2438:), which binds protons and neutrons equally to each other, has a limited range due to a rapid exponential decrease in this force with distance. However, the repelling electromagnetic force, which acts between protons to force nuclei apart, falls off with distance much more slowly (as the inverse square of distance). For nuclei larger than about four nucleons in diameter, the additional repelling force of additional protons more than offsets any binding energy that results between further added nucleons as a result of additional strong force interactions. Such nuclei become increasingly less tightly bound as their size increases, though most of them are still stable. Finally, nuclei containing more than 209 nucleons (larger than about 6 nucleons in diameter) are all too large to be stable, and are subject to spontaneous decay to smaller nuclei.
1432:, has tried since the 1950s to derive useful power from nuclear fusion reactions that combine small nuclei into bigger ones, typically to heat boilers, whose steam could turn turbines and produce electricity. No earthly laboratory can match one feature of the solar powerhouse: the great mass of the Sun, whose weight keeps the hot plasma compressed and confines the nuclear furnace to the Sun's core. Instead, physicists use strong magnetic fields to confine the plasma, and for fuel they use heavy forms of hydrogen, which burn more easily. Magnetic traps can be rather unstable, and any plasma hot enough and dense enough to undergo nuclear fusion tends to slip out of them after a short time. Even with ingenious tricks, the confinement in most cases lasts only a small fraction of a second.
905:
1544:. The weak force, like the strong force, has a short range, but is much weaker than the strong force. The weak force tries to make the number of neutrons and protons into the most energetically stable configuration. For nuclei containing less than 40 particles, these numbers are usually about equal. Protons and neutrons are closely related and are collectively known as nucleons. As the number of particles increases toward a maximum of about 209, the number of neutrons to maintain stability begins to outstrip the number of protons, until the ratio of neutrons to protons is about three to two.
2244:
2010:
reactants. Light elements can undergo energy-producing nuclear interactions by fusion or fission. All energy-producing nuclear interactions between two hydrogen isotopes and between hydrogen and helium-3 are fusion, as the product of these interactions include a heavier nucleus. However, the energy-producing nuclear interaction of a neutron with lithium–6 produces
Hydrogen-3 and Helium-4, each a lighter nucleus. By the definition above, this nuclear interaction is fission, not fusion. When fission is caused by a neutron, as in this case, it is called induced fission.
1418:, nuclei began to stick together. When this began to happen, protons combined into deuterium and then helium, with some protons changing in the process to neutrons (plus positrons, positive electrons, which combine with electrons and annihilate into gamma-ray photons). This released nuclear energy now keeps up the high temperature of the Sun's core, and the heat also keeps the gas pressure high, keeping the Sun at its present size, and stopping gravity from compressing it any more. There is now a stable balance between gravity and pressure.
1307:, contains a proton and a neutron. The most common isotope of helium contains two protons and two neutrons, and those of carbon, nitrogen and oxygen – six, seven and eight of each particle, respectively. However, a helium nucleus weighs less than the sum of the weights of the two heavy hydrogen nuclei which combine to make it. The same is true for carbon, nitrogen and oxygen. For example, the carbon nucleus is slightly lighter than three helium nuclei, which can combine to make a carbon nucleus. This difference is known as the mass defect.
1448:(a nucleus with 26 protons), the fusion process no longer releases energy. In even heavier nuclei energy is consumed, not released, by combining similarly sized nuclei. With such large nuclei, overcoming the electric repulsion (which affects all protons in the nucleus) requires more energy than is released by the nuclear attraction (which is effective mainly between close neighbors). Conversely, energy could actually be released by breaking apart nuclei heavier than iron.
3133:
918:
1568:, and furthermore the helium product does not harm the environment, so some consider nuclear fusion a good alternative to supply our energy needs. Experiments to carry out this form of fusion have so far only partially succeeded. Sufficiently hot deuterium and tritium must be confined. One technique is to use very strong magnetic fields, because charged particles (like those trapped in the Earth's radiation belt) are guided by magnetic field lines.
1201:, it was apparent that their magnetic forces might be 20 or 30 newtons, attractive if properly oriented. A pair of protons would do 10 joules of work to each other as they approach – that is, they would need to release energy of 0.5 MeV in order to stick together. On the other hand, once a pair of nucleons magnetically stick, their external fields are greatly reduced, so it is difficult for many nucleons to accumulate much magnetic energy.
2373:
133:
25:
4432:
1609:. In the simplest beta decay, neutrons are converted to protons by emitting a negative electron and an antineutrino. This is always possible outside a nucleus because neutrons are more massive than protons by an equivalent of about 2.5 electrons. In the opposite process, which only happens within a nucleus, and not to free particles, a proton may become a neutron by ejecting a
1985:(gamma rays), or both. Note that for radioactive decay, it is not strictly necessary for the binding energy to increase. What is strictly necessary is that the mass decrease. If a neutron turns into a proton and the energy of the decay is less than 0.782343 MeV, the difference between the masses of the neutron and proton multiplied by the speed of light squared, (such as
1378:, which holds nucleons together. The electric force may be weaker than the strong nuclear force, but the strong force has a much more limited range: in an iron nucleus, each proton repels the other 25 protons, while the nuclear force only binds close neighbors. So for larger nuclei, the electrostatic forces tend to dominate and the nucleus will tend over time to break up.
1493:), and the best sources of energy are therefore nuclei whose weights are as far removed from iron as possible. One can combine the lightest ones—nuclei of hydrogen (protons)—to form nuclei of helium, and that is how the Sun generates its energy. Alternatively, one can break up the heaviest ones—nuclei of uranium or plutonium—into smaller fragments, and that is what
997:. In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what the binding energy means.
1955:. If an atom of lower average binding energy per nucleon is changed into two atoms of higher average binding energy per nucleon, energy is emitted. (The average here is the weighted average.) Also, if two atoms of lower average binding energy fuse into an atom of higher average binding energy, energy is emitted. The chart shows that fusion, or combining, of
1348:. By this formula, adding energy also increases mass (both weight and inertia), whereas removing energy decreases mass. For example, a helium atom containing four nucleons has a mass about 0.8% less than the total mass of four hydrogen atoms (each containing one nucleon). The helium nucleus has four nucleons bound together, and the
2737:
1584:
The net binding energy of a nucleus is that of the nuclear attraction, minus the disruptive energy of the electric force. As nuclei get heavier than helium, their net binding energy per nucleon (deduced from the difference in mass between the nucleus and the sum of masses of component nucleons) grows
1509:
overcomes the repulsion and causes them to stick together. The nuclear force is a close-range force (it is strongly attractive at a distance of 1.0 fm and becomes extremely small beyond a distance of 2.5 fm), and virtually no effect of this force is observed outside the nucleus. The nuclear
1413:
Thermal energy appears as the motion of atoms and molecules: the higher the temperature of a collection of particles, the greater is their velocity and the more violent are their collisions. When the temperature at the center of the newly formed Sun became great enough for collisions between hydrogen
3770:
In the table above it can be seen that the decay of a neutron, as well as the transformation of tritium into helium-3, releases energy; hence, it manifests a stronger bound new state when measured against the mass of an equal number of neutrons (and also a lighter state per number of total hadrons).
