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 ...

splits a heavy nucleus such as

uranium Uranium is a chemical element; it has chemical symbol, symbol U and atomic number 92. It is a silvery-grey metal in the actinide series of the periodic table. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons. Ura ...

plutonium Plutonium is a chemical element; it has symbol Pu and atomic number 94. It is a silvery-gray actinide metal that tarnishes when exposed to air, and forms a dull coating when oxidized. The element normally exhibits six allotropes and four ...

into two lighter nuclei, which are called fission products. Yield refers to the fraction of a fission product produced per fission. Yield can be broken down by: # Individual

isotope Isotopes are distinct nuclear species (or ''nuclides'') of the same chemical element. They have the same atomic number (number of protons in their Atomic nucleus, nuclei) and position in the periodic table (and hence belong to the same chemica ...

Chemical element A chemical element is a chemical substance whose atoms all have the same number of protons. The number of protons is called the atomic number of that element. For example, oxygen has an atomic number of 8: each oxygen atom has 8 protons in its ...

spanning several isotopes of different

mass number The mass number (symbol ''A'', from the German word: ''Atomgewicht'', "atomic 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 appro ...

but same

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of pro ...

. # Nuclei of a given

regardless of

. Known as "chain yield" because it represents a

decay chain In nuclear science a decay chain refers to the predictable series of radioactive disintegrations undergone by the nuclei of certain unstable chemical elements. Radioactive isotopes do not usually decay directly to stable isotopes, but rather ...

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 ...

. Isotope and element yields will change as the fission products undergo beta decay, while chain yields do not change after completion of

neutron emission Neutron emission is a mode of radioactive decay in which one or more neutrons are ejected from a Atomic nucleus, nucleus. It occurs in the most neutron-rich/proton-deficient nuclides, and also from excited states of other nuclides as in photodisin ...

by a few neutron-rich initial fission products ( delayed neutrons), with

half-life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...

measured in seconds. A few isotopes can be produced directly by fission, but not by beta decay because the would-be precursor with atomic number one less is stable and does not decay (atomic number grows by 1 during beta decay). Chain yields do not account for these "shadowed" isotopes; however, they have very low yields (less than a millionth as much as common fission products) because they are far less neutron-rich than the original heavy nuclei. Yield is usually stated as

percentage In mathematics, a percentage () is a number or ratio expressed as a fraction (mathematics), fraction of 100. It is often Denotation, denoted using the ''percent sign'' (%), although the abbreviations ''pct.'', ''pct'', and sometimes ''pc'' are ...

per fission, so that the total yield percentages sum to 200%. Less often, it is stated as percentage of all fission product.

Definitions

There are several types of yields. For the most common fission reactions, the decay of the fission products preserve mass number. Thus the products form decay chains of constant mass. That makes the ''independent yield'' especially useful.Mills, R. W. (1995). Fission product yield evaluation (Doctoral dissertation, University of Birmingham). The ''independent yield'' is a product of three factors, Y(A) the ''sum yield'' or ''mass yield'',

f(A,Z)

the ''fractional independent yield'', and R(A,Z,I) the isomeric yield ratio:

\textrm(A,Z,I) = \textrm(A)\cdot f(A,Z) \cdot R(A,Z,I)

Here possible product of fission can be represented by a triplet (A,Z,I), where A is the

, Z is the

, and I is an integer for isomeric excited state, numbered from 0 for the ground state. For each decay chain (mass number A) the fractional independent yields and isomeric yield formulas sum to one:

\Sigma_Z f(A,Z) = \Sigma_I R(A,Z,I) = 1

and the independent yields sum to the sum yield for each chain:

\textrm(A) = \Sigma_ \textrm(A,Z,I).

The independent yield excludes delayed neutron emission. The ''cumulative yield,'', c(A,Z,I), of a nuclide (A,Z,I) is the total number of atoms produced by one fission over all time. The ''chain yield'', Ch(A), is the sum of all the cumulative yields for one mass chain for one fission. The independent, cumulative, and chain yields are given as percent per fission, that is as the yield of products per 100 fission reaction.

