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Activity | |
---|---|
Common symbols | A |
SI unit | becquerel |
Other units | rutherford, curie |
In SI base units | s^{−1} |
Specific activity | |
---|---|
Common symbols | a |
SI unit | becquerel per kilogram |
Other units | rutherford per gram, curie per gram |
In SI base units | s^{−1} kg^{−1} |
Specific activity is the activity per quantity of a radionuclide and is a physical property of that radionuclide.^{[1]}^{[2]}
Activity is a quantity related to radioactivity, for which the SI unit is the becquerel (Bq), equal to one reciprocal second.^{[3]} The becquerel is defined as the number of radioactive transformations per second that occur in a particular radionuclide. The older, non-SI unit of activity is the curie (Ci), which is 3.7×10^{10} transformations per second.
Since the probability of radioactive decay for a given radionuclide is a fixed physical quantity (with some slight exceptions, see changing decay rates), the number of decays that occur in a given time of a specific number of atoms of that radionuclide is also a fixed physical quantity (if there are large enough numbers of atoms to ignore statistical fluctuations).
Thus, specific activity is defined as the activity per quantity of atoms of a particular radionuclide. It is usually given in units of Bq/g, but another commonly used unit of activity is the curie (Ci) allowing the definition of specific activity in Ci/g. The amount of specific activity should not be confused with level of exposure to ionizing radiation and thus the exposure or absorbed dose. The absorbed dose is the quantity important in assessing the effects of ionizing radiation on humans.
Formulation
Relationship between λ and T_{1/2}
Radioactivity is expressed as the decay rate of a particular radionuclide with decay constant λ and the number of atoms N:
The integral solution is described by exponential decay:
where N_{0} is the initial quantity of atoms at time t = 0.
Half-life T_{1/2} is defined as the length of time for half of a given quantity of radioactive atoms to undergo radioactive decay:
Taking the natural logarithm of both sides, the half-life is given by
Conversely, the decay constant λ can be derived from the half-life T_{1/2} as
Calculation of specific activity
The mass of the radionuclide is given by
where M is molar mass of the radionuclide, and N_{A} is the Avogadro constant. Practically, the mass number A of the radionuclide is within a fraction of 1% of the molar mass expressed in g/mol and can be used as an approximation.
Specific radioactivity a is defined as radioactivity per unit mass of the radionuclide:
Thus, specific radioactivity can also be described by
This equation is simplified to
When the unit of half-life is in years instead of seconds:
Example: specific activity of Ra-226
For example, specific radioactivity of radium-226 with a half-life of 1600 years is obtained as
This value derived from radium-226 was defined as unit of radioactivity known as the curie (Ci).
Calculation of half-life from specific activity
Experimentally measured specific activity can be used to calculate the half-life of a radionuclide.
Where decay constant λ is related to specific radioactivity a by the following equation:
Therefore, the half-life can also be described by
Example: half-life of Rb-87
One gram of rubidium-87 and a radioactivity count rate that, after taking solid angle effects into account, is consistent with a decay rate of 3200 decays per second corresponds to a specific activity of 3.2×10^{6} Bq/kg. Rubidium atomic mass is 87 g/mol, so one gram is 1/87 of a mole. Plugging in the numbers:
Applications
The specific activity of radionuclides is particularly relevant when it comes to select them for production for therapeutic pharmaceuticals, as well as for immunoassays or other diagnostic procedures, or assessing radioactivity in certain environments, among several other biomedical applications.^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}^{[9]}
Quantity | Unit | Symbol | Derivation | Year | SI equivalence |
---|---|---|---|---|---|
Activity (A) | becquerel | Bq | s^{−1} | 1974 | SI unit |
curie | Ci | 3.7 × 10^{10} s^{−1} | 1953 | 3.7×10^{10} Bq | |
rutherford | Rd | 10^{6} s^{−1} | 1946 | 1,000,000 Bq | |
Exposure (X) | coulomb per kilogram | C/kg | C⋅kg^{−1} of air | 1974 | SI unit |
röntgen | R | esu / 0.001293 g of air | 1928 | 2.58 × 10^{−4} C/kg | |
Absorbed dose (D) | gray | Gy | J⋅kg^{−1} | 1974 | SI unit |
erg per gram | erg/g | erg⋅g^{−1} | 1950 | 1.0 × 10^{−4} Gy | |
rad | rad | 100 erg⋅g^{−1} | 1953 | 0.010 Gy | |
Equivalent dose (H) | sievert | Sv | J⋅kg^{−1} × W_{R} | 1977 | SI unit |
röntgen equivalent man | rem | 100 erg⋅g^{−1} x W_{R} | 1971 | 0.010 Sv |
References
- ^ Breeman, Wouter A. P.; Jong, Marion; Visser, Theo J.; Erion, Jack L.; Krenning, Eric P. (2003). "Optimising conditions for radiolabelling of DOTA-peptides with ^{90}Y, ^{111}In and ^{177}Lu at high specific activities". European Journal of Nuclear Medicine and Molecular Imaging. 30 (6): 917–920. doi:10.1007/s00259-003-1142-0. ISSN 1619-7070. PMID 12677301.
