nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies th ...

, the Geiger–Nuttall law or Geiger–Nuttall rule relates the

decay constant A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate ...

of a

radioactive Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is conside ...

isotope Isotopes are distinct nuclear species (or ''nuclides'') of the same chemical element. They have the same atomic number (number of protons in their Atomic nucleus, nuclei) and position in the periodic table (and hence belong to the same chemica ...

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 The decay energy is the energy change of a nucleus having undergone a radioactive decay. Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This decay, or loss of energ ...

, 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 Johannes Wilhelm Geiger ( , ; ; 30 September 1882 – 24 September 1945) was a German nuclear physicist. He is known as the inventor of the Geiger counter, a device used to detect ionizing radiation, and for carrying out the Rutherford scatt ...

and John Mitchell Nuttall as a relation between the decay constant and the range of alpha particles in air, in its modern form the Geiger–Nuttall law is :

\log_T_=\frac+B(Z)

where ''

T_

'' is the

half-life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...

, ''E'' the total

kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

(of the alpha particle and the daughter nucleus), and ''A'' and ''B'' are coefficients that depend on the isotope's

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of pro ...

''Z''. The law works best for nuclei with even atomic number and even

atomic mass Atomic mass ( or ) is the mass of a single atom. The atomic mass mostly comes from the combined mass of the protons and neutrons in the nucleus, with minor contributions from the electrons and nuclear binding energy. The atomic mass of atoms, ...

. The trend is still there for even-odd, odd-even, and odd-odd nuclei but is not as pronounced.

Cluster decays

The Geiger–Nuttall law has even been extended to describe

cluster decay Cluster decay, also named heavy particle radioactivity, heavy ion radioactivity or heavy cluster decay," is a rare type of nuclear decay in which an atomic nucleus emits a small "cluster" of neutrons and protons, more than in an alpha particle, ...

s, decays where atomic nuclei larger than helium are released, e.g. silicon and carbon.

Derivation

A simple way to derive this law is to consider an

alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay but may also be produce ...

in the

atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the Department_of_Physics_and_Astronomy,_University_of_Manchester , University of Manchester ...

as a

particle in a box In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes the movement of a free particle in a small space surrounded by impenetrable barriers. The model is mainly used a ...

. The particle is in a

bound state A bound state is a composite of two or more fundamental building blocks, such as particles, atoms, or bodies, that behaves as a single object and in which energy is required to split them. In quantum physics, a bound state is a quantum state of a ...

because of the presence of the

strong interaction In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is one of the four known fundamental interaction, fundamental interactions. It confines Quark, quarks into proton, protons, n ...

potential. It will constantly bounce from one side to the other, and due to the possibility of

quantum tunneling In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...

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. This calculation was first performed by physicist

George Gamow George Gamow (sometimes Gammoff; born Georgiy Antonovich Gamov; ; 4 March 1904 – 19 August 1968) was a Soviet and American polymath, theoretical physicist and cosmologist. He was an early advocate and developer of Georges Lemaître's Big Ba ...

in 1928.G. Gamow (1928) "Zur Quantentheorie des Atomkernes" (On the quantum theory of the atomic nucleus), ''Zeitschrift für Physik'', vol. 51, pages 204-212.

References

* {{DEFAULTSORT:Geiger-Nuttall law Nuclear physics Eponymous equations of physics

Cluster decays

Derivation

See also

References