In
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 ...
, properties of a
nucleus
Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to:
*Atomic nucleus, the very dense central region of an atom
* Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA
Nucl ...
depend on
evenness or oddness of its
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 ...
(proton number) ''Z'',
neutron number
The neutron number, symbol ''N'', is the number of neutrons in a nuclide.
Atomic number (proton number) plus neutron number equals mass number: . The difference between the neutron number and the atomic number is known as the neutron excess: . ...
''N'' and, consequently, of their sum, the
mass number
The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approxima ...
''A''. Most importantly, oddness of both ''Z'' and ''N'' tends to lower the
nuclear binding energy
Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the atomic nucleus, nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable n ...
, making odd nuclei generally less stable. This effect is not only experimentally observed, but is included in the
semi-empirical mass formula
In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approx ...
and explained by some other
nuclear model
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 based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron i ...
s, such as the
nuclear shell model
In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model is a model of the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels. The first shell m ...
. This difference of nuclear binding energy between neighbouring nuclei, especially of odd-''A''
isobars, has important consequences for
beta decay
In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...
.
The
nuclear spin is zero for even-Z, even N nuclei, integer for all even-''A'' nuclei, and odd half-integer for all odd-''A'' nuclei.
The
neutron–proton ratio
The neutron–proton ratio (N/Z ratio or nuclear ratio) of an atomic nucleus is the ratio of its number of neutrons to its number of protons. Among stable nuclei and naturally occurring nuclei, this ratio generally increases with increasing atomi ...
is not the only factor affecting nuclear stability. Adding neutrons to isotopes can vary their nuclear spins and nuclear shapes, causing differences in
neutron capture
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, ...
cross sections and
gamma spectroscopy
Gamma-ray spectroscopy is the quantitative study of the energy spectra of gamma-ray sources, such as in the nuclear industry, geochemical investigation, and astrophysics.
Most radioactive sources produce gamma rays, which are of various energi ...
and
nuclear magnetic resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
properties. If too many or too few neutrons are present with regard to the
nuclear binding energy
Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the atomic nucleus, nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable n ...
optimum, the nucleus becomes unstable and subject to certain types of
nuclear decay
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 consid ...
. Unstable nuclides with a nonoptimal number of neutrons or protons decay by
beta decay
In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...
(including positron decay),
electron capture
Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shells. Thi ...
, or other means, such as
spontaneous fission
Spontaneous fission (SF) is a form of radioactive decay that is found only in very heavy chemical elements. The nuclear binding energy of the elements reaches its maximum at an atomic mass number of about 56 (e.g., iron-56); spontaneous breakdo ...
and
cluster decay.
Even mass number
Even-mass-number nuclides, which comprise 150/251 = ~60% of all stable nuclides, are
boson
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
s, i.e., they have integer
spin. 146 of the 151 are even-proton, even-neutron (EE) nuclides, which necessarily have spin 0 because of pairing. The remainder of the stable bosonic nuclides are five odd-proton, odd-neutron stable nuclides (, , , and ), all having a non-zero integer spin.
Pairing effects
Beta decay of an even–even nucleus produces an odd–odd nucleus, and vice versa. An even number of protons or of neutrons are more stable (higher
binding energy
In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
) because of
pairing effects, so even–even nuclei are much more stable than odd–odd. One effect is that there are few stable odd–odd nuclides, but another effect is to prevent beta decay of many even–even nuclei into another even–even nucleus of the same mass number but lower energy, because decay proceeding one step at a time would have to pass through an odd–odd nucleus of higher energy.
Double beta decay
In nuclear physics, double beta decay is a type of radioactive decay in which two neutrons are simultaneously transformed into two protons, or vice versa, inside an atomic nucleus. As in single beta decay, this process allows the atom to move clos ...
directly from even–even to even–even skipping over an odd–odd nuclide is only occasionally possible, and even then with a
half-life
Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...
greater than a billion times the
age of the universe
In physical cosmology, the age of the universe is the time elapsed since the Big Bang. Astronomers have derived two different measurements of the age of the universe:
a measurement based on direct observations of an early state of the universe, ...
. For example, the double beta emitter has a half-life of years. This makes for a larger number of stable even–even nuclides, with
some mass numbers having two stable nuclides, and some elements (atomic numbers) having as many as
seven
7 is a number, numeral, and glyph.
