/g}}{3.7 \times 10^{10}}$$
$$SA_{TBq/g} = \frac{SA_{Bq/g}}{10^{12}}$$
The atoms per gram is simply \(N_A / M\).
Higher specific activity means more radiation per gram of material. Isotopes with short half-lives have very high specific activity—even nanograms produce significant radiation. Isotopes with long half-lives have low specific activity and can exist in macroscopic quantities. If your result seems extremely large (>10¹⁸ Bq/g), the isotope is very short-lived and only picogram-scale quantities are typically handled.
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I-131 has a specific activity of about 4,597 TBq/g (~124,000 Ci/g). A typical thyroid therapy dose of 3,700 MBq requires less than 1 microgram of pure I-131.
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U-238 has only about 12,400 Bq/g (~0.34 μCi/g), which is why natural uranium can be handled safely with basic precautions despite being radioactive.
Specific activity is the radioactive activity per unit mass of a pure isotope sample, typically expressed in Bq/g or Ci/g. It is an intrinsic property depending only on the isotope's half-life and atomic mass. Higher specific activity means more radioactive decays per gram of material.
Carrier-free specific activity is the theoretical maximum—the activity per gram when the sample contains only the radioactive isotope with no stable isotopes of the same element. In practice, samples often contain carrier (stable isotopes), reducing the effective specific activity below the theoretical maximum.
A short half-life means a large decay constant (λ = ln2/t½), which means each atom has a high probability of decaying per second. Since specific activity is λ×Nₐ/M, a larger λ directly increases the activity per gram. Essentially, short-lived atoms decay so quickly that even a small number produces intense radiation.
In nuclear medicine, specific activity determines how much mass of a radiopharmaceutical corresponds to the prescribed activity. High specific activity is desirable because it means the chemical amount injected is negligible—avoiding pharmacological effects and ensuring the tracer truly traces without perturbing the system being studied.
The specific activity of a pure isotope sample does not change over time—as atoms decay, both the total activity and the total mass decrease proportionally. However, if the decay produces another radioactive isotope (daughter), the apparent specific activity of the mixed sample can change as the daughter builds up.
Some reference values: Tc-99m: ~5.3×10¹⁸ Bq/g; I-131: ~4.6×10¹⁵ Bq/g; Co-60: ~4.2×10¹³ Bq/g; Cs-137: ~3.2×10¹² Bq/g; Ra-226: ~3.7×10¹⁰ Bq/g (1 Ci/g by definition); U-238: ~1.24×10⁴ Bq/g. This 14-order-of-magnitude range reflects the enormous variation in half-lives.
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