3527:
Fe has the lowest nucleon-specific mass of the four nuclides listed in this table, but this does not imply it is the strongest bound atom per hadron, unless the choice of beginning hadrons is completely free. Iron releases the largest energy if any 56 nucleons are allowed to build a nuclide—changing
2267:
increases. This increase is generated by increasing forces per nucleon in the nucleus, as each additional nucleon is attracted by other nearby nucleons, and thus more tightly bound to the whole. Helium-4 and oxygen-16 are particularly stable exceptions to the trend (see figure on the right). This is
1613:
and an electron neutrino. This is permitted if enough energy is available between parent and daughter nuclides to do this (the required energy difference is equal to 1.022 MeV, which is the mass of 2 electrons). If the mass difference between parent and daughter is less than this, a proton-rich
1536:
The binding energy of helium is the energy source of the Sun and of most stars. The sun is composed of 74 percent hydrogen (measured by mass), an element having a nucleus consisting of a single proton. Energy is released in the Sun when 4 protons combine into a helium nucleus, a process in which two
1440:
Small nuclei that are larger than hydrogen can combine into bigger ones and release energy, but in combining such nuclei, the amount of energy released is much smaller compared to hydrogen fusion. The reason is that while the overall process releases energy from letting the nuclear attraction do its
2312:
of Ni to form Fe may be energetically possible in an extremely hot star core, due to this beta decay conversion of neutrons to protons. This favors the creation of Fe, the nuclide with the lowest mass per nucleon. However, at high temperatures not all matter will be in the lowest energy state. This
1634:
more than trace quantities in nature, uranium U, are unstable, but having a half-life of 4.5 billion years, close to the age of the Earth, they are still relatively abundant; they (and other nuclei heavier than helium) have formed in stellar evolution events like supernova explosions preceding the
1633:
The curve of binding energy is a graph that plots the binding energy per nucleon against atomic mass. This curve has its main peak at iron and nickel and then slowly decreases again, and also a narrow isolated peak at helium, which is more stable than other low-mass nuclides. The heaviest nuclei in
1385:
is reached (84 protons), nuclei can no longer accommodate their large positive charge, but emit their excess protons quite rapidly in the process of alpha radioactivity—the emission of helium nuclei, each containing two protons and two neutrons. (Helium nuclei are an especially stable combination.)
2206:
This practice is useful for other reasons, too: stripping all the electrons from a heavy unstable nucleus (thus producing a bare nucleus) changes the lifetime of the nucleus, or the nucleus of a stable neutral atom can likewise become unstable after stripping, indicating that the nucleus cannot be
1580:
of light elements, such as carbon, nitrogen and oxygen, the most stable combination of neutrons and of protons occurs when the numbers are equal (this continues to element 20, calcium). However, in heavier nuclei, the disruptive energy of protons increases, since they are confined to a tiny volume
1547:
The protons of hydrogen combine to helium only if they have enough velocity to overcome each other's mutual repulsion sufficiently to get within range of the strong nuclear attraction. This means that fusion only occurs within a very hot gas. Hydrogen hot enough for combining to helium requires an
1225:
The fact that nuclei do not clump together (fuse) under normal conditions suggests that the nuclear force must be weaker than the electric repulsion at larger distances, but stronger at close range. Therefore, it has short-range characteristics. An analogy to the nuclear force is the force between
2275:
The region of increasing binding energy is followed by a region of relative stability (saturation) in the sequence from about mass 30 through about mass 90. In this region, the nucleus has become large enough that nuclear forces no longer completely extend efficiently across its width. Attractive
1597:
To reduce the disruptive energy, the weak interaction allows the number of neutrons to exceed that of protons—for instance, the main isotope of iron has 26 protons and 30 neutrons. Isotopes also exist where the number of neutrons differs from the most stable number for that number of nucleons. If
2468:). The nuclear fission of a few light elements (such as Lithium) occurs because Helium-4 is a product and a more tightly bound element than slightly heavier elements. Both processes produce energy as the sum of the masses of the products is less than the sum of the masses of the reacting nuclei.
2009:
The energy-producing nuclear interaction of light elements requires some clarification. Frequently, all light element energy-producing nuclear interactions are classified as fusion, however by the given definition above fusion requires that the products include a nucleus that is heavier than the
1128:
are combined to form heavier nuclei such as helium. The Sun and other stars use nuclear fusion to generate thermal energy which is later radiated from the surface, a type of stellar nucleosynthesis. In any exothermic nuclear process, nuclear mass might ultimately be converted to thermal energy,
2234:
happens to the nucleus, meaning that properties ascribed to the nucleus change in the event. In the field of physics the concept of "mass deficit" as a measure for "binding energy" means "mass deficit of the neutral atom" (not just the nucleus) and is a measure for stability of the whole atom.
1593:
is the most tightly bound nucleus in terms of binding energy per nucleon. (Nickel-62's higher binding energy does not translate to a larger mean mass loss than Fe, because Ni has a slightly higher ratio of neutrons/protons than does iron-56, and the presence of the heavier neutrons increases
3544:
neutrons, then Fe would release the most energy per nucleon, since it has a larger fraction of protons than Ni. However, if nuclei are required to be constructed of only the same number of protons and neutrons that they contain, then nickel-62 is the most tightly bound nucleus, per nucleon.
1233:
or electrical forces, the nuclear force is effective only at very short distances. At greater distances, the electrostatic force dominates: the protons repel each other because they are positively charged, and like charges repel. For that reason, the protons forming the nuclei of ordinary
1120:. Nuclear energy may be released by fission, when heavy atomic nuclei (like uranium and plutonium) are broken apart into lighter nuclei. The energy from fission is used to generate electric power in hundreds of locations worldwide. Nuclear energy is also released during fusion, when light
1585:
more and more slowly, reaching its peak at iron. As nucleons are added, the total nuclear binding energy always increases—but the total disruptive energy of electric forces (positive protons repelling other protons) also increases, and past iron, the second increase outweighs the first.
3306:(number of nucleons in the nuclide). If we assume the reference nucleon has the mass of a neutron (so that all "total" binding energies calculated are maximal) we could define the total binding energy as the difference from the mass of the nucleus, and the mass of a collection of
1638:. The most common isotope of thorium, Th, also undergoes alpha particle emission, and its half-life (time over which half a number of atoms decays) is even longer, by several times. In each of these, radioactive decay produces daughter isotopes that are also unstable, starting a
1513:
The energy of the nucleus is negative with regard to the energy of the particles pulled apart to infinite distance (just like the gravitational energy of planets of the Solar System), because energy must be utilized to split a nucleus into its individual protons and neutrons.
2307:
in stars. However, it is not binding energy per defined nucleon (as defined above), which controls exactly which nuclei are made, because within stars, neutrons and protons can inter-convert to release even more energy per generic nucleon. In fact, it has been argued that
1370:
As a rule, very light elements can fuse comparatively easily, and very heavy elements can break up via fission very easily; elements in the middle are more stable and it is difficult to make them undergo either fusion or fission in an environment such as a laboratory.
2486:
Nuclear binding energy can be computed from the difference in mass of a nucleus, and the sum of the masses of the number of free neutrons and protons that make up the nucleus. Once this mass difference, called the mass defect or mass deficiency, is known, Einstein's
3779:
numbers of neutrons and protons, but rather in decreases in the total mass of the nuclide/per nucleon, with the reaction. (Note that the
Binding Energy given above for hydrogen-1 is the atomic binding energy, not the nuclear binding energy which would be zero.)