- ^ de Goeij, J. J. M.; Bonardi, M. L. (2005). "How do we define the concepts specific activity, radioactive concentration, carrier, carrier-free and no-carrier-added?". Journal of Radioanalytical and Nuclear Chemistry. 263 (1): 13–18. doi:10.1007/s10967-005-0004-6. ISSN 0236-5731.
- ^ "SI units for ionizing radiation: becquerel". Resolutions of the 15th CGPM (Resolution 8). 1975. Retrieved 3 July 2015.
- ^ Duursma, E. K. "Specific activity of radionuclides sorbed by marine sediments in relation to the stable element composition". Radioactive contamination of the marine environment (1973): 57–71.
- ^ Wessels, Barry W. (1984). "Radionuclide selection and model absorbed dose calculations for radiolabeled tumor associated antibodies". Medical Physics. 11 (5): 638–645. Bibcode:1984MedPh..11..638W. doi:10.1118/1.595559. ISSN 0094-2405. PMID 6503879.
- ^ I. Weeks, I. Beheshti, F. McCapra, A. K. Campbell, J. S. Woodhead (August 1983). "Acridinium esters as high-specific-activity labels in immunoassay". Clinical Chemistry. 29 (8): 1474–1479. doi:10.1093/clinchem/29.8.1474. PMID 6191885.CS1 maint: uses authors parameter (link)
- ^ Neves, M.; Kling, A.; Lambrecht, R. M. (2002). "Radionuclide production for therapeutic radiopharmaceuticals". Applied Radiation and Isotopes. 57 (5): 657–664. doi:10.1016/S0969-8043(02)00180-X. ISSN 0969-8043. PMID 12433039.
- ^ Mausner, Leonard F. (1993). "Selection of radionuclides for radioimmunotherapy". Medical Physics. 20 (2): 503–509. Bibcode:1993MedPh..20..503M. doi:10.1118/1.597045. ISSN 0094-2405. PMID 8492758.
- ^ Murray, A. S.; Marten, R.; Johnston, A.; Martin, P. (1987). "Analysis for naturally occuring [sic] radionuclides at environmental concentrations by gamma spectrometry". Journal of Radioanalytical and Nuclear Chemistry Articles. 115 (2): 263–288. doi:10.1007/BF02037443. ISSN 0236-5731.
Further reading
- Fetter, Steve; Cheng, E. T.; Mann, F. M. (1990). "Long-term radioactive waste from fusion reactors: Part II". Fusion Engineering and Design. 13 (2): 239–246. CiteSeerX 10.1.1.465.5945. doi:10.1016/0920-3796(90)90104-E. ISSN 0920-3796.
- Holland, Jason P.; Sheh, Yiauchung; Lewis, Jason S. (2009). "Standardized methods for the production of high specific-activity zirconium-89". Nuclear Medicine and Biology. 36 (7): 729–739. doi:10.1016/j.nucmedbio.2009.05.007. ISSN 0969-8051. PMC 2827875. PMID 19720285.
- McCarthy, Deborah W.; Shefer, Ruth E.; Klinkowstein, Robert E.; Bass, Laura A.; Margeneau, William H.; Cutler, Cathy S.; Anderson, Carolyn J.; Welch, Michael J. (1997). "Efficient production of high specific activity ^{64}Cu using a biomedical cyclotron". Nuclear Medicine and Biology. 24 (1): 35–43. doi:10.1016/S0969-8051(96)00157-6. ISSN 0969-8051. PMID 9080473.