Specific activity (symbol a) is the activity per unit mass of a radionuclide and is a physical property of that radionuclide. 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). 1 Ci/g = 37 TBq/kg.
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. 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 radioactive decays per second (37 GBq). Another unit of activity is the rutherford (Rd), which is defined as radioactive decays per second (1 MBq).
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 . Rubidium atomic mass is 87 g mol−1, so one gram is 1/87 of a mole. Plugging in the numbers:
Other calculations
For a given mass m (in grams) of an isotope with atomic mass ma (in g mol−1) and a half-life of t1/2 (in s), the radioactivity can be calculated using:
With = , 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 t1/2 of = , and has an atomic mass of 39.964 g/mol, so the amount of radioactivity associated with a gram of potassium is 30 Bq.
Examples IsotopeHalf-lifeMass of 1 curieSpecific Activity (a) (activity per 1 kg) 232Th years 9.1 tonnes 4.07 MBq (110 μCi or 4.07 Rd) 238U years 2.977 tonnes 12.58 MBq (340 μCi, or 12.58 Rd) 235U years 463 kg 79.92 MBq (2.160 mCi, or 79.92 Rd) 40K years140 kg 262.7 MBq (7.1 mCi, or 262.7 Rd) 129I years5.66 kg 6.66 GBq (180 mCi, or 6.66 kRd) 99Tc years58 g 629 GBq (17 Ci, or 629 kRd) 239Pu years16 g 2.331 TBq (63 Ci, or 2.331 MRd) 240Pu 6563 years 4.4 g 8.51 TBq (230 Ci, or 8.51MRd) 14C 5730 years0.22 g 166.5 TBq (4.5 kCi, or 166.5 MRd) 226Ra 1601 years 1.01 g 36.63 TBq (990 Ci, or 36.63 MRd) 241Am 432.6 years 0.29 g 126.91 TBq (3.43 kCi, or 126.91 MRd) 238Pu 88 years 59 mg 629 TBq (17 kCi, or 629 MRd) 137Cs 30.17 years 12 mg 3.071 PBq (83 kCi, or 3.071 GRd) 90Sr 28.8 years 7.2 mg 5.143 PBq (139 kCi, or 5.143 GRd) 241Pu 14 years 9.4 mg 3.922 PBq (106 kCi, or 3.922 GRd) 3H 12.32 years 104 μg 355.977 PBq (9.621 MCi, or 355.977 GRd) 228Ra 5.75 years3.67 mg 10.101 PBq (273 kCi, or 10.101 GRd) 60Co 1925 days883 μg 41.884 PBq (1.132 MCi, or 41.884 GRd) 210Po 138 days223 μg 165.908 PBq (4.484 MCi, or 165.908 GRd) 131I 8.02 days8 μg 4.625 EBq (125 MCi, or 4.625 TRd) 123I 13 hours518 ng 71.41 EBq (1.93 GCi, or 71.41 TRd) 212Pb 10.64 hours719 ng 51.43 EBq (1.39 GCi, or 51.43 TRd)
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.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.
References
Further reading