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'''Half-life''' is a term that can be used to quantify the rate of decay for any system that undergoes [[exponential decay]]. It is the time it takes for half of the sample to decay.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>

'''Half-life''' is a term that can be used to quantify the rate of decay for any system that undergoes [[exponential decay]]. It is the time it takes for half of the sample to decay.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>

Now we have a sample of 500,000,000 atoms. Because the half-life is independent of quantity, after another year we will be down to 125,000,000 remaining and after a further year 62,500,000.  

Now we have a sample of 500,000,000 atoms. Because the half-life is independent of quantity, after another year we will be down to 125,000,000 remaining and after a further year 62,500,000.  

After ten years we would mathematically expect to have 976,562.5 atoms left. Clearly half an atom is impossible, but this is the [[Expectation_(math)|expectation value]] for the result we would have.  

After ten years we would mathematically expect to have 976,562.5 atoms left. Clearly half an atom is impossible, but this is the [[Expectation (math)|expectation value]] for the result we would have.  

Note that if we had begun with a smaller sample, say half the size at 500,000,000 atoms, then the time for it to decay to around 976,000 atoms would not be 50% of the time for the larger sample, but in fact (in this case) 90%.

Note that if we had begun with a smaller sample, say half the size at 500,000,000 atoms, then the time for it to decay to around 976,000 atoms would not be 50% of the time for the larger sample, but in fact (in this case) 90%.

==Application==

==Application==

While different isotopes have different half-lives<ref>Avison J. ''The World of Physics''; Thomas Nelson and Sons; Cheltenham. p. 395, (1984) [http://books.google.com/books?id=DojwZzKAvN8C&lpg=PA395&dq=%22short%20half-life%22&pg=PA395#v=onepage&q=%22short%20half-life%22&f=false]</ref>, some being very short and difficult for scientists to study, the concept is a useful one for measuring and comparing the decay rates of different isotopes.

While different isotopes have different half-lives,<ref>Avison J. ''The World of Physics''; Thomas Nelson and Sons; Cheltenham. p. 395, (1984) [http://books.google.com/books?id=DojwZzKAvN8C&lpg=PA395&dq=%22short%20half-life%22&pg=PA395#v=onepage&q=%22short%20half-life%22&f=false]</ref> some being very short and difficult for scientists to study, the concept is a useful one for measuring and comparing the decay rates of different isotopes.

There are a number of practical applications.

There are a number of practical applications.

Calculations are further complicated by the fact that the waste may be a mixture of different isotopes, and that the results of decay may be isotopes with are themselves radioactive and have their own half-lives. The duration of subsequent half-life could be vastly different (longer or shorter) than that of the parent isotope.

Calculations are further complicated by the fact that the waste may be a mixture of different isotopes, and that the results of decay may be isotopes with are themselves radioactive and have their own half-lives. The duration of subsequent half-life could be vastly different (longer or shorter) than that of the parent isotope.

The concept is also useful in [[Radiometric_dating|radiometric dating]] such as with [[carbon|carbon-14]]. If a sample of a substance can be measured to have a certain amount of a decay product and the original amount of the parent isotope can be estimated or inferred then amount of decay can be used in combination with the half-life to estimate how long ago the substance formed.

The concept is also useful in [[radiometric dating]] such as with [[carbon|carbon-14]]. If a sample of a substance can be measured to have a certain amount of a decay product and the original amount of the parent isotope can be estimated or inferred then amount of decay can be used in combination with the half-life to estimate how long ago the substance formed.

==Explanation==  

==Explanation==

Exponential decay occurs in a situation where every atom of the sample of the isotope has the same fixed probability of decaying. For a given isotope this is expressed as <math>\lambda</math> - the probability that a particular atom will decay in the next second.

Exponential decay occurs in a situation where every atom of the sample of the isotope has the same fixed probability of decaying. For a given isotope this is expressed as <math>\lambda</math> - the probability that a particular atom will decay in the next second.

The [[creationist]] blog [[Answers in Genesis]] suggests that half-life varies over time.<ref>[http://www.answersingenesis.org/articles/am/v1/n1/creation-research Raising the Bar on Creation Research - by Don DeYoung, Ph.D.]</ref>

The [[creationist]] blog [[Answers in Genesis]] suggests that half-life varies over time.<ref>[http://www.answersingenesis.org/articles/am/v1/n1/creation-research Raising the Bar on Creation Research - by Don DeYoung, Ph.D.]</ref>

However, indirect observations can allow us to infer radioactive decay rates over much longer time-scales. For example we can measure gamma radiation rates at specific frequencies from distant [[supernovae]] and compare this to the rate expected for the mass of the star. This has given rates for supernoave as distant as 169,000 [[light year|light years]] which are consistent with those measured today. Thus it would seem decay rates have been the same for at least the past 169,000 years.<ref>http://www.talkorigins.org/indexcc/CF/CF210.html</ref>

However, indirect observations can allow us to infer radioactive decay rates over much longer time-scales. For example we can measure gamma radiation rates at specific frequencies from distant [[supernovae]] and compare this to the rate expected for the mass of the star. This has given rates for supernoave as distant as 169,000 [[light year]]s which are consistent with those measured today. Thus it would seem decay rates have been the same for at least the past 169,000 years.<ref>http://www.talkorigins.org/indexcc/CF/CF210.html</ref>

More recent measurements have noted some slight cyclic changes in decay rates on a 33-day period.<ref>http://www.purdue.edu/newsroom/research/2010/100830FischbachJenkinsDec.html</ref> While no definite explanation has been found, it is notable that 33 days is also the rotation period of the [[Sun]]'s core. It is possible that [[neutrino]] emissions from the sun are affecting either the measuring equipment or the rate of decay (making it stimulated rather than spontaneous). However, since this variation is cyclic it does not have any significant effect on radiometric calculations. It might however be important when calculating doses in the field of [[radiotherapy]].  

More recent measurements have noted some slight cyclic changes in decay rates on a 33-day period.<ref>http://www.purdue.edu/newsroom/research/2010/100830FischbachJenkinsDec.html</ref> While no definite explanation has been found, it is notable that 33 days is also the rotation period of the [[Sun]]'s core. It is possible that [[neutrino]] emissions from the sun are affecting either the measuring equipment or the rate of decay (making it stimulated rather than spontaneous). However, since this variation is cyclic it does not have any significant effect on radiometric calculations. It might however be important when calculating doses in the field of [[radiotherapy]].  

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==See Also==

==See also==

*[[Radiometric dating]]

*[[Radiometric dating]]

*[[Carbon dating]]

*[[Carbon dating]]

[[Category:physics]]

[[Category:Physics]]