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Specific activity is the activity per unit mass of a
radionuclide A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation; transfer ...
and is a physical property of that radionuclide. Activity is a quantity (for which the
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
is the
becquerel The becquerel (; symbol: Bq) is the unit of radioactivity in the International System of Units (SI). One becquerel is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. For applications relat ...
) related to radioactivity, and is defined as the number of radioactive transformations per second that occur in a particular radionuclide. The unit of activity is the becquerel (Bq), which is defined as one radioactive decay per second. The older, non-SI unit of activity is the curie (Ci), which is radioactive decay per second. Another unit of activity is the Rutherford, which is defined as radioactive decay per second. Since the probability of
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...
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). Thus, specific activity is defined as the activity per unit mass of a particular radionuclide. It is usually given in units of Bq/kg, but another commonly used unit of activity is the curie (Ci), allowing specific activity to be given the unit 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 Absorbed dose is a dose quantity which is the measure of the energy deposited in matter by ionizing radiation per unit mass. Absorbed dose is used in the calculation of dose uptake in living tissue in both radiation protection (reduction of harmf ...
is the quantity important in assessing the effects of ionizing radiation on humans.


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'': : -\frac = \lambda N. The integral solution is described by
exponential decay A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate ...
: : N = N_0 e^, where ''N''0 is the initial quantity of atoms at time ''t'' = 0.
Half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable at ...
T1/2 is defined as the length of time for half of a given quantity of radioactive atoms to undergo radioactive decay: : \frac = N_0 e^. Taking the natural logarithm of both sides, the half-life is given by : T_ = \frac. Conversely, the decay constant ''λ'' can be derived from the half-life ''T''1/2 as : \lambda = \frac.


Calculation of specific activity

The mass of the radionuclide is given by : = \frac
text Text may refer to: Written word * Text (literary theory), any object that can be read, including: **Religious text, a writing that a religious tradition considers to be sacred **Text, a verse or passage from scripture used in expository preachin ...
\times
text Text may refer to: Written word * Text (literary theory), any object that can be read, including: **Religious text, a writing that a religious tradition considers to be sacred **Text, a verse or passage from scripture used in expository preachin ...
where ''M'' is
molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecula ...
of the radionuclide, and ''N''A is the
Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining con ...
. Practically, the
mass number The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approxima ...
''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: : a
text Text may refer to: Written word * Text (literary theory), any object that can be read, including: **Religious text, a writing that a religious tradition considers to be sacred **Text, a verse or passage from scripture used in expository preachin ...
= \frac = \frac. Thus, specific radioactivity can also be described by : a = \frac. This equation is simplified to : a
text Text may refer to: Written word * Text (literary theory), any object that can be read, including: **Religious text, a writing that a religious tradition considers to be sacred **Text, a verse or passage from scripture used in expository preachin ...
\approx \frac. When the unit of half-life is in years instead of seconds: : a
text Text may refer to: Written word * Text (literary theory), any object that can be read, including: **Religious text, a writing that a religious tradition considers to be sacred **Text, a verse or passage from scripture used in expository preachin ...
= \frac \approx \frac.


Example: specific activity of Ra-226

For example, specific radioactivity of radium-226 with a half-life of 1600 years is obtained as : a_\text
text Text may refer to: Written word * Text (literary theory), any object that can be read, including: **Religious text, a writing that a religious tradition considers to be sacred **Text, a verse or passage from scripture used in expository preachin ...
= \frac \approx 3.7 \times 10^
text Text may refer to: Written word * Text (literary theory), any object that can be read, including: **Religious text, a writing that a religious tradition considers to be sacred **Text, a verse or passage from scripture used in expository preachin ...
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 Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable at ...
of a radionuclide. Where decay constant ''λ'' is related to specific radioactivity ''a'' by the following equation: : \lambda = \frac. Therefore, the half-life can also be described by : T_ = \frac.


Example: half-life of Rb-87

One gram of
rubidium-87 Rubidium (37Rb) has 36 isotopes, with naturally occurring rubidium being composed of just two isotopes; 85Rb (72.2%) and the radioactive 87Rb (27.8%). Normal mixes of rubidium are radioactive enough to fog photographic film in approximately 30 to ...
and a radioactivity count rate that, after taking
solid angle In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The po ...
effects into account, is consistent with a decay rate of 3200 decays per second corresponds to a specific activity of . Rubidium
atomic mass The atomic mass (''m''a or ''m'') is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1&nbs ...
is 87 g/mol, so one gram is 1/87 of a mole. Plugging in the numbers: : T_ = \frac \approx \frac \approx 1.5 \times 10^\text \approx 47\text.


Examples


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 An immunoassay (IA) is a biochemical test that measures the presence or concentration of a macromolecule or a small molecule in a solution through the use of an antibody (usually) or an antigen (sometimes). The molecule detected by the immunoassa ...
or other diagnostic procedures, or assessing radioactivity in certain environments, among several other biomedical applications.


References


Further reading

* * * {{Authority control Units of radioactivity