Mass vs. yield curve

If a graph of the

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

or mole yield of fission products against the

of the fragments is drawn then it has two peaks, one in the area zirconium through to

palladium Palladium is a chemical element; it has symbol Pd and atomic number 46. It is a rare and lustrous silvery-white metal discovered in 1802 by the English chemist William Hyde Wollaston. He named it after the asteroid Pallas (formally 2 Pallas), ...

and one at

xenon Xenon is a chemical element; it has symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as the ...

through to

neodymium Neodymium is a chemical element; it has Symbol (chemistry), symbol Nd and atomic number 60. It is the fourth member of the lanthanide series and is considered to be one of the rare-earth element, rare-earth metals. It is a hard (physics), hard, sli ...

. This is because the fission event causes the nucleus to split in an asymmetric manner, as nuclei closer to magic numbers are more stable. Yield vs. Z - This is a typical distribution for the fission of

. Note that in the calculations used to make this graph the activation of fission products was ignored and the fission was assumed to occur in a single moment rather than a length of time. In this bar chart results are shown for different cooling times (time after fission). Fission yield volatile 2

Because of the stability of nuclei with even numbers 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 and/or

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 the curve of yield against element is not a smooth curve. It tends to alternate. In general, the higher the energy of the state that undergoes nuclear fission, the more likely a symmetric fission is, hence as the neutron energy increases and/or the energy of the

fissile In nuclear engineering, fissile material is material that can undergo nuclear fission when struck by a neutron of low energy. A self-sustaining thermal Nuclear chain reaction#Fission chain reaction, chain reaction can only be achieved with fissil ...

atom increases, the valley between the two peaks becomes more shallow; for instance, the curve of yield against mass for Pu-239 has a more shallow valley than that observed for U-235, when the neutrons are thermal neutrons. The curves for the fission of the later actinides tend to make even more shallow valleys. In extreme cases such as ²⁵⁹Fm, only one peak is seen. Yield is usually expressed relative to number of fissioning nuclei, not the number of fission product nuclei, that is, yields should sum to 200%. The table in the next section ("Ordered by yield") gives yields for notable

radioactive 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 ...

(with half-lives greater than one year, plus iodine-131) fission products, and (the few most absorptive) neutron poison fission products, from thermal neutron fission of U-235 (typical of

nuclear power Nuclear power is the use of nuclear reactions to produce electricity. Nuclear power can be obtained from nuclear fission, nuclear decay and nuclear fusion reactions. Presently, the vast majority of electricity from nuclear power is produced by ...

reactors), computed fro

The yields in the table sum to only 45.5522%, including 34.8401% which have half-lives greater than one year: The remainder and the unlisted 54.4478% decay with half-lives less than one year into nonradioactive nuclei. This is before accounting for the effects of any subsequent neutron capture; e.g.: * Xenon-135, ¹³⁵Xe capturing a neutron and becoming nearly stable ¹³⁶Xe, rather than decaying to ¹³⁵Cs which is radioactive with a half-life of 2.3 million years * Nonradioactive ¹³³Cs capturing a neutron and becoming ¹³⁴Cs, which is radioactive with a half-life of 2 years * Many of the fission products with mass 147 or greater such as ¹⁴⁷Pm, ¹⁴⁹Sm, ¹⁵¹Sm, and ¹⁵⁵Eu have significant cross sections for neutron capture, so that one heavy fission product atom can undergo multiple successive neutron captures. Besides fission products, the other types of radioactive products are *

containing ²³⁸Pu, ²³⁹Pu, ²⁴⁰Pu, ²⁴¹Pu, and ²⁴²Pu, * minor actinides including ²³⁷Np, ²⁴¹Am, ²⁴³Am, curium isotopes, and perhaps

californium Californium is a synthetic chemical element; it has symbol Cf and atomic number 98. It was first synthesized in 1950 at Lawrence Berkeley National Laboratory (then the University of California Radiation Laboratory) by bombarding curium with al ...

