Decay scheme

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The decay scheme of a radioactive substance is a graphical presentation of all the transitions occurring in a decay, and of their relationships. Examples are shown below.

Contents

It is useful to think of the decay scheme as placed in a coordinate system, where the vertical axis is energy, increasing from bottom to top, and the horizontal axis is the proton number, increasing from left to right. The arrows indicate the emitted particles. For the gamma rays (vertical arrows), the gamma energies are given; for the beta decay (oblique arrow), the maximum beta energy.

Examples

Decay scheme of Co Cobalt-60 Decay Scheme.svg
Decay scheme of Co

These relations can be quite complicated; a simple case is shown here: the decay scheme of the radioactive cobalt isotope cobalt-60. [1] 60Co decays by emitting an electron (beta decay) with a half-life of 5.272 years into an excited state of 60Ni, which then decays very fast to the ground state of 60Ni, via two gamma decays.

All known decay schemes can be found in the Table of Isotopes., [2] [3]

Nickel is to the right of cobalt, since its proton number (28) is higher by one than that of cobalt (27). In beta decay, the proton number increases by one. For a positron decay and also for an alpha decay (see below), the oblique arrow would go from right to left since in these cases, the proton number decreases.

Since energy is conserved and since the particles emitted carry away energy, arrows can only go downward (vertically or at an angle) in a decay scheme.

Decay scheme of Au Au-198 Decay Scheme.svg
Decay scheme of Au

A somewhat more complicated scheme is shown here: the decay of the nuclide 198Au [4] which can be produced by irradiating natural gold in a nuclear reactor. 198Au decays via beta decay to one of two excited states or to the ground state of the mercury isotope 198Hg. In the figure, mercury is to the right of gold, since the atomic number of gold is 79, that of mercury is 80. The excited states decay after very short times (2.5 and 23 ps, resp.; 1 picosecond is a millionth of a millionth of a second) to the ground state.

Decay scheme of Tc Tc-99m Decay Scheme.svg
Decay scheme of Tc

While excited nuclear states are usually very short lived, decaying almost immediately after a beta decay (see above), the excited state of the technetium isotope shown here to the right is comparatively long lived. It is therefore called "metastable" (hence the "m" in 99mTc [5] ). It decays to the ground state via gamma decay with a half-life of 6 hours.

Decay Scheme of Po Polonium 210.png
Decay Scheme of Po

Here, to the left, we now have an alpha decay. It is the decay of the element Polonium [6] discovered by Marie Curie, with mass number 210. The isotope 210Po is the penultimate member of the uranium-radium-decay series; it decays into a stable lead-isotope with a half-life of 138 days. In almost all cases, the decay is via the emission of an alpha particle of 5.305 MeV. Only in one case of 100000, an alpha particle of lower energy appears; in this case, the decay leads to an excited level of 206Pb, which then decays to the ground state via gamma radiation.

Selection Rules

Co Decay, with spins and parities shown 60Co Decay.jpg
Co Decay, with spins and parities shown

Alpha- beta- and gamma rays can only be emitted if the conservation laws (energy, angular momentum, parity) are obeyed. This leads to so-called selection rules.

Applications for gamma decay can be found in Multipolarity of gamma radiation. To discuss such a rule in a particular case, it is necessary to know angular momentum and parity for every state. The figure shows the 60Co decay scheme again, with spins and parities given for every state.

Related Research Articles

Alpha decay Emission of alpha particles by a decaying radioactive atom

Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an atomic number that is reduced by two. An alpha particle is identical to the nucleus of a helium-4 atom, which consists of two protons and two neutrons. It has a charge of +2 e and a mass of 4 u. For example, uranium-238 decays to form thorium-234. Alpha particles have a charge +2 e, but as a nuclear equation describes a nuclear reaction without considering the electrons – a convention that does not imply that the nuclei necessarily occur in neutral atoms – the charge is not usually shown. Alpha decay typically occurs in the heaviest nuclides. Theoretically, it can occur only in nuclei somewhat heavier than nickel, where the overall binding energy per nucleon is no longer a minimum and the nuclides are therefore unstable toward spontaneous fission-type processes. In practice, this mode of decay has only been observed in nuclides considerably heavier than nickel, with the lightest known alpha emitters being the lightest isotopes of tellurium. Exceptionally, however, beryllium-8 decays to two alpha particles. Alpha decay is by far the most common form of cluster decay, where the parent atom ejects a defined daughter collection of nucleons, leaving another defined product behind. It is the most common form because of the combined extremely high nuclear binding energy and a relatively small mass of the alpha particle. Like other cluster decays, alpha decay is fundamentally a quantum tunneling process. Unlike beta decay, it is governed by the interplay between both the nuclear force and the electromagnetic force. Alpha particles have a typical kinetic energy of 5 MeV and have a speed of about 15,000,000 m/s, or 5% of the speed of light. There is surprisingly small variation around this energy, due to the heavy dependence of the half-life of this process on the energy produced. Because of their relatively large mass, the electric charge of +2 e and relatively low velocity, alpha particles are very likely to interact with other atoms and lose their energy, and their forward motion can be stopped by a few centimeters of air. Approximately 99% of the helium produced on Earth is the result of the alpha decay of underground deposits of minerals containing uranium or thorium. The helium is brought to the surface as a by-product of natural gas production.

