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{{About|specific activity radioactivity|the use in biochemistry|Enzyme assay#Specific activity}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
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{{technical|date=January 2014}}
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In [[nuclear sciences]] and technologies, "activity" is the SI quantity related to the phenomenon of natural and artificial [[radioactivity]]. The SI unit of "activity" is [[becquerel]] (Bq) while that of "'''specific activity'''" is Bq/g. The old unit of "activity" was [[curie]] (Ci) making "specific activity", Ci/g.
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== Half-life ==
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Experimentally-measured specific activity can be used to calculate the [[half-life]] of a radioactive element.
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


The definition of half-life ('''T<sub>1/2</sub>''') is that
<!--'''PNG''' (currently default in production)
the half life T<sub>1/2</sub> of an isotope is the length of time at which half
:<math forcemathmode="png">E=mc^2</math>
of a given quantity has decayed into another isotope, usually of a different element:
Or more generally:
Starting with '''''N<sub>0</sub>''''', atoms of an element, the number of atoms, '''''N''''',
remaining after time, '''''t''''', is given by:


: <math>N=N_0\left(\frac{1}{2}\right)^{t \over T_{1/2} }</math>
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


The natural log of both sides
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


: <math>\ln(N)=\ln(N_0)+\left(\frac{t}{T_{1/2} }\right)\ln\left(\frac{1}{2}\right)</math>
==Demos==


The derivative with respect to time, ''t''
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


: <math>\frac{1}{N}\frac{dN}{dt}=\frac{\ln\left(\frac{1}{2}\right)}{T_{1/2} }</math>


Multiplying both sides by ''N''
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** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


: <math>\frac{dN}{dt}=\frac{N\ln\left(\frac{1}{2}\right)}{T_{1/2} }</math>
==Test pages ==


Yields
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
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: <math>\frac{dN}{dt}=\frac{-0.693\,N}{T_{1/2} }</math>
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
''dN''/''dt'' represents the decay rate of atoms. The negative sign shows that the rate is negative, so the number of atoms is decreasing with time. Rearranging terms:
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
: <math>T_{1/2}=\frac{-0.693\,N}{\frac{dN}{dt} }</math>
 
=== 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 {{val|3.2|e=6|u=Bq/kg}}. Rubidium's atomic weight is 87, so one gram is one 87th of a mole, or ''N''={{val|6.9|e=21}} atoms. Plugging in the numbers:
 
: <math>T_{1/2}=\frac{-0.693(6.9\times 10^{21})}{-3200\text{ s}^{-1} }=1.5\times 10^{18}\text{ s or 47 billion years}</math>
 
== Formulation ==
 
Radioactivity is expressed as the decay rate of a particular [[radionuclide]] with decay constant ''λ'' and the number of atoms ''N'':
 
: <math>-\frac{dN}{dt}= \lambda N</math>
 
Mass of the radionuclide is given by
 
: <math>\frac{N}{N_A} [\text{mol}] \times {m} [\text {g } \text{mol}^{-1}]</math>
 
where ''m'' is [[mass number]] of the radionuclide and ''N<sub>A</sub>'' is [[Avogadro's constant]].
 
Specific radioactivity ''S'' is defined as radioactivity per unit mass of the radionuclide:
 
: <math>S [\text {Bq/g}] = \frac{\lambda N}{m N/N_A} = \frac{\lambda N_A}{m}</math>
 
In addition, decay constant ''λ'' is related to the half-life ''T<sub>1/2</sub>'' by the following equation:
 
: <math>{\lambda} = \frac{ln2}{T_{1/2}}</math>
 
Thus, specific radioactivity can also be described by
 
: <math>S = \frac{ln2 \times {N_A}}{T_{1/2} \times {m}}</math>
 
This equation is simplified by
 
: <math>S [\text {Bq/g}] \simeq \frac{4.17\times 10^{23}}{T_{1/2} [s]\times m}</math>
 
When the unit of half-life converts a year
 
: <math> S [\text {Bq/g}] = \frac{ln2 \times {N_A}}{T_{1/2} [s] \times {m}} = \frac{ln2 \times {N_A}}{T_{1/2}[year] \times365\times24\times60\times60 \times m} \simeq \frac{1.32\times 10^{16} }{T_{1/2}[year] \times m}</math>
 
For example, specific radioactivity of [[Isotopes of radium|radium 226]] with a half-life of 1600 years is obtained by
 
: <math> \frac{1.32\times 10^{16} }{1600[year] \times 226} \simeq {3.7} \times 10^{10} [\text {Bq/g}] </math>
 
This value derived from radium 226 was defined as unit of radioactivity known as [[Curie]] (Ci).
 
[[Category:Units of radioactivity]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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