7 or seven may also refer to:
* AD 7, the seventh year of the AD era
* 7 BC, the seventh year before the AD era
* The month of
July
Music Artists
* Seven (Swiss singer) (born 1978), a Swiss recording artist ...
.
For example, the extreme stability of helium-4 due to a double pairing of two protons and two neutrons prevents any nuclides containing five or eight nucleons from existing for long enough to serve as platforms for the buildup of heavier elements via
nuclear fusion
Nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles ( neutrons or protons). The difference in mass between the reactants and products is manifest ...
in
Big Bang nucleosynthesis
In physical cosmology, Big Bang nucleosynthesis (abbreviated BBN, also known as primordial nucleosynthesis) is the production of nuclei other than those of the lightest isotope of hydrogen ( hydrogen-1, 1H, having a single proton as a nucleu ...
; only in stars is there enough time for this (see
triple alpha process
The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei (alpha particles) are transformed into carbon.
Triple-alpha process in stars
Helium accumulates in the cores of stars as a result of the proton–pro ...
). This is also the reason why decays so quickly into two
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 ...
, making
beryllium
Beryllium is a chemical element with the symbol Be and atomic number 4. It is a steel-gray, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with other elements to form m ...
the only even-numbered element that is
monoisotopic.
Even proton, even neutron
There are 145 stable even–even nuclides, forming ~58% of the 251 stable nuclides. There are also 22 primordial long-lived even–even nuclides. As a result, many of the 41 even-numbered elements from 2 to 82 have
many primordial isotopes. Half of these even-numbered elements have six or more stable isotopes. The lightest stable even-even isotope is and the heaviest is . These are also the lightest and heaviest known
doubly magic
In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus. As a result, atomic nuclei with a 'magic' number of protons or neutron ...
nuclides.
is the final decay product of , a primordial radionuclide with an even proton and neutron number. is another notable primordial radionuclide with a half life of 4.468 billion years, and produces almost half of all radioactive heat within the Earth.
All even–even nuclides have
spin 0 in their ground state, due to the
Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulated ...
(See
Pairing Effects for more details).
Odd proton, odd neutron
Only five stable nuclides contain both an odd number of protons and an odd number of neutrons. The first four "odd–odd" nuclides occur in low mass nuclides, for which changing a proton to a neutron or vice versa would lead to a very lopsided proton–neutron ratio (, , , and ; spins 1, 1, 3, 1). All four of these isotopes have the same number of protons and neutrons, and they all have an odd number for their
nuclear spin. The only other observationally "stable" odd–odd nuclide is (spin 9), the only primordial
nuclear isomer
A nuclear isomer is a metastable state of an atomic nucleus, in which one or more nucleons (protons or neutrons) occupy excited state, higher energy levels than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited ...
, which has not yet been observed to decay despite experimental attempts. Also, four long-lived radioactive odd–odd nuclides ( (the most common radioisotope in the human body), ,,; spins 4, 6, 5, 7) occur naturally. As in the case of decay of high spin nuclides by
beta decay
In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...
(including
electron capture
Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shells. Thi ...
),
gamma decay
A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically sh ...
, or
internal conversion
Internal conversion is a non-radioactive, atomic decay process where an excited nucleus interacts electromagnetically with one of the orbital electrons of an atom. This causes the electron to be emitted (ejected) from the atom. Thus, in internal ...
is greatly inhibited if the only decay possible between
isobar nuclides (or in the case of between nuclear isomers of the same nuclide) involves high multiples of a change in spin of 1 unit, the "preferred" change of spin that is associated with rapid decay. This high-spin inhibition of decay is the cause of the five heavy stable or long-lived odd-proton, odd-neutron nuclides discussed above. For an example of this effect where the spin effect is subtracted, tantalum-180, the odd–odd low-spin (theoretical) decay product of primordial tantalum-180m, itself has a half life of only about eleven hours.