1421:
Different nuclear reactions may predominate at different stages of the Sun's existence, including the proton–proton reaction and the carbon–nitrogen cycle—which involves heavier nuclei, but whose final product is still the combination of protons to form helium.
2548:
2346:
is copiously made by staged build-up of 14 helium nuclei inside supernovas, where it has no time to decay to iron before being released into the interstellar medium in a matter of a few minutes, as the supernova explodes. However, nickel-56 then decays to
3074:
takes into account the fact that in the absence of other effects the most stable arrangement has equal numbers of protons and neutrons; this is because the n–p interaction in a nucleus is stronger than either the n−n or p−p interaction. The pairing term
2283:
Finally, in the heavier elements, there is a gradual decrease in binding energy per nucleon as atomic number increases. In this region of nuclear size, electromagnetic repulsive forces are beginning to overcome the strong nuclear force attraction.
4040:
2508:(1 Da) is defined as 1/12 of the mass of a C atom—but the atomic mass of a H atom (which is a proton plus electron) is 1.007825 Da, so each nucleon in C has lost, on average, about 0.8% of its mass in the form of binding energy.
1581:
and repel each other. The energy of the strong force holding the nucleus together also increases, but at a slower rate, as if inside the nucleus, only nucleons close to each other are tightly bound, not ones more widely separated.
2195:. As a consequence, the listed mass deficits are not a measure of the stability or binding energy of isolated nuclei, but for the whole atoms. There is a very practical reason for this, namely that it is very hard to totally
1552:
of the Sun, where such pressure is provided by the enormous weight of the layers above the core, pressed inwards by the Sun's strong gravity. The process of combining protons to form helium is an example of nuclear fusion.
2433:
The fact that the maximum binding energy is found in medium-sized nuclei is a consequence of the trade-off in the effects of two opposing forces that have different range characteristics. The attractive nuclear force
1621:
Among the heaviest nuclei, starting with tellurium nuclei (element 52) containing 104 or more nucleons, electric forces may be so destabilizing that entire chunks of the nucleus may be ejected, usually as
1778:
1834:
The nuclear mass defect is usually converted into nuclear binding energy, which is the minimum energy required to disassemble the nucleus into its constituent nucleons. This conversion is done with the
2351:
within a few weeks, then this radioisotope finally decays to iron-56 with a half life of about 77.3 days. The radioactive decay-powered light curve of such a process has been observed to happen in
3536:
as in the bound nucleus, is Ni. Thus, the true absolute value of the total binding energy of a nucleus depends on what we are allowed to construct the nucleus out of. If all nuclei of mass number
3136:
A graphical representation of the semi-empirical binding energy formula. The binding energy per nucleon in MeV (highest numbers in yellow, in excess of 8.5 MeV per nucleon) is plotted for various
2330:
Elements with high binding energy per nucleon, like iron and nickel, cannot undergo fission, but they can theoretically undergo fusion with hydrogen, deuterium, helium, and carbon, for instance:
1505:
An example that illustrates nuclear binding energy is the nucleus of C (carbon-12), which contains 6 protons and 6 neutrons. The protons are all positively charged and repel each other, but the
993:. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the
3900:
Energy
Education is an interactive curriculum supplement for secondary-school science students, funded by the U. S. Department of Energy and the Texas State Energy Conservation Office (SECO)
1355:
For lighter elements, the energy that can be released by assembling them from lighter elements decreases, and energy can be released when they fuse. This is true for nuclei lighter than
1132:
In order to quantify the energy released or absorbed in any nuclear transmutation, one must know the nuclear binding energies of the nuclear components involved in the transmutation.
2327:, for neutral condensed matter consisting of Fe atoms—however, in these conditions nuclei of atoms are inhibited from fusing into the most stable and low energy state of matter.
4396:"Mass number, number of protons, name of isotope, mass [MeV/c^2], binding energy [MeV] and binding energy per nucleus [MeV] for different atomic nuclei"
3072:
1367:). Nuclear power is generated at present by breaking up uranium nuclei in nuclear power reactors, and capturing the released energy as heat, which is converted to electricity.
2992:
3119:
3895:
2732:{\displaystyle {\frac {E_{\text{B}}}{A\cdot {\text{MeV}}}}=a-{\frac {b}{A^{1/3}}}-{\frac {cZ^{2}}{A^{4/3}}}-{\frac {d\left(N-Z\right)^{2}}{A^{2}}}\pm {\frac {e}{A^{7/4}}}}
2359:. In a star, there are no good ways to create nickel-62 by alpha-addition processes, or else there would presumably be more of this highly stable nuclide in the universe.
2936:
1037:
The term "nuclear binding energy" may also refer to the energy balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new
1109:
reactions. Energy is consumed or released because of differences in the nuclear binding energy between the incoming and outgoing products of the nuclear transmutation.
2815:
2841:
2789:
2763:
1226:
two small magnets: magnets are very difficult to separate when stuck together, but once pulled a short distance apart, the force between them drops almost to zero.
4395:
2867:
2475:
deficits, according to the equivalence of mass and energy. The atomic binding energy is simply the amount of energy (and mass) released, when a collection of free
3012:
2890:
1518:
have measured the masses of nuclei, which are always less than the sum of the masses of protons and neutrons that form them, and the difference—by the formula
1326:
Mass defect (also called "mass deficit") is the difference between the mass of an object and the sum of the masses of its constituent particles. Discovered by
2501:
can be used to compute the binding energy of any nucleus. Early nuclear physicists used to refer to computing this value as a "packing fraction" calculation.
2938:
is a surface tension effect and is proportional to the number of nucleons that are situated on the nuclear surface; it is largest for light nuclei. The term
4189:
The energy released is slightly less than the binding energy of helium because the starting point is four protons, rather than two protons and two neutrons.
2299:. This is the approximate basic reason why iron and nickel are very common metals in planetary cores, since they are produced profusely as end products in
2247:
Binding energy per nucleon for a selection of nuclides. The nuclide with the highest value, Ni, does not appear. The horizontal lines are at 8 and 8.5 MeV.
2175:
The binding energy of an atom (including its electrons) is not exactly the same as the binding energy of the atom's nucleus. The measured mass deficits of
1182:. However, having the neutron between two protons (so their mutual repulsion decreases to 10 N) would attract the neutron only for an electric quadrupole
1296:
of the element. Different isotopes may have different properties – for example one might be stable and another might be unstable, and gradually undergo
1390:). The isotopes beyond uranium (atomic number 92) with the longest half-lives are plutonium-244 (80 million years) and curium-247 (16 million years).
1374:
The reason the trend reverses after iron is the growing positive charge of the nuclei, which tends to force nuclei to break up. It is resisted by the
1630:
also decays, very quickly, into two alpha particles.) This type of decay becomes more and more probable as elements rise in atomic weight past 104.
1034:
is the difference in mass. This 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed.