* reprocessed uranium containing ²³⁶U and other isotopes *

tritium Tritium () or hydrogen-3 (symbol T or H) is a rare and radioactive isotope of hydrogen with a half-life of ~12.33 years. The tritium nucleus (t, sometimes called a ''triton'') contains one proton and two neutrons, whereas the nucleus of the ...

* activation products of neutron capture by the reactor or bomb structure or the environment

Fission products from U-235

Cumulative fission yields

Cumulative fission yields give the amounts of nuclides produced either directly in the fission or by decay of other nuclides.

Ordered by mass number

Decays, even if lengthy, are given down to the stable nuclide. Decays with half lives longer than a century are marked with a single asterisk (), while decays with a half life longer than a hundred million years are marked with two asterisks ().

Half lives, decay modes, and branching fractions

Ordered by thermal neutron absorption cross section

{, class="wikitable sortable" ! Barns !! Yield !! Isotope !! ''t''_½ !! Comment , - , align= , , 6.3333% , , ¹³⁵I → ¹³⁵Xe , , 6.57 h , , Most important neutron poison;

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, wh ...

rapidly converts ¹³⁵Xe to ¹³⁶Xe; remainder decays (9.14 h) to ¹³⁵Cs (2.3 My). , - , align= , , 0.0065% , , ¹⁵⁷Gd , , ∞ , , Neutron poison, but low yield. , - , align= , , 1.0888% , , ¹⁴⁹Sm , , ∞ , , 2nd most important neutron poison. , - , align= , , 0.0003% , , ^113mCd , , 14.1 y , , Most will be destroyed by neutron capture. , - , align= , , 0.4203% , , ¹⁵¹Sm , , 90 y , , Most will be destroyed by neutron capture. , - , align=
60,900 , , 0.0330% , , ¹⁵⁵Eu → ¹⁵⁵Gd , , 4.76 y , , Both neutron poisons. , - , align= , , 2.2713% , , ¹⁴⁷Pm , , 2.62 y, , Suitable for

radioisotope thermoelectric generator A radioisotope thermoelectric generator (RTG, RITEG), or radioisotope power system (RPS), is a type of nuclear battery that uses an array of thermocouples to convert the Decay heat, heat released by the decay of a suitable radioactive material i ...

s with annual or semi-annual refueling. , - , align= , , 2.8336% , , ¹³¹I , , 8.02 d , - , align=
140 , , 6.7896% , , ¹³³Cs → ¹³⁴Cs , , ∞
2.065 y , ,

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, wh ...

converts a few percent of nonradioactive ¹³³Cs to ¹³⁴Cs, which has very low direct yield because

stops at ¹³⁴Xe; further capture will add to long-lived ¹³⁵Cs. , - , align= , , 6.0507% , , ⁹⁹Tc , , 211 ky , , Candidate for disposal by nuclear transmutation. , - , align= , , 0.6576% , , ¹²⁹I , , 15.7 My , , Candidate for disposal by nuclear transmutation. , - , align= , , 6.2956% , , ⁹³Zr , , 1.53 My , , Transmutation impractical. , - , align= , , 0.1629% , , ¹⁰⁷Pd , , 6.5 My , - , align= , , 0.2717% , , ⁸⁵Kr , , 10.78 y , - , align= , , 5.7518% , , ⁹⁰Sr , , 28.9 y , - , align= , , 0.3912% , , ¹⁰⁶Ru , , 373.6 d , - , align= , , 6.0899% , , ¹³⁷Cs , , 30.17 y , - , , , 0.0297% , , ¹²⁵Sb , , 2.76 y , - , , , 0.0236% , , ¹²⁶Sn , , 230 ky , - , , , 0.0508% , , ⁷⁹Se , , {{ntsh, 327000 327 ky , -

References

External links

HANDBOOK OF NUCLEAR DATA FOR SAFEGUARDS: DATABASE EXTENSIONS, AUGUST 2008
* '
The Live Chart of Nuclides - IAEA
'' Color-map of yields, and detailed data by click on a nuclide. Nuclear fission Nuclear chemistry