|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| In [[nuclear physics]], '''secular equilibrium''' is a situation in which the quantity of a [[radioactive]] [[isotope]] remains constant because its production rate (e.g., due to decay of a parent isotope) is equal to its decay rate.
| | Hi there, I am Alyson Boon although it is not the title on my beginning certification. Some time ago she selected real psychic readings - [http://www.publicpledge.com/blogs/post/7034 publicpledge.com] - to reside in Alaska and her mothers [http://www.article-galaxy.com/profile.php?a=143251 real psychic readings] and fathers reside nearby. What me and my family adore is doing ballet but I've been taking on new issues lately. Invoicing is my profession.<br><br>Feel free to visit my website :: clairvoyant psychic - [http://www.prograd.uff.br/novo/facts-about-growing-greater-organic-garden visit this link], |
| | |
| ==Secular equilibrium in radioactive decay==
| |
| <!-- Image with unknown copyright status removed: [[Image:Secular Equilibrium.GIF]] -->
| |
| Secular equilibrium can only occur in a radioactive decay chain if the [[half-life]] of the daughter radionuclide B is much shorter than the half-life of the parent radionuclide A. In such a situation, the decay rate of A, and hence the production rate of B, is approximately constant, because the half-life of A is very long compared to the timescales being considered. The quantity of radionuclide B builds up until the number of B atoms decaying per unit time becomes equal to the number being produced per unit time; the quantity of radionuclide B then reaches a constant, ''equilibrium'' value. Assuming the initial concentration of radionuclide B is zero, full equilibrium usually takes several half-lives of radionuclide B to establish.
| |
| | |
| The quantity of radionuclide B when secular equilibrium is reached is determined by the quantity of its parent A and the half-lives of the two radionuclide. This can be seen from the time rate of change of the number of atoms of radionuclide B:
| |
| | |
| :<math>\frac{dN_B}{dt} = \lambda_A N_A - \lambda_B N_B</math> ,
| |
| | |
| where λ<sub>A</sub> and λ<sub>B</sub> are the [[exponential decay|decay constants]] of radionuclide A and B, related to their half-lives t<sub>1/2</sub> by <math>\lambda = ln(2)/t_{1/2}</math>, and N<sub>A</sub> and N<sub>B</sub> are the number of atoms of A and B at a given time.
| |
| | |
| Secular equilibrium occurs when <math>dN_B/dt = 0</math>, or
| |
| | |
| :<math>N_B = \frac{\lambda_A}{\lambda_B}N_A</math> . | |
| | |
| Over long enough times, comparable to the half-life of radionuclide A, the secular equilibrium is only approximate; N<sub>A</sub> decays away according to
| |
| | |
| :<math>N_A(t) = N_A(0) e^{-\lambda_A t}</math> , | |
| | |
| and the "equilibrium" quantity of radionuclide B declines in turn. For times short compared to the half-life of A, <math>\lambda_A t \ll 1</math> and the exponential can be approximated as 1.
| |
| | |
| ==See also==
| |
| * [[Bateman Equation]]
| |
| *[[Transient equilibrium]]
| |
| | |
| ==References==
| |
| *[http://www.iupac.org/goldbook/S05532.pdf IUPAC definition]
| |
| *[http://www.epa.gov/rpdweb00/understand/equilibrium.html EPA definition]
| |
| | |
| {{physics-stub}}
| |
| | |
| [[Category:Radioactivity]]
| |
Hi there, I am Alyson Boon although it is not the title on my beginning certification. Some time ago she selected real psychic readings - publicpledge.com - to reside in Alaska and her mothers real psychic readings and fathers reside nearby. What me and my family adore is doing ballet but I've been taking on new issues lately. Invoicing is my profession.
Feel free to visit my website :: clairvoyant psychic - visit this link,