2892:
is called the saturation contribution and ensures that the binding energy per nucleon is the same for all nuclei to a first approximation. The term
2342:
It is generally believed that iron-56 is more common than nickel isotopes in the universe for mechanistic reasons, because its unstable progenitor
1174:
carry a positive charge and repel each other. If two protons were touching, their repulsion force would be almost 40 newtons. Because each of the
1246:). They cannot get close enough for the nuclear force, which attracts them to each other, to become important. Only under conditions of extreme
4405:
1406:
and dust, from which the Earth and other planets also arose. The gravitational pull released energy and heated the early Sun, much in the way
4215:
1598:
changing one proton into a neutron or one neutron into a proton increases the stability (lowering the mass), then this will happen through
1455:, the electric repulsion is so strong that some of them spontaneously eject positive fragments, usually nuclei of helium that form stable
1441:
work, energy must first be injected to force together positively charged protons, which also repel each other with their electric charge.
2276:
nuclear forces in this region, as atomic mass increases, are nearly balanced by repellent electromagnetic forces between protons, as the
2212:
1363:. For heavier nuclei, more energy is needed to bind them, and that energy may be released by breaking them up into fragments (known as
949:
863:
89:
2471:
As seen above in the example of deuterium, nuclear binding energies are large enough that they may be easily measured as fractional
61:
1959:
nuclei to form heavier atoms releases energy, as does fission of uranium, the breaking up of a larger nucleus into smaller parts.
1672:
4436:
2394:
42:
3907:
4417:
Jagdish K. Tuli, Nuclear Wallet Cards, 7th edition, April 2005, Brookhaven
National Laboratory, US National Nuclear Data Center
1564:. The Earth's oceans contain a large amount of deuterium that could be used and tritium can be made in the reactor itself from
68:
3812:
1618:, in which a proton simply electron captures one of the atom's K orbital electrons, emits a neutrino, and becomes a neutron.
3843:
How to solve for nuclear binding energy. Guides to solving many of the types of quantitative problems found in
Chemistry 116
3528:
one to another if necessary, The highest binding energy per hadron, with the hadrons starting as the same number of protons
1292:, which is often roughly a similar number. Two atoms of the same element having different numbers of neutrons are known as
4306:
Bosch, F.; et al. (1996). "Observation of bound-state beta minus decay of fully ionized Re: Re–Os
Cosmochronometry".
1178:
carries total charge zero, a proton could electrically attract a neutron if the proton could induce the neutron to become
1186:
arrangement. Higher multipoles, needed to satisfy more protons, cause weaker attraction, and quickly become implausible.
212:
3838:
1650:
Calculation can be employed to determine the nuclear binding energy of nuclei. The calculation involves determining the
75:
2420:
1556:
Producing helium from normal hydrogen would be practically impossible on earth because of the difficulty in creating
108:
2402:
516:
57:
1402:
process works as follows: five billion years ago, the new Sun formed when gravity pulled together a vast cloud of
904:
1320:
708:
2444:
produces energy by combining the very lightest elements into more tightly bound elements (such as hydrogen into
2398:
413:
46:
1654:, converting it into energy, and expressing the result as energy per mole of atoms, or as energy per nucleon.
1635:
942:
1589:(Fe) is the most efficiently bound nucleus meaning that it has the least average mass per nucleon. However,
4124:
3789:
3815:(addresses the mass and kinetic energy of the parts that bind the various quarks together inside a hadron)
2535:
2517:
2488:
1864:
1341:
1331:
1065:
into pieces, excess energy is emitted as gamma rays and the kinetic energy of various ejected particles (
1009:
726:
696:
197:
4457:
3903:
3172:
The following table lists some binding energies and mass defect values. Notice also that we use 1
3017:
2252:
1375:
1344:. The decrease in mass is equal to the energy emitted in the reaction of an atom's creation divided by
773:
323:
4198:
N R Sree Harsha, "The tightly bound nuclei in the liquid drop model", Eur. J. Phys. 39 035802 (2018),
2941:
1982:
1639:
1049:), either process can result in release of this binding energy. This energy may be made available as
659:
82:
4452:
3875:
3867:
3794:
3078:
2383:
2005:, the breaking of a heavy nucleus into two (or more rarely three) lighter nuclei, and some neutrons
1863:
to a form of energy, which can remove some mass when the energy is removed, is consistent with the
1414:
nuclei to overcome their electric repulsion, and bring them into the short range of the attractive
1381:
As nuclei grow bigger still, this disruptive effect becomes steadily more significant. By the time
935:
922:
654:
358:
4467:
4462:
4308:
4263:
4219:
3800:
3771:
Such reactions are not driven by changes in binding energies as calculated from previously fixed
2387:
1836:
1486:
of heavier elements. Generally, the heavier the nuclei are, the faster they spontaneously decay.
1190:
1179:
1072:
These nuclear binding energies and forces are on the order of one million times greater than the
649:
546:
511:
207:
35:
4065:
Pourshahian, Soheil (2017-09-01). "Mass Defect from
Nuclear Physics to Mass Spectral Analysis".
2895:
1386:
Because of this process, nuclei with more than 94 protons are not found naturally on Earth (see
1839:: E = ∆mc². However it must be expressed as energy per mole of atoms or as energy per nucleon.
703:
318:
3806:
2794:
2227:
in a strict sense, but has a non-vanishing probability of being located inside the nucleus).
1062:
828:
713:
605:
2820:
2768:
2742:
2208:
768:
4360:
4317:
4272:
4074:
2435:
1626:, which consist of two protons and two neutrons (alpha particles are fast helium nuclei). (
1540:
The conversion of protons to neutrons is the result of another nuclear force, known as the
994:
966:
838:
813:
630:
3167:
2846:
8:
4165:
2309:
2243:
1605:
The two methods for this conversion are mediated by the weak force, and involve types of
733:
612:
506:
449:
442:
432:
373:
368:
202:
4364:
4321:
4276:
4078:
1005:
4394:
From the difference of binding energy, 5.467 = 642.891 − 545.262 − 92.162, values from
4106:
4026:
3126:
2997:
2875:
1515:
1479:
1219:
1160:
676:
671:
486:
3994:
3969:
3932:
4333:
4288:
4098:
4090:
3122:
2352:
2223:
models of heavy atoms, the electron orbits partially inside the nucleus (it does not
1974:
1297:
1242:(a process that also would require some protons to combine with electrons and become
1198:
1098:
1073:
848:
843:
803:
681:
420:
408:
391:
363:
333:
174:
4110:
4368:
4325:
4280:
4199:
4082:
2216:
2180:
1615:
1403:
1273:
1167:
1094:
868:
858:
788:
541:
459:
427:
247:
179:
3854:
4400:
4351:
Fewell, M. P. (1995). "The atomic nuclide with the highest mean binding energy".
4018:
2449:
2304:
2002:
1930:
1847:
Nuclear energy is released by the splitting (fission) or merging (fusion) of the
1817:
1623:
1494:
1456:
1364:
1327:
1152:
1144:
1113:
1066:
1046:
853:
833:
808:
738:
625:
553:
499:
464:
124:
4329:
4284:
3906:
and the Texas State Energy
Conservation Office (SECO). July 2010. Archived from
2272:, meaning their protons and neutrons both fill their respective nuclear shells.
