Specific activity

In the context of radioactivity, activity or total activity (symbol A) is a physical quantity defined as the number of radioactive transformations per second that occur in a particular radionuclide.[1] The unit of activity is the becquerel (symbol Bq), which is defined equivalent to reciprocal seconds (symbol s-1). The older, non-SI unit of activity is the curie (Ci), which is 3.7×1010 radioactive decay per second. Another unit of activity is the rutherford, which is defined as 1×106 radioactive decay per second.

Activity
Common symbols
A
SI unitbecquerel
Other units
rutherford, curie
In SI base unitss−1
Specific activity
Common symbols
a
SI unitbecquerel per kilogram
Other units
rutherford per gram, curie per gram
In SI base unitss−1⋅kg−1

Specific activity (symbol a) is the activity per unit mass of a radionuclide and is a physical property of that radionuclide.[2][3] It is usually given in units of becquerel per kilogram (Bq/kg), but another commonly used unit of specific activity is the curie per gram (Ci/g).

The specific activity should not be confused with level of exposure to ionizing radiation and thus the exposure or absorbed dose, which is the quantity important in assessing the effects of ionizing radiation on humans.

Since the probability of radioactive decay for a given radionuclide within a set time interval is fixed (with some slight exceptions, see changing decay rates), the number of decays that occur in a given time of a given mass (and hence a specific number of atoms) of that radionuclide is also a fixed (ignoring statistical fluctuations).

Formulation

Relationship between λ and T1/2

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 N0 is the initial quantity of atoms at time t = 0.

Half-life T1/2 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 T1/2 as

Calculation of specific activity

The mass of the radionuclide is given by

where M is molar mass of the radionuclide, and NA 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 3.2×106 Bq/kg. Rubidium atomic mass is 87 g/mol, so one gram is 1/87 of a mole. Plugging in the numbers:

Other calculations

For a given mass (in grams) of an isotope with atomic mass (in g/mol) and a half-life of (in s), the radioactivity can be calculated using:

With = 6.02214076×1023 mol−1, the Avogadro constant.

Since is the number of moles (), the amount of radioactivity can be calculated by:

For instance, on average each gram of potassium contains 117 micrograms of 40K (all other naturally occurring isotopes are stable) that has a of 1.277×109 years = 4.030×1016 s,[4] and has an atomic mass of 39.964 g/mol,[5] so the amount of radioactivity associated with a gram of potassium is 30 Bq.

Examples

IsotopeHalf-lifeMass of 1 curieSpecific activity (Ci/g)
232Th1.405×1010 years9.1 tonnes1.1×10−7 (110,000 pCi/g, 0.11 μCi/g)
238U4.471×109 years2.977 tonnes3.4×10−7 (340,000 pCi/g, 0.34 μCi/g)
235U7.038×108 years463 kg2.2×10−6 (2,160,000 pCi/g, 2.2 μCi/g)
40K1.25×109 years140 kg7.1×10−6 (7,100,000 pCi/g, 7.1 μCi/g)
129I15.7×106 years5.66 kg0.00018
99Tc211×103 years58 g0.017
239Pu24.11×103 years16 g0.063
240Pu6563 years4.4 g0.23
14C5730 years0.22 g4.5
226Ra1601 years1.01 g0.99
241Am432.6 years0.29 g3.43
238Pu88 years59 mg17
137Cs30.17 years12 mg83
90Sr28.8 years7.2 mg139
241Pu14 years9.4 mg106
3H12.32 years104 μg9,621
228Ra5.75 years3.67 mg273
60Co1925 days883 μg1,132
210Po138 days223 μg4,484
131I8.02 days8 μg125,000
123I13 hours518 ng1,930,000
212Pb10.64 hours719 ng1,390,000

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.[6][7][8][9][10][11]

References

  1. "SI units for ionizing radiation: becquerel". Resolutions of the 15th CGPM (Resolution 8). 1975. Retrieved 3 July 2015.
  2. Breeman, Wouter A. P.; Jong, Marion; Visser, Theo J.; Erion, Jack L.; Krenning, Eric P. (2003). "Optimising conditions for radiolabelling of DOTA-peptides with 90Y, 111In and 177Lu 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. S2CID 9652140.
  3. 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. S2CID 97433328.
  4. "Table of Isotopes decay data". Lund University. 1990-06-01. Retrieved 2014-01-12.
  5. "Atomic Weights and Isotopic Compositions for All Elements". NIST. Retrieved 2014-01-12.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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. 115 (2): 263–288. doi:10.1007/BF02037443. ISSN 0236-5731. S2CID 94361207.

Further reading

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