Neutron number

Last updated February 10, 2024

The neutron number (symbol N) is the number of neutrons in a nuclide.

Atomic number (proton number) plus neutron number equals mass number: $Z + N = A$ . The difference between the neutron number and the atomic number is known as the neutron excess: $D = N - Z = A - 2 Z$ .

Neutron number is not written explicitly in nuclide symbol notation, but can be inferred as it is the difference between the two left-hand numbers (atomic number and mass).

Element	C: Carbon, no specific isotope
Isotope/Nuclide	¹⁴ C: Carbon-14 specifically.
With atomic number	¹⁴ ₆C: Carbon-14. No more specific (carbon always has six protons) but may be more clear.

Nuclides that have the same neutron number but different proton numbers are called isotones. This word was formed by replacing the p in isotope with n for neutron. Nuclides that have the same mass number are called isobars. Nuclides that have the same neutron excess are called isodiaphers.^[1]

Chemical properties are primarily determined by proton number, which determines which chemical element the nuclide is a member of; neutron number has only a slight influence.

Neutron number is primarily of interest for nuclear properties. For example, actinides with odd neutron number are usually fissile (fissionable with slow neutrons) while actinides with even neutron number are usually not fissile (but are fissionable with fast neutrons).

Only 58 stable nuclides have an odd neutron number, compared to 194 with an even neutron number. No odd-neutron-number isotope is the most naturally abundant isotope in its element, except for beryllium-9 (which is the only stable beryllium isotope), nitrogen-14, and platinum-195.

No stable nuclides have a neutron number of 19, 21, 35, 39, 45, 61, 89, 115, 123, or ≥ 127. There are 6 stable nuclides and one radioactive primordial nuclide with neutron number 82 (82 is the neutron number with the most stable nuclides, since it is a magic number): barium-138, lanthanum-139, cerium-140, praseodymium-141, neodymium-142, and samarium-144, as well as the radioactive primordial nuclide xenon-136, which decays by a very slow double beta process. Except 20, 50 and 82 (all these three numbers are magic numbers), all other neutron numbers have at most 4 stable nuclides (in the case of 20, there are 5 stable nuclides ³⁶S, ³⁷Cl, ³⁸Ar, ³⁹K, and ⁴⁰Ca, and in the case for 50, there are 5 stable nuclides: ⁸⁶Kr, ⁸⁸Sr, ⁸⁹Y, ⁹⁰Zr, and ⁹²Mo, and 1 radioactive primordial nuclide, ⁸⁷Rb). Most odd neutron numbers have at most one stable nuclide (exceptions are 1 (²H and ³He), 5 (⁹Be and ¹⁰B), 7 (¹³C and ¹⁴N), 55 (⁹⁷Mo and ⁹⁹Ru) and 107 (¹⁷⁹Hf and ^180mTa)). However, some even neutron numbers also have only one stable nuclide; these numbers are 0 (¹H), 2 (⁴He), 4 (⁷Li), 84 (¹⁴²Ce), 86 (¹⁴⁶Nd) and 126 (²⁰⁸Pb), the case of 84 is special, since ¹⁴²Ce is theoretically unstable to double beta decay, and the nuclides with 84 neutrons which are theoretically stable to both beta decay and double beta decay are ¹⁴⁴Nd and ¹⁴⁶Sm, but both nuclides are observed to alpha decay.^[2] (In theory, no stable nuclides have neutron number 19, 21, 35, 39, 45, 61, 71, 83–91, 95, 96, and ≥ 99) Besides, no nuclides with neutron number 19, 21, 35, 39, 45, 61, 71, 89, 115, 123, 147, ... are stable to beta decay (see Beta-decay stable isobars).

Only two stable nuclides have fewer neutrons than protons: hydrogen-1 and helium-3. Hydrogen-1 has the smallest neutron number, 0.

Related Research Articles

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 Da. For example, uranium-238 decays to form thorium-234.

Stable nuclides are nuclides that are not radioactive and so do not spontaneously undergo radioactive decay. When such nuclides are referred to in relation to specific elements, they are usually termed stable isotopes.

<span class="mw-page-title-main">Nuclide</span> Atomic species

A nuclide is a class of atoms characterized by their number of protons, Z, their number of neutrons, N, and their nuclear energy state.

In nuclear engineering, fissile material is material that can undergo nuclear fission when struck by a neutron of low energy. A self-sustaining thermal chain reaction can only be achieved with fissile material. The predominant neutron energy in a system may be typified by either slow neutrons or fast neutrons. Fissile material can be used to fuel thermal-neutron reactors, fast-neutron reactors and nuclear explosives.

<span class="mw-page-title-main">Decay chain</span> Series of radioactive decays

In nuclear science, the decay chain refers to a series of radioactive decays of different radioactive decay products as a sequential series of transformations. It is also known as a "radioactive cascade". The typical radioisotope does not decay directly to a stable state, but rather it decays to another radioisotope. Thus there is usually a series of decays until the atom has become a stable isotope, meaning that the nucleus of the atom has reached a stable state.

In nuclear physics, a magic number is a number of nucleons such that they are arranged into complete shells within the atomic nucleus. As a result, atomic nuclei with a 'magic' number of protons or neutrons are much more stable than other nuclei. The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126.

Protactinium (₉₁Pa) has no stable isotopes. The four naturally occurring isotopes allow a standard atomic weight to be given.

Technetium (₄₃Tc) is one of the two elements with Z < 83 that have no stable isotopes; the other such element is promethium. It is primarily artificial, with only trace quantities existing in nature produced by spontaneous fission or neutron capture by molybdenum. The first isotopes to be synthesized were ⁹⁷Tc and ⁹⁹Tc in 1936, the first artificial element to be produced. The most stable radioisotopes are ⁹⁷Tc, ⁹⁸Tc, and ⁹⁹Tc.