2188:
4203:
2480:
2441:
2220:
1996:
1915:
1848:
1827:
1806:
1795:
1399:
1387:
1349:
1281:
1267:
1121:
1117:
1058:
1042:
1038:
1004:
of an atomic nucleus is less than the sum of the individual masses of the free
974:
909:
763:
758:
637:
570:
378:
313:
290:
277:
264:
164:
142:
4240:
4086:
2263:
is observed to exhibit generally increasing binding energy per nucleon as the
1571:
4446:
4094:
3803:(energy required to free an electron from its atomic orbital or from a solid)
3173:
3145:
2505:
2277:
2231:
1788:
1506:
1460:
1428:
1415:
1206:
1156:
1148:
1054:
888:
883:
878:
873:
823:
481:
454:
298:
237:
190:
169:
1548:
enormous pressure to keep it confined, but suitable conditions exist in the
4337:
4292:
4102:
2269:
1990:
1663:
1560:. Research is being undertaken on developing a process using deuterium and
818:
793:
778:
523:
471:
328:
4261:
Jung, M.; et al. (1992). "First observation of bound-state β decay".
3809:(energy required to disassemble an atom into free electrons and a nucleus)
4041:"20.8: Converting Mass to Energy: Mass Defect and Nuclear Binding Energy"
2264:
1986:
1978:
1627:
1483:
1316:
1251:
1222:, which binds quarks into nucleons at an even smaller level of distance.
1102:
783:
476:
398:
251:
3132:
1933:
in 1896, when he found that photographic plates stored in the dark near
1666:, and the sum of the masses of the constituent nucleons. It is given by
1238:—for instance, in a balloon filled with hydrogen—do not combine to form
3633:
3168:
Example values deduced from experimentally measured atom nuclide masses
2994:
is the
Coulomb electrostatic repulsion; this becomes more important as
1967:
1606:
1599:
1549:
1541:
1194:
1106:
753:
743:
600:
580:
403:
273:
1482:, though they can be produced artificially or as intermediates in the
1008:
protons and neutrons. The difference in mass can be calculated by the
3667:
3492:
2457:
2348:
2343:
2300:
2288:
1944:
1590:
1557:
1407:
1304:
1140:
798:
748:
575:
563:
558:
437:
4372:
2372:
24:
3735:
3153:
2511:
2476:
2356:
2256:
2200:
2176:
1956:
1610:
1382:
1352:
which holds them together is, in effect, the missing 0.8% of mass.
1247:
1243:
1235:
1175:
1147:(negative attracts positive). Furthermore, electrons are sometimes
1125:
1077:
132:
3701:
3599:
3394:
3137:
2465:
2453:
2296:
2292:
2215:
heavy ion accelerator. This is also evident from phenomena like
1993:), the average binding energy per nucleon will actually decrease.
1952:
1948:
1934:
1586:
1577:
1565:
1561:
1490:
1475:
1471:
1467:
1293:
1289:
1288:(always the same number for a given element), and some number of
1230:
1215:
1171:
990:
986:
260:
233:
225:
157:
147:
1657:
1614:
nucleus may still convert protons to neutrons by the process of
1112:
The best-known classes of exothermic nuclear transmutations are
4431:
2461:
2445:
2313:
energetic maximum should also hold for ambient conditions, say
2260:
1926:
1919:
1860:
1360:
1285:
1239:
982:
970:
152:
16:
Minimum energy required to separate particles within a nucleus
2291:
is the most tightly bound nucleus (per nucleon), followed by
1938:
1662:
Nuclear mass defect is defined as the difference between the
1510:
force also pulls neutrons together, or neutrons and protons.
2452:
produces energy by splitting the heaviest elements (such as
1773:{\displaystyle \Delta m=Zm_{p}+(A-Z)m_{n}-M=Zm_{p}+Nm_{n}-M}
1478:) spontaneously break up too quickly to appear in nature as
3336:
binding energy per nucleon" would be this value divided by
2472:
2207:
treated independently. Examples of this have been shown in
2183:
1999:, two atomic nuclei fuse together to form a heavier nucleus
1981:
nucleus decays spontaneously by emitting either particles,
1856:
1852:
1572:
The binding energy maximum and ways to approach it by decay
1452:
1445:
1356:
1303:
The hydrogen nucleus contains just one proton. Its isotope
1277:
1255:
1001:
978:
2196:
3129:. When A is odd, the pairing term is identically zero.
1645:
4208:
1941:
plates (X-rays had recently been discovered in 1895).
1489:
Iron nuclei are the most stable nuclei (in particular
4067:
Journal of the
American Society for Mass Spectrometry
3797:(binding energy between the atoms in a chemical bond)
3187:. To calculate the binding energy we use the formula
3081:
3020:
3000:
2944:
2898:
2878:
2849:
2823:
2797:
2771:
2745:
2551:
1675:
1093:
An absorption or release of nuclear energy occurs in
4170:"From Stargazers to Starships" Public domain content
3974:"From Stargazers to Starships" Public domain content
3937:"From Stargazers to Starships" Public domain content
2362:
1218:
of nuclei together. This force is a residuum of the
2015:
Light element energy-producing nuclear interactions
1459:. This spontaneous break-up is one of the forms of
49:. Unsourced material may be challenged and removed.
3227:denotes the number of protons in the nuclides and
3113:
3066:
3006:
2986:
2930:
2884:
2861:
2835:
2809:
2783:
2757:
2731:
1772:
4444:
2512:Semiempirical formula for nuclear binding energy
2199:heavy elements, i.e. strip them of all of their
4017:
3888:
2238:
1393:
1330:in 1905, it can be explained using his formula
1155:); this link between atoms is referred to as a
4406:Max Planck Institute for Gravitational Physics
1053:and can be used to produce electricity, as in
4159:
4157:
4155:
4153:
4151:
4149:
4147:
4145:
4143:
4141:
3859:
1658:Conversion of nuclear mass defect into energy
943:
3310:free neutrons. In other words, it would be (
2460:) into more tightly bound elements (such as
1159:and is responsible for the formation of all
1105:reactions and those that release energy are
4064:
3963:
3961:
3959:
3957:
3955:
3953:
3872:Hyperphysics – a free web resource from GSU
3156:(x-axis). The highest numbers are seen for
2401:. Unsourced material may be challenged and
2170:
1602:, meaning the nuclide will be radioactive.
1170:does not hold nuclei together, because all
4138:
3931:Stern, Dr. David P. (September 23, 2004).
3833:
3831:
3829:
2179:are always listed as mass deficits of the
1642:that ends in some stable isotope of lead.
1528:—gives the binding energy of the nucleus.
950:
936:
4164:Stern, Dr. David P. (February 11, 2009).
3968:Stern, Dr. David P. (November 15, 2004).
3926:
3924:
2421:Learn how and when to remove this message
1500:
1451:With the nuclei of elements heavier than
109:Learn how and when to remove this message
3950:
3540:were to be allowed to be constructed of
3131:
3014:increases. The symmetry correction term
2242:
1537:of them are also converted to neutrons.
1272:There are around 94 naturally occurring
1151:or transferred to them (by processes of
4241:"Marie Curie – X-rays and Uranium Rays"
3826:
1925:Nuclear energy was first discovered by
1594:nickel-62's average mass per nucleon).
