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 based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron ...
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 , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
s to its number of
protons. 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
The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called the ...
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 each element 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 with the 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 t ...
(''Z'' = 20), there exists a stable isotope with ''N''/''Z'' ratio of one, with the exception of
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 ...
(''N''/''Z'' = 1.25) and every element with odd atomic number between 9 and 19 inclusive (''N'' = ''Z'' + 1).
Hydrogen-1
Hydrogen (1H) has three naturally occurring isotopes, sometimes denoted , , and . and are stable, while has a half-life of years. Heavier isotopes also exist, all of which are synthetic and have a half-life of less than one zeptosecond (10∠...
(''N''/''Z'' ratio = 0) and
helium-3 (''N''/''Z'' ratio = 0.5) are the only stable isotopes with neutron–proton ratio under one.
Uranium-238 has the highest ''N''/''Z'' ratio of any
primordial nuclide at 1.587,
while
lead-208
Lead (82Pb) has four stable isotopes: 204Pb, 206Pb, 207Pb, 208Pb. Lead-204 is entirely a primordial nuclide and is not a radiogenic nuclide. The three isotopes lead-206, lead-207, and lead-208 represent the ends of three decay chains: the uraniu ...
has the highest ''N''/''Z'' ratio of any known stable isotope at 1.537.
Radioactive decay 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) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an at ...
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 ...
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. Thi ...
also increase the ratio, while
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 ...
decreases the ratio.
Nuclear waste
Radioactive waste is a type of hazardous waste that contains radioactive material. Radioactive waste is a result of many activities, including nuclear medicine, nuclear research, nuclear power generation, rare-earth mining, and nuclear weapons ...
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 maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given ra ...
or close to a minimum.
From the liquid drop model, this bonding energy is approximated by empirical
Bethe–Weizsäcker formula
:
Given a value of
and ignoring the contributions of nucleon spin pairing (i.e. ignoring the
term), the binding energy is a quadratic expression in
that is minimized when the neutron-proton ratio is
.
See also
*
Isotope#Variation in properties between isotopes
*
Nuclear fission
*
Nuclear drip line
The nuclear drip line is the boundary beyond which atomic nuclei decay by the emission of a proton or neutron.
An arbitrary combination of protons and neutrons does not necessarily yield a stable nucleus. One can think of moving up and/or to ...
Nuclear physics
Ratios
References
{{nuclear-stub