Beta decay Type of radioactive decay

In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in so-called positron emission. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form what is called the nuclear band or valley of stability. For either electron or positron emission to be energetically possible, the energy release or Q value must be positive.

Neutron Subatomic particle with no electric charge

The neutron is a subatomic particle, symbol
n
or
n0
, which has a neutral charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behave similarly within the nucleus, and each has a mass of approximately one atomic mass unit, they are both referred to as nucleons. Their properties and interactions are described by nuclear physics.

Nuclear physics Field of physics that deals with the structure and behavior of atomic nuclei

Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. Other forms of nuclear matter are also studied.

A radionuclide is an atom that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation; transferred to one of its electrons to release it as a conversion electron; or used to create and emit a new particle from the nucleus. During those processes, the radionuclide is said to undergo radioactive decay. These emissions are considered ionizing radiation because they are powerful enough to liberate an electron from another atom. The radioactive decay can produce a stable nuclide or will sometimes produce a new unstable radionuclide which may undergo further decay. Radioactive decay is a random process at the level of single atoms: it is impossible to predict when one particular atom will decay. However, for a collection of atoms of a single element the decay rate, and thus the half-life (t1/2) for that collection, can be calculated from their measured decay constants. The range of the half-lives of radioactive atoms has no known limits and spans a time range of over 55 orders of magnitude.

Beta particle Ionizing radiation

A beta particle, also called beta ray or beta radiation, is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during the process of beta decay. There are two forms of beta decay, β decay and β+ decay, which produce electrons and positrons respectively.

Nuclear isomer Metastable excited state of a nuclide

A nuclear isomer is a metastable state of an atomic nucleus, in which one or more nucleons (protons or neutrons) occupy higher energy levels than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited states have half-lives 100 to 1000 times longer than the half-lives of the excited nuclear states that decay with a "prompt" half life (ordinarily on the order of 10−12 seconds). The term "metastable" is usually restricted to isomers with half-lives of 10−9 seconds or longer. Some references recommend 5 × 10−9 seconds to distinguish the metastable half life from the normal "prompt" gamma-emission half-life. Occasionally the half-lives are far longer than this and can last minutes, hours, or years. For example, the 180m
73
Ta
nuclear isomer survives so long that it has never been observed to decay (at least 1015 years). The half-life of a nuclear isomer can even exceed that of the ground state of the same nuclide, as shown by 180m
73
Ta
as well as 210m
83
Bi
, 242m
95
Am
and multiple holmium isomers.

Radioactive decay Method of decay in atomic nuclei

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha decay, beta decay, and gamma decay, all of which involve emitting one or more particles or photons. The weak force is the mechanism that is responsible for beta decay, while the other two are governed by the usual electromagnetic and strong forces.

Proton emission

Proton emission is a rare type of radioactive decay in which a proton is ejected from a nucleus. Proton emission can occur from high-lying excited states in a nucleus following a beta decay, in which case the process is known as beta-delayed proton emission, or can occur from the ground state of very proton-rich nuclei, in which case the process is very similar to alpha decay. For a proton to escape a nucleus, the proton separation energy must be negative—the proton is therefore unbound, and tunnels out of the nucleus in a finite time. Proton emission is not seen in naturally occurring isotopes; proton emitters can be produced via nuclear reactions, usually using linear particle accelerators.

Internal conversion

Internal conversion is a non-radioactive decay process wherein an excited nucleus interacts electromagnetically with one of the orbital electrons of the atom. This causes the electron to be emitted (ejected) from the atom. Thus, in an internal conversion process, a high-energy electron is emitted from the radioactive atom, but not from the nucleus. For this reason, the high-speed electrons resulting from internal conversion are not called beta particles, since the latter come from beta decay, where they are newly created in the nuclear decay process.

Neutron activation Induction of radioactivity by neutron radiation

Neutron activation is the process in which neutron radiation induces radioactivity in materials, and occurs when atomic nuclei capture free neutrons, becoming heavier and entering excited states. The excited nucleus decays immediately by emitting gamma rays, or particles such as beta particles, alpha particles, fission products, and neutrons. Thus, the process of neutron capture, even after any intermediate decay, often results in the formation of an unstable activation product. Such radioactive nuclei can exhibit half-lives ranging from small fractions of a second to many years.