4445:
4350:
4125:"On the Interaction of Natural Forces"
3921:
1101:; those that absorb energy are called
4305:
4163:
3995:"It's Elemental – The Element Helium"
3967:
3930:
3813:Quantum chromodynamics binding energy
2739:where the coefficients are given by:
1842:
1646:Calculation of nuclear binding energy
1466:Nuclei heavier than lead (except for
1204:Therefore, another force, called the
1041:is available when light nuclei fuse (
4260:
3865:
2399:adding citations to reliable sources
2366:
2255:, the series of light elements from
1962:Nuclear energy is released by three
1261:
1135:
973:that is required to disassemble the
47:adding citations to reliable sources
18:
3344:Most strongly bound nuclides atoms
1977:, where a neutron or proton in the
1947:has the highest binding energy per
1435:
1254:(for example, within the core of a
1191:proton and neutron magnetic moments
13:
3231:their number of neutrons. We take
1676:
1444:For elements that weigh more than
1258:), can such a process take place.
14:
4479:
4424:
3121:is purely empirical; it is + for
3067:{\displaystyle -d(N-Z)^{2}/A^{2}}
2363:Binding energy and nuclide masses
1531:
1088:
4430:
3549:Some light nuclides resp. atoms
2371:
1903:
1284:containing a specific number of
1143:and nuclei are kept together by
917:
916:
903:
131:
23:
4411:
4388:
4379:
4344:
4299:
4254:
4233:
4192:
4183:
4117:
3970:"A Review of Nuclear Structure"
2987:{\displaystyle -cZ^{2}/A^{4/3}}
2287:At the peak of binding energy,
2253:periodic table of elements
2186:of that isotope, and mostly in
1855:(s). The conversion of nuclear
1083:
1045:), or when heavy nuclei split (
1026:is the nuclear binding energy,
34:needs additional citations for
4058:
4033:
4011:
3987:
3845:. Purdue University. July 2010
3040:
3027:
1713:
1701:
1342:equivalence of energy and mass
1310:
1:
4021:; Thorndike, Alan M. (1964).
3819:
3114:{\displaystyle \pm e/A^{7/4}}
2211:experiments performed at the
2133:Li + He → He + He + p
1636:formation of the Solar System
3790:Gravitational binding energy
2239:Nuclear binding energy curve
2157:B + p → He + He + He
2092:He + Li → He + He + p
2084:He + He → He + p + p
1394:Nuclear reactions in the Sun
1305:deuterium, or heavy hydrogen
7:
4353:American Journal of Physics
4330:10.1103/PhysRevLett.77.5190
4285:10.1103/PhysRevLett.69.2164
3783:
2518:Semi-empirical mass formula
2303:and in the final stages of
2149:Li + H → He + He + n
1300:to become another element.
1149:shared by neighboring atoms
1030:is the speed of light, and
697:High-energy nuclear physics
10:
4484:
3904:U. S. Department of Energy
2931:{\displaystyle -b/A^{1/3}}
2515:
2101:
2020:
1463:exhibited by some nuclei.
1376:strong nuclear interaction
1314:
1265:
4087:10.1007/s13361-017-1741-9
4025:. Princeton, New Jersey:
1983:electromagnetic radiation
1429:controlled nuclear fusion
1074:electron binding energies
4216:"Turning Lead into Gold"
4204:10.1088/1361-6404/aaa345
4166:"Nuclear Binding Energy"
3876:Georgia State University
3868:"Nuclear Binding Energy"
3839:"Nuclear binding energy"
3795:Bond-dissociation energy
2538:for the binding energy (
2171:Binding energy for atoms
1315:Not to be confused with
1145:electrostatic attraction
989:, known collectively as
58:"Nuclear binding energy"
4309:Physical Review Letters
4264:Physical Review Letters
3866:Nave, Rod (July 2010).
3801:Electron binding energy
3579:total binding energy /
3374:total binding energy /
2810:{\displaystyle c=0.585}
2489:mass–energy equivalence
2141:Li + p → He + He
2125:Li + H → He + He
2117:Li + p → He + He
1865:mass–energy equivalence
1837:mass-energy equivalence
1280:of each element have a
1061:. When a large nucleus
208:Interacting boson model
4437:Nuclear binding energy
3164:
3115:
3068:
3008:
2988:
2932:
2886:
2863:
2837:
2836:{\displaystyle d=19.3}
2811:
2785:
2784:{\displaystyle b=13.0}
2759:
2758:{\displaystyle a=14.0}
2733:
2536:semi-empirical formula
2248:
2076:H + He → He + p
1823:M is the nuclear mass.
1774:
1501:Nuclear binding energy
1340:, which describes the
1319:in nuclear physics or
1180:electrically polarized
963:Nuclear binding energy
3807:Atomic binding energy
3135:
3116:
3069:
3009:
2989:
2933:
2887:
2864:
2838:
2812:
2786:
2760:
2734:
2479:are joined to form a
2246:
2068:H + H → He + n
2060:H + H → He + n
1775:
1425:A branch of physics,
1323:in mass spectrometry.
1212:residual strong force
981:into its constituent
595:High-energy processes
293:– equal all the above
191:Models of the nucleus
4439:at Wikimedia Commons
4045:Chemistry LibreTexts
4023:Elementary Particles
3079:
3018:
2998:
2942:
2896:
2876:
2862:{\displaystyle e=33}
2847:
2821:
2795:
2769:
2743:
2549:
2526:nucleons, including
2436:strong nuclear force
2395:improve this section
2219:. Theoretically, in
2052:H + H → H + p
1937:were blackened like
1673:
1542:weak (nuclear) force
1076:of light atoms like
995:strong nuclear force
967:experimental physics
631:nuclear astrophysics
43:improve this article
4365:1995AmJPh..63..653F
4322:1996PhRvL..77.5190B
4277:1992PhRvL..69.2164J
4079:2017JASMS..28.1836P
3550:
3532:and total nucleons
3345:
3325: −
3298:denotes the sum of
3216: −
2522:For a nucleus with
2310:photodisintegration
2209:bound-state β decay
2105:
2024:
2017:
1652:nuclear mass defect
1480:primordial elements
613:Photodisintegration
536:Capturing processes
450:Spontaneous fission
443:Internal conversion
374:Valley of stability
369:Island of stability
203:Nuclear shell model
4027:David Van Nostrand
3999:education.jlab.org
3548:
3503:−66.7461 MeV
3437:−62.1534 MeV
3405:−60.6054 MeV
3343:
3165:
3111:
3064:
3004:
2984:
2928:
2882:
2859:
2833:
2807:
2781:
2755:
2729:
2545:) per nucleon is:
2353:type II supernovae
2249:
2103:
2022:
2013:
1843:Fission and fusion
1770:
1516:Mass spectrometers
1220:strong interaction
1161:chemical compounds
910:Physics portal
704:Quark–gluon plasma
487:Radiogenic nuclide
4458:Nuclear chemistry
4435:Media related to
4385:M.P. Fewell, 1995
4316:(26): 5190–5193.
4271:(15): 2164–2167.
4029:. pp. 11–12.
3933:"Nuclear Physics"
3768:
3767:
3591:binding energy /
3525:
3524:
3469:−64.472 MeV
3386:binding energy /
3140:as a function of
3007:{\displaystyle Z}
2885:{\displaystyle a}
2727:
2699:
2651:
2611:
2577:
2574:
2561:
2504:For example, the
2431:
2430:
2423:
2268:because they are
2168:
2167:
2164:
2163:
2099:
2098:
1975:Radioactive decay
1895:= energy release,
1298:radioactive decay
1262:Physics of nuclei
1136:The nuclear force
1129:emitted as heat.