Many odd–odd radionuclides (like tantalum-180) with comparatively short half lives are known. Almost invariably, these decay by positive or negative beta decay, in order to produce stable even–even isotopes which have paired protons and paired neutrons. In some odd–odd radionuclides where the ratio of protons to neutrons is neither excessively large nor excessively small (i.e., falling too far from the ratio of maximal stability), this decay can proceed in either direction, turning a proton into a neutron, or vice versa. An example is , which can decay either by positron emission to , or by electron emission to .
Of the nine primordial odd–odd nuclides (five stable and four radioactive with long half lives), only is the most common isotope of a common element. This is the case because proton capture on is the rate-limiting step of the
CNO-I cycle. The nuclides and are minority isotopes of elements that are themselves rare compared to other light elements, while the other six isotopes make up only a tiny percentage of the natural abundance of their elements. For example, is thought to be the rarest of the 251
stable nuclide
Stable nuclides are nuclides that are not radioactive and so (unlike radionuclides) do not spontaneously undergo radioactive decay. When such nuclides are referred to in relation to specific elements, they are usually termed stable isotopes.
Th ...
s.
None of the primordial (i.e., stable or nearly stable) odd–odd nuclides have spin 0 in the ground state. This is because the single unpaired neutron and unpaired proton have a larger
nuclear force
The nuclear force (or nucleon–nucleon interaction, residual strong force, or, historically, strong nuclear force) is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nucle ...
attraction to each other if their spins are aligned (producing a total spin of at least 1 unit), instead of anti-aligned. See
deuterium
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
for the simplest case of this nuclear behavior.
Odd mass number
For a given odd mass number, there is exactly one
beta-stable nuclide. There is not a difference in binding energy between even–odd and odd–even comparable to that between even–even and odd–odd, leaving other nuclides of the same mass number (
isobars) free to
beta decay
In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...
toward the lowest-mass nuclide. For mass numbers of 147, 151, and 209+, the beta-stable isobar of that mass number has been observed to undergo
alpha decay
Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an at ...
. (In theory, mass number 143 to 155, 160 to 162, and 165+ can also alpha decay.) This gives a total of 101 stable nuclides with odd mass numbers. There are another nine radioactive primordial nuclides (which by definition all have relatively long half lives, greater than 80 million years) with odd mass numbers.
Odd-mass-number nuclides are
fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...
s, i.e. have
half-integer spin. Generally speaking, since odd-mass-number nuclides always have an even number of either neutrons or protons, the even-numbered particles usually form part of a "core" in the nucleus with a spin of zero. The nucleon with the odd number (whether protons or neutrons) then form a second core with nucleons paired off, with most of the nuclear spin due to the orbital angular momentum and spin angular momentum of the last remaining nucleon. In all, 29 of the 110 primordial odd-mass nuclides have spin 1/2, 30 have spin 3/2, 24 have spin 5/2, 17 have spin 7/2, and nine have spin 9/2.
The odd-mass number stable nuclides are divided (roughly evenly) into odd-proton–even-neutron, and odd-neutron–even-proton nuclides, which are more thoroughly discussed below.
Odd proton, even neutron
These 48 stable nuclides, stabilized by their even numbers of paired neutrons, form most of the stable isotopes of the odd-numbered elements; the very few odd–odd nuclides comprise the others. There are 41 odd-numbered elements with ''Z'' = 1 through 81, of which 30 (including hydrogen, since
zero is an even number) have one stable odd-even isotope, the elements
technetium
Technetium is a chemical element with the symbol Tc and atomic number 43. It is the lightest element whose isotopes are all radioactive. All available technetium is produced as a synthetic element. Naturally occurring technetium is a spontaneous ...
() and
promethium () have no stable isotopes, and nine elements:
chlorine
Chlorine is a chemical element with the Symbol (chemistry), symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate betwee ...
(),
potassium
Potassium is the chemical element with the symbol K (from Neo-Latin ''kalium'') and atomic number19. Potassium is a silvery-white metal that is soft enough to be cut with a knife with little force. Potassium metal reacts rapidly with atmosphe ...
(),
copper
Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...
(),
gallium
Gallium is a chemical element with the symbol Ga and atomic number 31. Discovered by French chemist Paul-Émile Lecoq de Boisbaudran in 1875, Gallium is in group 13 of the periodic table and is similar to the other metals of the group (aluminiu ...
