In nuclear physics, the Geiger–Nuttall law or Geiger–Nuttall rule relates the decay constant of a radioactiveisotope 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.
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.
Formulated in 1911 by Hans Geiger and John Mitchell Nuttall as a relation between the decay constant and the range of alpha particles in air,[1] in its modern form[2] the Geiger–Nuttall law is
where is the half-life, E the total kinetic energy (of the alpha particle and the daughter nucleus), and A and B are coefficients that depend on the isotope's atomic numberZ. 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 is not as pronounced.
Cluster decaysEdit
The Geiger–Nuttall law has even been extended to describe cluster decays,[3] decays where atomic nuclei larger than helium are released, e.g. silicon and carbon.
DerivationEdit
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 through the potential barrier, each time it bounces, there will be a small likelihood for it to escape.
A knowledge of this quantum mechanical effect enables one to obtain this law, including coefficients, via direct calculation.[4] This calculation was first performed by physicist George Gamow in 1928.[5]
ReferencesEdit
^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.
^Qi, C; Andreyev, A. N.; Huyse, M.; Liotta, R. J.; Van Duppen, P.; Wyss, R. (2014). "On the Validity of the Geiger-Nuttall Alpha-Decay Law and its Microscopic Basis". Phys. Lett. B. 734: 203–206. arXiv:1405.5633. doi:10.1016/j.physletb.2014.05.066.
^Ren, Zhongzhou; Xu, Chang; Wang, Zaijun (2004). "New perspective on complex cluster radioactivity of heavy nuclei". Phys. Rev. C. 70: 034304. doi:10.1103/PhysRevC.70.034304.
^. www.phy.uct.ac.za. Archived from the original on 24 February 2009. Retrieved 14 January 2022.
^G. Gamow (1928) "Zur Quantentheorie des Atomkernes" (On the quantum theory of the atomic nucleus), Zeitschrift für Physik, vol. 51, pages 204-212.
geiger, nuttall, nuclear, physics, geiger, nuttall, rule, relates, decay, constant, radioactive, isotope, with, energy, alpha, particles, emitted, roughly, speaking, states, that, short, lived, isotopes, emit, more, energetic, alpha, particles, than, long, liv. 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 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 Formulated in 1911 by Hans Geiger and John Mitchell Nuttall as a relation between the decay constant and the range of alpha particles in air 1 in its modern form 2 the Geiger Nuttall law is log 10 T 1 2 A Z E B Z displaystyle log 10 T 1 2 frac A Z sqrt E B Z where T 1 2 displaystyle T 1 2 is the half life E the total kinetic energy of the alpha particle and the daughter nucleus and A and B are coefficients that depend on the isotope s atomic number Z 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 is not as pronounced Cluster decays EditThe Geiger Nuttall law has even been extended to describe cluster decays 3 decays where atomic nuclei larger than helium are released e g silicon and carbon Derivation EditA 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 through the potential barrier each time it bounces there will be a small likelihood for it to escape A knowledge of this quantum mechanical effect enables one to obtain this law including coefficients via direct calculation 4 This calculation was first performed by physicist George Gamow in 1928 5 References Edit H Geiger and J M Nuttall 1911 The ranges of the a 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 a particles from uranium Philosophical Magazine Series 6 vol 23 no 135 pages 439 445 Qi C Andreyev A N Huyse M Liotta R J Van Duppen P Wyss R 2014 On the Validity of the Geiger Nuttall Alpha Decay Law and its Microscopic Basis Phys Lett B 734 203 206 arXiv 1405 5633 doi 10 1016 j physletb 2014 05 066 Ren Zhongzhou Xu Chang Wang Zaijun 2004 New perspective on complex cluster radioactivity of heavy nuclei Phys Rev C 70 034304 doi 10 1103 PhysRevC 70 034304 Gamow theory of alpha decay www phy uct ac za Archived from the original on 24 February 2009 Retrieved 14 January 2022 G Gamow 1928 Zur Quantentheorie des Atomkernes On the quantum theory of the atomic nucleus Zeitschrift fur Physik vol 51 pages 204 212 Weisstein Eric Wolfgang ed Geiger Nuttall Law ScienceWorld Retrieved from https en wikipedia org w index php title Geiger Nuttall law amp oldid 1136752301, wikipedia, wiki, book, books, library,
