Specific activity

Last updated
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
Ra 226 radiation source. Activity 3300 Bq (3.3 kBq) Radium 226 radiation source 1.jpg
Ra 226 radiation source. Activity 3300 Bq (3.3 kBq)

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.

Contents

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)
232Th 1.405×1010 years9.1 tonnes1.1×10−7 (110,000 pCi/g, 0.11 μCi/g)
238U 4.471×109 years2.977 tonnes3.4×10−7 (340,000 pCi/g, 0.34 μCi/g)
235U 7.038×108 years463 kg2.2×10−6 (2,160,000 pCi/g, 2.2 μCi/g)
40K 1.25×109 years140 kg7.1×10−6 (7,100,000 pCi/g, 7.1 μCi/g)
129I 15.7×106 years5.66 kg0.00018
99Tc 211×103 years58 g0.017
239Pu 24.11×103 years16 g0.063
240Pu 6563 years4.4 g0.23
14C 5730 years0.22 g4.5
226Ra 1601 years1.01 g0.99
241Am 432.6 years0.29 g3.43
238Pu 88 years59 mg17
137Cs 30.17 years12 mg83
90Sr 28.8 years7.2 mg139
241Pu 14 years9.4 mg106
3H 12.32 years104 μg9,621
228Ra 5.75 years3.67 mg273
60Co 1925 days883 μg1,132
210Po 138 days223 μg4,484
131I 8.02 days8 μg125,000
123I 13 hours518 ng1,930,000
212Pb 10.64 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]

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References

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Further reading