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 the ...

, the Geiger–Nuttall law or Geiger–Nuttall rule relates the decay constant 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 consi ...

isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numb ...

with the energy of the

alpha particles 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 prod ...

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 Johannes Wilhelm "Hans" Geiger (; ; 30 September 1882 – 24 September 1945) was a German physicist. He is best known as the co-inventor of the detector component of the Geiger counter and for the Geiger–Marsden experiment which discover ...

and

John Mitchell Nuttall John Mitchell Nuttall (21 July 1890 – 28 January 1958) was an English physicist, born in Todmorden. He is best remembered for his work with the physicist Hans Geiger, which resulted in the Geiger–Nuttall law of radioactive decay. Nuttall gra ...

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_\lambda=-a_1\frac+a_2

where ''λ'' is the decay constant (λ = ln2/half-life), ''Z'' the

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...

, ''E'' the total

kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acc ...

(of the alpha particle and the daughter nucleus), and ''a''₁ and ''a''₂ are constants. 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.

Cluster decays

The Geiger–Nuttall law has even been extended to describe cluster decays, 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 pr ...

in the atomic nucleus 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 a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypo ...

. The particle is in a

bound state Bound or bounds may refer to: Mathematics * Bound variable * Upper and lower bounds, observed limits of mathematical functions Physics * Bound state, a particle that has a tendency to remain localized in one or more regions of space Geography * ...

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

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 (March 4, 1904 – August 19, 1968), born Georgiy Antonovich Gamov ( uk, Георгій Антонович Гамов, russian: Георгий Антонович Гамов), was a Russian-born Soviet and American polymath, theoret ...

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