1099:radioactive decay
1095:nuclear reactions
1010:Einstein equation
960:
959:
646:
392:Radioactive decay
348:Nuclear stability
175:Nuclear structure
119:
118:
111:
93:
4475:
4434:
4418:
4415:
4409:
4392:
4386:
4383:
4377:
4376:
4348:
4342:
4341:
4303:
4297:
4296:
4258:
4252:
4251:
4249:
4248:
4237:
4231:
4230:
4228:
4227:
4218:. Archived from
4212:
4206:
4196:
4190:
4187:
4181:
4180:
4178:
4177:
4161:
4136:
4135:
4133:
4132:
4121:
4115:
4114:
4073:(9): 1836–1843.
4062:
4056:
4055:
4053:
4052:
4037:
4031:
4030:
4019:Frisch, David H.
4015:
4009:
4008:
4006:
4005:
3991:
3985:
3984:
3982:
3981:
3965:
3948:
3947:
3945:
3944:
3928:
3919:
3918:
3916:
3915:
3896:"Nuclear Energy"
3892:
3886:
3885:
3883:
3882:
3863:
3857:
3853:
3851:
3850:
3835:
3551:
3547:
3346:
3342:
3293:
3292:
3287:
3273:
3272:
3267:
3264:
3250:
3249:
3244:
3186:
3181:
3162:
3152:, the number of
3123:even–even nuclei
3120:
3118:
3117:
3112:
3110:
3109:
3105:
3092:
3073:
3071:
3070:
3065:
3063:
3062:
3053:
3048:
3047:
3013:
3011:
3010:
3005:
2993:
2991:
2990:
2985:
2983:
2982:
2978:
2965:
2960:
2959:
2937:
2935:
2934:
2929:
2927:
2926:
2922:
2909:
2891:
2889:
2888:
2883:
2868:
2866:
2865:
2860:
2842:
2840:
2839:
2834:
2816:
2814:
2813:
2808:
2790:
2788:
2787:
2782:
2764:
2762:
2761:
2756:
2738:
2736:
2735:
2730:
2728:
2726:
2725:
2721:
2705:
2700:
2698:
2697:
2688:
2687:
2686:
2681:
2677:
2657:
2652:
2650:
2649:
2645:
2632:
2631:
2630:
2617:
2612:
2610:
2609:
2605:
2589:
2578:
2576:
2575:
2572:
2563:
2562:
2559:
2553:
2500:
2426:
2419:
2415:
2412:
2406:
2375:
2367:
2337:
2326:
2319:
2217:electron capture
2194:
2112:Approx. Q (MeV)
2106:
2102:
2044:H + H → He
2036:H + H → He
2031:Approx. Q (MeV)
2025:
2021:
2018:
2012:
1791:(atomic number).
1779:
1777:
1776:
1771:
1763:
1762:
1747:
1746:
1725:
1724:
1697:
1696:
1616:electron capture
1527:
1495:nuclear reactors
1436:Combining nuclei
1185:
1021:
952:
945:
938:
925:
920:
919:
912:
908:
907:
784:Skłodowska-Curie
644:
460:Neutron emission
228:' classification
180:Nuclear reaction
135:
121:
120:
114:
107:
103:
100:
94:
92:
51:
27:
19:
4483:
4482:
4478:
4477:
4476:
4474:
4473:
4472:
4453:Nuclear physics
4443:
4442:
4427:
4422:
4421:
4416:
4412:
4401:Einstein Online
4393:
4389:
4384:
4380:
4373:10.1119/1.17828
4349:
4345:
4304:
4300:
4259:
4255:
4246:
4244:
4239:
4238:
4234:
4225:
4223:
4214:
4213:
4209:
4197:
4193:
4188:
4184:
4175:
4173:
4162:
4139:
4130:
4128:
4123:
4122:
4118:
4063:
4059:
4050:
4048:
4039:
4038:
4034:
4016:
4012:
4003:
4001:
3993:
3992:
3988:
3979:
3977:
3966:
3951:
3942:
3940:
3929:
3922:
3913:
3911:
3894:
3893:
3889:
3880:
3878:
3864:
3860:
3848:
3846:
3837:
3836:
3827:
3822:
3786:
3656:0.0000000146 Da
3331:
3324:
3285:
3283:
3281:
3275:
3265:
3262:
3260:
3258:
3252:
3242:
3240:
3238:
3232:
3222:
3215:
3204:
3197:
3179:
3177:
3170:
3157:
3101:
3097:
3093:
3088:
3080:
3077:
3076:
3058:
3054:
3049:
3043:
3039:
3019:
3016:
3015:
2999:
2996:
2995:
2974:
2970:
2966:
2961:
2955:
2951:
2943:
2940:
2939:
2918:
2914:
2910:
2905:
2897:
2894:
2893:
2877:
2874:
2873:
2872:The first term
2848:
2845:
2844:
2822:
2819:
2818:
2796:
2793:
2792:
2770:
2767:
2766:
2744:
2741:
2740:
2717:
2713:
2709:
2704:
2693:
2689:
2682:
2667:
2663:
2662:
2658:
2656:
2641:
2637:
2633:
2626:
2622:
2618:
2616:
2601:
2597:
2593:
2588:
2571:
2564:
2558:
2554:
2552:
2550:
2547:
2546:
2544:
2520:
2514:
2492:
2450:nuclear fission
2427:
2416:
2410:
2407:
2392:
2376:
2365:
2335:
2321:
2314:
2305:silicon burning
2241:
2187:
2173:
1931:Henri Becquerel
1845:
1818:mass of neutron
1815:
1804:
1758:
1754:
1742:
1738:
1720:
1716:
1692:
1688:
1674:
1671:
1670:
1660:
1648:
1640:chain of decays
1624:alpha particles
1574:
1550:central regions
1534:
1519:
1503:
1457:alpha particles
1438:
1396:
1365:nuclear fission
1328:Albert Einstein
1324:
1313:
1270:
1264:
1183:
1153:quantum physics
1138:
1114:nuclear fission
1091:
1086:
1067:nuclear fission
1047:nuclear fission
1013:
969:is the minimum
956:
915:
902:
901:
894:
893:
729:
719:
718:
699:
689:
688:
633:
629:
626:Nucleosynthesis
618:
617:
596:
588:
587:
537:
529:
528:
502:
500:Nuclear fission
492:
491:
465:Proton emission
394:
384:
383:
349:
341:
340:
242:
229:
218:
217:
193:
125:Nuclear physics
115:
104:
98:
95:
52:
50:
40:
28:
17:
12:
11:
5:
4481:
4471:
4470:
4468:Binding energy
4465:
4463:Nuclear fusion
4460:
4455:
4441:
4440:
4426:
4425:External links
4423:
4420:
4419:
4410:
4387:
4378:
4359:(7): 653–658.
