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 is the
becquerel) 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
In computing, a CURIE (or ''Compact URI'') defines a generic, abbreviated syntax for expressing Uniform Resource Identifiers (URIs). It is an abbreviated URI expressed in a compact syntax, and may be found in both XML and non-XML grammars. A 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
Ionizing radiation (or ionising radiation), including nuclear radiation, consists of subatomic particles or electromagnetic waves that have sufficient energy to ionize atoms or molecules by detaching electrons from them. Some particles can travel ...
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'':
:
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 ...
:
:
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 ato ...
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
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 ''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
Radium (88Ra) has no stable or nearly stable isotopes, and thus a standard atomic weight cannot be given. The longest lived, and most common, isotope of radium is 226Ra with a half-life of . 226Ra occurs in the decay chain of 238U (often referre ...
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
In computing, a CURIE (or ''Compact URI'') defines a generic, abbreviated syntax for expressing Uniform Resource Identifiers (URIs). It is an abbreviated URI expressed in a compact syntax, and may be found in both XML and non-XML grammars. A 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 ato ...
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
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:
:
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 immunoass ...
or other diagnostic procedures, or assessing radioactivity in certain environments, among several other biomedical applications.
References
Further reading
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Units of radioactivity