Neutron capture Atomic nuclear process

Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. Since neutrons have no electric charge, they can enter a nucleus more easily than positively charged protons, which are repelled electrostatically.

Radiochemistry is the chemistry of radioactive materials, where radioactive isotopes of elements are used to study the properties and chemical reactions of non-radioactive isotopes. Much of radiochemistry deals with the use of radioactivity to study ordinary chemical reactions. This is very different from radiation chemistry where the radiation levels are kept too low to influence the chemistry.

Delayed nuclear radiation is a form of nuclear decay. When an isotope decays into a very short-lived isotope and then decays again to a relatively long-lived isotope, the products of the second decay are delayed. The short-lived isotope is usually a meta-stable nuclear isomer.

Cobalt-60 Radioactive isotope of cobalt

Cobalt-60 (60Co) is a synthetic radioactive isotope of cobalt with a half-life of 5.2713 years. It is produced artificially in nuclear reactors. Deliberate industrial production depends on neutron activation of bulk samples of the monoisotopic and mononuclidic cobalt isotope 59
Co
. Measurable quantities are also produced as a by-product of typical nuclear power plant operation and may be detected externally when leaks occur. In the latter case the incidentally produced 60
Co
is largely the result of multiple stages of neutron activation of iron isotopes in the reactor's steel structures via the creation of its 59
Co
precursor. The simplest case of the latter would result from the activation of 58
Fe
. 60
Co
undergoes beta decay to the stable isotope nickel-60. The activated nickel nucleus emits two gamma rays with energies of 1.17 and 1.33 MeV, hence the overall equation of the nuclear reaction is:

Yrast is a technical term in nuclear physics that refers to a state of a nucleus with a minimum of energy for a given angular momentum. Yr is a Swedish adjective sharing the same root as the English whirl. Yrast is the superlative of yr and can be translated whirlingest, although it literally means "dizziest" or "most bewildered". The yrast levels are vital to understanding reactions, such as off-center heavy ion collisions, that result in high-spin states.

Gamma ray Energetic electromagnetic radiation arising from radioactive decay of atomic nuclei

A gamma ray, or gamma radiation, is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves and so imparts the highest photon energy. Paul Villard, a French chemist and physicist, discovered gamma radiation in 1900 while studying radiation emitted by radium. In 1903, Ernest Rutherford named this radiation gamma rays based on their relatively strong penetration of matter; in 1900 he had already named two less penetrating types of decay radiation alpha rays and beta rays in ascending order of penetrating power.

Alpha particle Helium-4 nucleus; particle of two protons and two neutrons

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 produced in other ways. Alpha particles are named after the first letter in the Greek alphabet, α. The symbol for the alpha particle is α or α2+. Because they are identical to helium nuclei, they are also sometimes written as He2+
or 4
2
He2+
indicating a helium ion with a +2 charge. Once the ion gains electrons from its environment, the alpha particle becomes a normal helium atom 4
2
He
.

Wu experiment Nuclear physics experiment

The Wu experiment was a particle and nuclear physics experiment conducted in 1956 by the Chinese American physicist Chien-Shiung Wu in collaboration with the Low Temperature Group of the US National Bureau of Standards. The experiment's purpose was to establish whether or not conservation of parity (P-conservation), which was previously established in the electromagnetic and strong interactions, also applied to weak interactions. If P-conservation were true, a mirrored version of the world would behave as the mirror image of the current world. If P-conservation were violated, then it would be possible to distinguish between a mirrored version of the world and the mirror image of the current world.

Even and odd atomic nuclei classification of nuclei by proton, neutron and/or nucleon numbers, as many physical properties depend whether these are even or odd

In nuclear physics, properties of a nucleus depend on evenness or oddness of its atomic number Z, neutron number N and, consequently, of their sum, the mass number A. Most importantly, oddness of both Z and N tends to lower the nuclear binding energy, making odd nuclei generally less stable. This effect is not only experimentally observed, but is included in the semi-empirical mass formula and explained by some other nuclear models, such as the nuclear shell model. This difference of nuclear binding energy between neighbouring nuclei, especially of odd-A isobars, has important consequences for beta decay.

References

  1. K.H.Lieser Einführung in die Kernchemie (1991) S.223, Abb. (7-22); ISBN   3-527-28329-3
  2. C.M. Lederer, J.M. Hollander, I. Perlman: Table of Isotopes, Wiley (1968)
  3. ie.lbl.gov/toi/
  4. K.H.Lieser, Nuclear and Radiochemistry (2001), p.61, Fig 5.12; ISBN   3-527-30317-0
  5. H.Krieger, Grundlagen der Strahlungsphysik und des Strahlenschutzes (2007), S.117, Fig 3.15; ISBN   978-3-8351-0199-9
  6. K.H.Lieser, Nuclear and Radiochemistry (2001), p.52, Fig 5.4; ISBN   3-527-30317-0