Beryllium (₄Be) has 11 known isotopes and 3 known isomers, but only one of these isotopes is stable and a primordial nuclide. As such, beryllium is considered a monoisotopic element. It is also a mononuclidic element, because its other isotopes have such short half-lives that none are primordial and their abundance is very low. Beryllium is unique as being the only monoisotopic element with both an even number of protons and an odd number of neutrons. There are 25 other monoisotopic elements but all have odd atomic numbers, and even numbers of neutrons.

Plutonium (₉₄Pu) is an artificial element, except for trace quantities resulting from neutron capture by uranium, and thus a standard atomic weight cannot be given. Like all artificial elements, it has no stable isotopes. It was synthesized long before being found in nature, the first isotope synthesized being ²³⁸Pu in 1940. Twenty plutonium radioisotopes have been characterized. The most stable are plutonium-244 with a half-life of 80.8 million years, plutonium-242 with a half-life of 373,300 years, and plutonium-239 with a half-life of 24,110 years. All of the remaining radioactive isotopes have half-lives that are less than 7,000 years. This element also has eight meta states; all have half-lives of less than one second.

A table or chart of nuclides is a two-dimensional graph of isotopes of the elements, in which one axis represents the number of neutrons and the other represents the number of protons in the atomic nucleus. Each point plotted on the graph thus represents a nuclide of a known or hypothetical chemical element. This system of ordering nuclides can offer a greater insight into the characteristics of isotopes than the better-known periodic table, which shows only elements and not their isotopes. The chart of the nuclides is also known as the Segrè chart, after the Italian physicist Emilio Segrè.

<span class="mw-page-title-main">Valley of stability</span> Characterization of nuclide stability

In nuclear physics, the valley of stability is a characterization of the stability of nuclides to radioactivity based on their binding energy. Nuclides are composed of protons and neutrons. The shape of the valley refers to the profile of binding energy as a function of the numbers of neutrons and protons, with the lowest part of the valley corresponding to the region of most stable nuclei. The line of stable nuclides down the center of the valley of stability is known as the line of beta stability. The sides of the valley correspond to increasing instability to beta decay. The decay of a nuclide becomes more energetically favorable the further it is from the line of beta stability. The boundaries of the valley correspond to the nuclear drip lines, where nuclides become so unstable they emit single protons or single neutrons. Regions of instability within the valley at high atomic number also include radioactive decay by alpha radiation or spontaneous fission. The shape of the valley is roughly an elongated paraboloid corresponding to the nuclide binding energies as a function of neutron and atomic numbers.

<span class="mw-page-title-main">Isotope</span> Different atoms of the same element

Isotopes are distinct nuclear species of the same chemical element. They have the same atomic number and position in the periodic table, but differ in nucleon numbers due to different numbers of neutrons in their nuclei. While all isotopes of a given element have almost the same chemical properties, they have different atomic masses and physical properties.

<span class="mw-page-title-main">Primordial nuclide</span> Nuclides predating the Earths formation (found on Earth)

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 interstellar medium from which the solar system was formed, and were formed in, or after, the Big Bang, by nucleosynthesis in stars and supernovae followed by mass ejection, by cosmic ray spallation, and potentially from other processes. They are the stable nuclides plus the long-lived fraction of radionuclides surviving in the primordial solar nebula through planet accretion until the present; 286 such nuclides are known.

Beta-decay stable isobars are the set of nuclides which cannot undergo beta decay, that is, the transformation of a neutron to a proton or a proton to a neutron within the nucleus. A subset of these nuclides are also stable with regards to double beta decay or theoretically higher simultaneous beta decay, as they have the lowest energy of all isobars with the same mass number.

<span class="mw-page-title-main">Isobar (nuclide)</span> Atoms with the same number of nucleons

Isobars are atoms (nuclides) of different chemical elements that have the same number of nucleons. Correspondingly, isobars differ in atomic number but have the same mass number. An example of a series of isobars is ⁴⁰S, ⁴⁰Cl, ⁴⁰Ar, ⁴⁰K, and ⁴⁰Ca. While the nuclei of these nuclides all contain 40 nucleons, they contain varying numbers of protons and neutrons.

A monoisotopic element is an element which has only a single stable isotope (nuclide). There are 26 such elements, as listed.

The Mattauch isobar rule, formulated by Josef Mattauch in 1934, states that if two adjacent elements on the periodic table have isotopes of the same mass number, one of these isotopes must be radioactive. Two nuclides that have the same mass number (isobars) can both be stable only if their atomic numbers differ by more than one. In fact, for currently observationally stable nuclides, the difference can only be 2 or 4, and in theory, two nuclides that have the same mass number cannot be both stable, but many such nuclides which are theoretically unstable to double beta decay have not been observed to decay, e.g. ¹³⁴Xe. However, this rule cannot make predictions on the half-lives of these radioisotopes.

<span class="mw-page-title-main">Even and odd atomic nuclei</span> Nuclear physics classification method

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

↑ Teh Fu Yen, Chemistry for Engineers (Imperial College Press, 2008), p.265
↑ Audi, G.; Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S. (2017). "The NUBASE2016 evaluation of nuclear properties" (PDF). Chinese Physics C. 41 (3): 030001. Bibcode:2017ChPhC..41c0001A. doi:10.1088/1674-1137/41/3/030001.

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[1] Teh Fu Yen, Chemistry for Engineers (Imperial College Press, 2008), p.265

[NUBASE2016-2] Audi, G.; Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S. (2017). "The NUBASE2016 evaluation of nuclear properties" (PDF). Chinese Physics C. 41 (3): 030001. Bibcode:2017ChPhC..41c0001A. doi:10.1088/1674-1137/41/3/030001.

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