This articlemay be too technical for most readers to understand. Pleasehelp improve it tomake it understandable to non-experts, without removing the technical details.(January 2014) (Learn how and when to remove this message)

Activity
Ra 226 radiation source. Activity 3300 Bq (3.3 kBq)
Common symbols	A
SI unit	becquerel
Other units	rutherford,curie
InSI base units	s−1

Specific activity (symbola) is the activityper unit mass of aradionuclide and is a physical property of that radionuclide.^[1][2]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).

In the context ofradioactivity, activity or total activity (symbolA) is aphysical quantity defined as the number of radioactive transformations per second that occur in a particularradionuclide.^[3] The unit of activity is thebecquerel (symbol Bq), which is defined equivalent toreciprocal seconds (symbol s⁻¹). The older, non-SI unit of activity is thecurie (Ci), which is3.7×10¹⁰ radioactive decays per second. Another unit of activity is therutherford, which is defined as1×10⁶ radioactive decays per second.

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

Since the probability ofradioactive decay for a given radionuclide within a set time interval is fixed (with some slight exceptions, seechanging 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).

Radioactivity is expressed as the decay rate of a particular radionuclide with decay constantλ and the number of atomsN:

${\displaystyle -\frac{dN}{dt}=\lambda N.}$

The integral solution is described byexponential decay:

${\displaystyle N=N_0{e}^{-\lambda t},}$

whereN₀ is the initial quantity of atoms at timet = 0.

Half-lifeT_1/2 is defined as the length of time for half of a given quantity of radioactive atoms to undergo radioactive decay:

${\displaystyle \frac{N_0}{2}=N_0{e}^{-\lambda T_{1/2}}.}$

Taking the natural logarithm of both sides, the half-life is given by

${\displaystyle T_{1/2}=\frac{\ln 2}{\lambda }.}$

Conversely, the decay constantλ can be derived from the half-lifeT_1/2 as

${\displaystyle \lambda =\frac{\ln 2}{T_{1/2}}.}$

The mass of the radionuclide is given by

${\displaystyle m=\frac{N}{N_{\text{A}}}[\text{mol}]\times M[\text{g/mol}],}$

whereM ismolar mass of the radionuclide, andN_A is theAvogadro constant. Practically, themass numberA 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 radioactivitya is defined as radioactivity per unit mass of the radionuclide:

${\displaystyle a[\text{Bq/g}]=\frac{\lambda N}{MN/N_{\text{A}}}=\frac{\lambda N_{\text{A}}}{M}.}$

Thus, specific radioactivity can also be described by

${\displaystyle a=\frac{N_{\text{A}}\ln 2}{T_{1/2}\times M}.}$

This equation is simplified to

${\displaystyle a[\text{Bq/g}]\approx \frac{4.17\times {10}^{23}[{\text{mol}}^{-1}]}{T_{1/2}[s]\times M[\text{g/mol}]}.}$

When the unit of half-life is in years instead of seconds:

${\displaystyle a[\text{Bq/g}]=\frac{4.17\times {10}^{23}[{\text{mol}}^{-1}]}{T_{1/2}[\text{year}]\times 365\times 24\times 60\times 60[\text{s/year}]\times M}\approx \frac{1.32\times {10}^{16}[{\text{mol}}^{-1}\cdot {\text{s}}^{-1}\cdot \text{year}]}{T_{1/2}[\text{year}]\times M[\text{g/mol}]}.}$

For example, specific radioactivity ofradium-226 with a half-life of 1600 years is obtained as

${\displaystyle a_{\text{Ra-226}}[\text{Bq/g}]=\frac{1.32\times {10}^{16}}{1600\times 226}\approx 3.7\times {10}^{10}[\text{Bq/g}].}$

This value derived from radium-226 was defined as unit of radioactivity known as thecurie (Ci).

Experimentally measured specific activity can be used to calculate thehalf-life of a radionuclide.

Where decay constantλ is related to specific radioactivitya by the following equation:

${\displaystyle \lambda =\frac{a\times M}{N_{\text{A}}}.}$

Therefore, the half-life can also be described by

${\displaystyle T_{1/2}=\frac{N_{\text{A}}\ln 2}{a\times M}.}$

One gram ofrubidium-87 and a radioactivity count rate that, after takingsolid angle effects into account, is consistent with a decay rate of 3200 decays per second corresponds to a specific activity of3.2×10⁶ Bq/kg. Rubidiumatomic mass is 87 g/mol, so one gram is 1/87 of a mole. Plugging in the numbers:

${\displaystyle T_{1/2}=\frac{N_{\text{A}}\times \ln 2}{a\times M}\approx \frac{6.022\times {10}^{23}{\text{ mol}}^{-1}\times 0.693}{3200{\text{ s}}^{-1}\cdot {\text{g}}^{-1}\times 87\text{ g/mol}}\approx 1.5\times {10}^{18}\text{ s}\approx 47\text{ billion years}.}$

This section may need to be cleaned up. It has been merged fromBecquerel.

For a given mass${\displaystyle m}$ (in grams) of an isotope withatomic mass${\displaystyle m_{\text{a}}}$ (in g/mol) and ahalf-life of${\displaystyle t_{1/2}}$ (in s), the radioactivity can be calculated using:

${\displaystyle A_{\text{Bq}}=\frac{m}{m_{\text{a}}}{N}_{\text{A}}\frac{\ln 2}{t_{1/2}}}$

With${\displaystyle N_{\text{A}}}$ =6.02214076×10²³ mol⁻¹, theAvogadro constant.

Since${\displaystyle m/m_{\text{a}}}$ is the number of moles (${\displaystyle n}$), the amount of radioactivity${\displaystyle A}$ can be calculated by:

${\displaystyle A_{\text{Bq}}=n{N}_{\text{A}}\frac{\ln 2}{t_{1/2}}}$

For instance, on average each gram ofpotassium contains 117 micrograms of⁴⁰K (all other naturally occurring isotopes are stable) that has a${\displaystyle t_{1/2}}$ of1.277×10⁹ 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.

The specific activity of radionuclides is particularly relevant when it comes to select them for production for therapeutic pharmaceuticals, as well as forimmunoassays or other diagnostic procedures, or assessing radioactivity in certain environments, among several other biomedical applications.^{[6][7][8][9][10][11]}

• Fetter, Steve; Cheng, E. T.; Mann, F. M. (1990). "Long-term radioactive waste from fusion reactors: Part II".Fusion Engineering and Design.13 (2):239–246.CiteSeerX 10.1.1.465.5945.doi:10.1016/0920-3796(90)90104-E.ISSN 0920-3796.
• Holland, Jason P.; Sheh, Yiauchung; Lewis, Jason S. (2009)."Standardized methods for the production of high specific-activity zirconium-89".Nuclear Medicine and Biology.36 (7):729–739.doi:10.1016/j.nucmedbio.2009.05.007.ISSN 0969-8051.PMC 2827875.PMID 19720285.
• McCarthy, Deborah W.; Shefer, Ruth E.; Klinkowstein, Robert E.; Bass, Laura A.; Margeneau, William H.; Cutler, Cathy S.; Anderson, Carolyn J.; Welch, Michael J. (1997). "Efficient production of high specific activity⁶⁴Cu using a biomedical cyclotron".Nuclear Medicine and Biology.24 (1):35–43.doi:10.1016/S0969-8051(96)00157-6.ISSN 0969-8051.PMID 9080473.

• Radioactivity quantities

• Articles with short description
• Short description is different from Wikidata
• Wikipedia articles that are too technical from January 2014
• All articles that are too technical