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| In [[nuclear physics]], the '''Geiger–Nuttall law''' or '''Geiger–Nuttall rule''' relates the [[decay constant]] of a [[radioactive]] [[isotope]] with the energy of the [[alpha particles]] emitted. Roughly speaking, it states that short-lived isotopes emit more energetic alpha particles than long-lived ones.
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| The relationship also shows that half-lives are exponentially dependent on decay energy, so that very large changes in half-life make comparatively small differences in decay energy, and thus alpha particle energy. In practice, this means that alpha particles from all alpha-emitting isotopes across many orders of magnitude of difference in half-life, all nevertheless have about the same decay energy.
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| Formulated in 1911 by [[Hans Geiger]] and [[John Mitchell Nuttall]],<ref>H. Geiger and J.M. Nuttall (1911) "The ranges of the α particles from various radioactive substances and a relation between range and period of transformation," ''Philosophical Magazine'', Series 6, vol. 22, no. 130, pages 613-621. See also: H. Geiger and J.M. Nuttall (1912) "The ranges of α particles from uranium," ''Philosophical Magazine'', Series 6, vol. 23, no. 135, pages 439-445.</ref> in its modern form the Geiger–Nuttall law is
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| :<math>\ln\lambda=-a_1\frac{Z}{\sqrt{E}}+a_2</math>
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| where ''λ'' is the [[decay constant]] ('''λ = ln2/half-life'''), ''Z'' the [[atomic number]], ''E'' the total [[kinetic energy]] (of the alpha particle and the daughter nucleus), and ''a''<sub>1</sub> and ''a''<sub>2</sub> are [[Constant (mathematics)|constant]]s. | |
| The law works best for nuclei with even atomic number and even atomic mass. The trend is still there for even-odd, odd-even, and odd-odd nuclei but not as pronounced.
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| == Cluster decays ==
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| The Geiger-Nuttall Law has even been extended to describe cluster decays [http://prola.aps.org/pdf/PRC/v70/i3/e034304], decays where atomic nuclei larger than Helium are released, e.g. Silicon and Carbon.
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| == Derivation ==
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| A simple way to derive this law is to consider an [[alpha particle]] in the atomic nucleus as a [[particle in a box]]. The particle is in a [[bound state]] because of the presence of the [[strong interaction]] potential. It will constantly bounce from one side to the other, and due to the possibility of [[quantum tunneling]] by the wave though the potential barrier, each time it bounces, there will be a small likelihood for it to escape.
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| A knowledge of this quantum mechanical effect enables one to obtain this law, including coefficients, via direct calculation.[http://www.phy.uct.ac.za/courses/phy300w/np/ch1/node38.html] This calculation was first performed by physicist [[George Gamow]] in 1928.<ref>G. Gamow (1928) "Zur Quantentheorie des Atomkernes" (On the quantum theory of the atomic nucleus), ''Zeitschrift für Physik'', vol. 51, pages 204-212.</ref>
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| == References ==
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| {{reflist}}
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| * {{ScienceWorld|title=Geiger-Nuttall Law|urlname=physics/Geiger-NuttallLaw}}
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| {{DEFAULTSORT:Geiger-Nuttall law}}
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| [[Category:Nuclear physics]]
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| {{nuclear-stub}}
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