neutron–proton ratio
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The neutron–proton ratio (N/Z ratio or nuclear ratio) of an
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 ...
is the
ratio In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of its number of
neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...
s to its number of
proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
s. Among stable nuclei and naturally occurring nuclei, this ratio generally increases with increasing atomic number. This is because electrical repulsive forces between protons scale with distance differently than
strong nuclear force 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 interactions. It confines quarks into protons, neutrons, and other hadron particles, an ...
attractions. In particular, most pairs of protons in large nuclei are not far enough apart, such that electrical repulsion dominates over the strong nuclear force, and thus proton density in stable larger nuclei must be lower than in stable smaller nuclei where more pairs of protons have appreciable short-range nuclear force attractions. For many elements with atomic number ''Z'' small enough to occupy only the first three nuclear shells, that is up to that of
calcium Calcium is a chemical element; it has symbol Ca and atomic number 20. As an alkaline earth metal, calcium is a reactive metal that forms a dark oxide-nitride layer when exposed to air. Its physical and chemical properties are most similar to it ...
(''Z'' = 20), there exists a stable isotope with ''N''/''Z'' ratio of one. The exceptions are
beryllium Beryllium is a chemical element; it has Symbol (chemistry), symbol Be and atomic number 4. It is a steel-gray, hard, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with ...
(''N''/''Z'' = 1.25) and every element with odd atomic number between 9 and 19 inclusive (though in those cases ''N'' = ''Z'' + 1 always allows for stability). Hydrogen-1 (''N''/''Z'' ratio = 0) and
helium-3 Helium-3 (3He see also helion) is a light, stable isotope of helium with two protons and one neutron. (In contrast, the most common isotope, helium-4, has two protons and two neutrons.) Helium-3 and hydrogen-1 are the only stable nuclides with ...
(''N''/''Z'' ratio = 0.5) are the only stable isotopes with neutron–proton ratio under one.
Uranium-238 Uranium-238 ( or U-238) is the most common isotope of uranium found in nature, with a relative abundance of 99%. Unlike uranium-235, it is non-fissile, which means it cannot sustain a chain reaction in a thermal-neutron reactor. However, it i ...
has the highest ''N''/''Z'' ratio of any
primordial nuclide In geochemistry, geophysics and nuclear physics, primordial nuclides, also known as primordial isotopes, are nuclides found on Earth that have existed in their current form since before Earth was formed. Primordial nuclides were present in the ...
at 1.587, while mercury-204 has the highest ''N''/''Z'' ratio of any known stable isotope at 1.55.
Radioactive 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 conside ...
generally proceeds so as to change the ''N''/''Z'' ratio to increase stability. If the ''N''/''Z'' ratio is greater than 1,
alpha decay Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus). The parent nucleus transforms or "decays" into a daughter product, with a mass number that is reduced by four and an a ...
increases the ''N''/''Z'' ratio, and hence provides a common pathway towards stability for decays involving large nuclei with too few neutrons.
Positron emission Positron emission, beta plus decay, or β+ decay is a subtype of radioactive decay called beta decay, in which a proton inside a radionuclide nucleus is converted into a neutron while releasing a positron and an electron neutrino (). Positron emi ...
and
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. Th ...
also increase the ratio, while
beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which an atomic nucleus emits a beta particle (fast energetic electron or positron), transforming into an isobar of that nuclide. For example, beta decay of a neutron ...
decreases the ratio.
Nuclear waste Radioactive waste is a type of hazardous waste that contains radioactive material. It is a result of many activities, including nuclear medicine, nuclear research, nuclear power generation, nuclear decommissioning, rare-earth mining, and nuclear ...
exists mainly because nuclear fuel has a higher stable ''N''/''Z'' ratio than its fission products.


Semi-empirical description

For stable nuclei, the neutron-proton ratio is such that the
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 ...
is at a
local minimum In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum, they may be defined either within a given range (the ''local'' or ''relative ...
or close to a minimum. From the liquid drop model, this bonding energy is approximated by empirical Bethe–Weizsäcker formula :E_ = a_ A - a_ A^ - a_ \frac - a_ \frac \pm \delta(A,Z). Given a value of A and ignoring the contributions of nucleon spin pairing (i.e. ignoring the \pm \delta(A,Z) term), the binding energy is a quadratic expression in Z that is minimized when the neutron-proton ratio is N/Z \approx 1 + \frac A^ .


See also

* *
Nuclear fission Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactiv ...
*
Nuclear drip line The nuclear drip line is the boundary beyond which atomic nuclei are unbound with respect to the emission of a proton or neutron. An arbitrary combination of protons and neutrons does not necessarily yield a stable atomic nucleus, nucleus. One ...


References


Nuclear physics Ratios {{nuclear-stub