(),
bromine
Bromine is a chemical element with the symbol Br and atomic number 35. It is the third-lightest element in group 17 of the periodic table (halogens) and is a volatile red-brown liquid at room temperature that evaporates readily to form a simila ...
(),
silver
Silver is a chemical element with the Symbol (chemistry), symbol Ag (from the Latin ', derived from the Proto-Indo-European wikt:Reconstruction:Proto-Indo-European/h₂erǵ-, ''h₂erǵ'': "shiny" or "white") and atomic number 47. A soft, whi ...
(),
antimony
Antimony is a chemical element with the symbol Sb (from la, stibium) and atomic number 51. A lustrous gray metalloid, it is found in nature mainly as the sulfide mineral stibnite (Sb2S3). Antimony compounds have been known since ancient time ...
(),
iridium
Iridium is a chemical element with the symbol Ir and atomic number 77. A very hard, brittle, silvery-white transition metal of the platinum group, it is considered the second-densest naturally occurring metal (after osmium) with a density of ...
(), and
thallium
Thallium is a chemical element with the Symbol (chemistry), symbol Tl and atomic number 81. It is a gray post-transition metal that is not found free in nature. When isolated, thallium resembles tin, but discolors when exposed to air. Chemists W ...
(), have two odd–even stable isotopes each. This makes a total of 30×1 + 9×2 = 48 stable odd–even isotopes. The lightest example of this type of nuclide is (protium) as
zero is an even number while the heaviest example is . There are also five primordial long-lived radioactive odd–even isotopes, , , , , and .
The last two were only recently found to decay, with half-lives greater than 10
18 years.
Even proton, odd neutron
These 53 stable nuclides have an even number of protons and an odd number of neutrons. By definition, they are all isotopes of even-''Z'' elements, where they are a minority in comparison to the even–even isotopes which are about 3 times as numerous. Among the 41 even-''Z'' elements that have a stable nuclide, only two elements (argon and cerium) have no even–odd stable nuclides. One element (tin) has three. There are 24 elements that have one even–odd nuclide and 13 that have two even–odd nuclides. The lightest example of this type of nuclide is and the heaviest is .
Of 34 primordial radionuclides there exist three even–odd nuclides (see table at right), including the
fissile
In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy. The predominant neutron energy may be typ ...
. Because of their odd neutron numbers, the even–odd nuclides tend to have large
neutron capture
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, ...
cross sections, due to the energy that results from neutron-pairing effects.
These stable even-proton odd-neutron nuclides tend to be uncommon by abundance in nature, generally because in order to form and contribute to the primordial abundance, they must have escaped capturing neutrons to form yet other stable even–even isotopes, during both the
s-process
The slow neutron-capture process, or ''s''-process, is a series of reactions in nuclear astrophysics that occur in stars, particularly asymptotic giant branch stars. The ''s''-process is responsible for the creation (nucleosynthesis) of approximat ...
and
r-process of neutron capture, during nucleosynthesis in stars. For this reason, only and are the most naturally abundant isotopes of their element, the former only by a small margin, and the latter only because the expected
beryllium-8
Beryllium-8 (8Be, Be-8) is a radionuclide with 4 neutrons and 4 protons. It is an unbound resonance and nominally an isotope of beryllium. It decays into two alpha particles with a half-life on the order of 8.19 seconds. This has important r ...
has lower
binding energy
In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
than two
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 ...
s and therefore immediately
alpha decay
Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an at ...
s.
Odd neutron number
Actinides
The actinide () or actinoid () series encompasses the 15 metallic chemical elements with atomic numbers from 89 to 103, actinium through lawrencium. The actinide series derives its name from the first element in the series, actinium. The inform ...
with odd neutron numbers are generally
fissile
In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy. The predominant neutron energy may be typ ...
(with
thermal neutron
The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term ''temperature'' is used, since hot, thermal and cold neutrons are moderated in a medium with ...
s), while those with even neutron numbers are generally not, though they are
fissionable
In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy. The predominant neutron energy may be typi ...
with
fast neutron
The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term ''temperature'' is used, since hot, thermal and cold neutrons are moderated in a medium with ...
s.
Only , , and have an odd neutron number and are the most naturally abundant isotope of their element.
References
{{reflist
Nuclear physics