4343:
4298:
4253:
4232:
4207:
4191:
4182:
4172:. NASA website
4137:
4116:
4057:
4032:
4010:
3986:
3976:. NASA website
3949:
3939:. NASA website
3920:
3887:
3858:
3824:
3823:
3821:
3818:
3817:
3816:
3810:
3804:
3798:
3792:
3785:
3782:
3766:
3765:
3762:
3759:
3756:
3753:
3750:
3747:
3744:
3741:
3738:
3732:
3731:
3728:
3725:
3722:
3719:
3716:
3713:
3710:
3707:
3704:
3698:
3697:
3694:
3691:
3688:
3685:
3682:
3679:
3676:
3673:
3670:
3664:
3663:
3660:
3657:
3654:
3651:
3648:
3645:
3642:
3639:
3636:
3630:
3629:
3626:
3623:
3620:
3617:
3614:
3611:
3608:
3605:
3602:
3596:
3595:
3589:
3588:binding energy
3586:
3583:
3577:
3571:
3568:
3565:
3560:
3555:
3523:
3522:
3519:
3516:
3513:
3510:
3507:
3504:
3501:
3498:
3495:
3489:
3488:
3485:
3482:
3479:
3476:
3473:
3470:
3467:
3464:
3461:
3457:
3456:
3453:
3450:
3447:
3444:
3441:
3438:
3435:
3432:
3429:
3425:
3424:
3421:
3418:
3415:
3412:
3409:
3406:
3403:
3400:
3397:
3391:
3390:
3384:
3383:binding energy
3381:
3378:
3372:
3366:
3363:
3360:
3355:
3350:
3329:
3322:
3288:(58) MeV/
3279:
3268:(30) MeV/
3256:
3245:(58) MeV/
3236:
3220:
3213:
3205:) +
3202:
3195:
3182:(23) MeV/
3169:
3166:
3148:(y-axis), vs.
3127:odd–odd nuclei
3108:
3104:
3100:
3096:
3091:
3087:
3084:
3061:
3057:
3052:
3046:
3042:
3038:
3035:
3032:
3029:
3026:
3023:
3003:
2981:
2977:
2973:
2969:
2964:
2958:
2954:
2950:
2947:
2925:
2921:
2917:
2913:
2908:
2904:
2901:
2881:
2858:
2855:
2852:
2832:
2829:
2826:
2806:
2803:
2800:
2780:
2777:
2774:
2754:
2751:
2748:
2724:
2720:
2716:
2712:
2708:
2703:
2696:
2692:
2685:
2680:
2676:
2673:
2670:
2666:
2661:
2655:
2648:
2644:
2640:
2636:
2629:
2625:
2621:
2615:
2608:
2604:
2600:
2596:
2592:
2587:
2584:
2581:
2570:
2567:
2557:
2542:
2516:Main article:
2513:
2510:
2442:Nuclear fusion
2429:
2428:
2379:
2377:
2370:
2364:
2361:
2340:
2339:
2240:
2237:
2172:
2169:
2166:
2165:
2162:
2161:
2158:
2154:
2153:
2150:
2146:
2145:
2142:
2138:
2137:
2134:
2130:
2129:
2126:
2122:
2121:
2118:
2114:
2113:
2110:
2100:
2097:
2096:
2093:
2089:
2088:
2085:
2081:
2080:
2077:
2073:
2072:
2069:
2065:
2064:
2061:
2057:
2056:
2053:
2049:
2048:
2045:
2041:
2040:
2037:
2033:
2032:
2029:
2007:
2006:
2000:
1994:
1916:speed of light
1908:
1907:
1896:
1885:
1884:
1875: = Δ
1844:
1841:
1832:
1831:
1828:neutron number
1824:
1821:
1813:
1810:
1807:mass of proton
1802:
1799:
1798:(mass number).
1796:nucleon number
1792:
1781:
1780:
1769:
1766:
1761:
1757:
1753:
1750:
1745:
1741:
1737:
1734:
1731:
1728:
1723:
1719:
1715:
1712:
1709:
1706:
1703:
1700:
1695:
1691:
1687:
1684:
1681:
1678:
1659:
1656:
1647:
1644:
1573:
1570:
1533:
1532:Nuclear fusion
1530:
1502:
1499:
1437:
1434:
1400:nuclear fusion
1395:
1392:
1388:periodic table
1350:binding energy
1312:
1309:
1276:on Earth. The
1268:Atomic nucleus
1266:Main article:
1263:
1260:
1168:electric force
1137:
1134:
1118:nuclear fusion
1090:
1089:Nuclear energy
1087:
1085:
1082:
1059:nuclear weapon
1051:nuclear energy
1043:nuclear fusion
1039:binding energy
958:
957:
955:
954:
947:
940:
932:
929:
928:
927:
926:
913:
896:
895:
892:
891:
886:
881:
876:
871:
866:
861:
856:
851:
846:
841:
836:
831:
826:
821:
816:
811:
806:
801:
796:
791:
786:
781:
776:
771:
766:
761:
756:
751:
746:
741:
736:
730:
725:
724:
721:
720:
717:
716:
711:
706:
700:
695:
694:
691:
690:
687:
686:
685:
684:
679:
674:
665:
664:
663:
662:
657:
652:
641:
640:
638:Nuclear fusion
634:
624:
623:
620:
619:
616:
615:
610:
609:
608:
597:
594:
593:
590:
589:
586:
585:
584:
583:
578:
568:
567:
566:
561:
551:
550:
549:
538:
535:
534:
531:
530:
527:
526:
521:
520:
519:
509:
503:
498:
497:
494:
493:
490:
489:
484:
479:
474:
468:
467:
462:
457:
452:
447:
446:
445:
440:
430:
425:
424:
423:
418:
417:
416:
401:
395:
390:
389:
386:
385:
382:
381:
379:Stable nuclide
376:
371:
366:
361:
356:
354:Binding energy
350:
347:
346:
343:
342:
339:
338:
337:
336:
326:
321:
316:
310:
309:
295:
294:
287:
286:
270:
269:
257:
256:
244:
243:
230:
224:
223:
220:
219:
216:
215:
210:
205:
200:
194:
189:
188:
185:
184:
183:
182:
177:
172:
167:
165:Nuclear matter
162:
161:
160:
155:
145:
137:
136:
128:
127:
117:
116:
31:
29:
22:
15:
9:
6:
4:
3:
2:
4480:
4469:
4466:
4464:
4461:
4459:
4456:
4454:
4451:
4450:
4448:
4438:
4433:
4429:
4428:
4414:
4407:
4403:
4402:
4397:
4391:
4382:
4374:
4370:
4366:
4362:
4358:
4354:
4347:
4339:
4335:
4331:
4327:
4323:
4319:
4315:
4311:
4310:
4302:
4294:
4290:
4286:
4282:
4278:
4274:
4270:
4266:
4265:
4257:
4242:
4236:
4222:on 2011-07-17
4221:
4217:
4211:
4205:
4201:
4195:
4186:
4171:
4167:
4160:
4158:
4156:
4154:
4152:
4150:
4148:
4146:
4144:
4142:
4126:
4120:
4112:
4108:
4104:
4100:
4096:
4092:
4088:
4084:
4080:
4076:
4072:
4068:
4061:
4046:
4042:
4036:
4028:
4024:
4020:
4014:
4000:
3996:
3990:
3975:
3971:
3964:
3962:
3960:
3958:
3956:
3954:
3938:
3934:
3927:
3925:
3910:on 2011-02-26
3909:
3905:
3901:
3897:
3891:
3877:
3873:
3869:
3862:
3856:
3844:
3840:
3834:
3832:
3830:
3825:
3814:
3811:
3808:
3805:
3802:
3799:
3796:
3793:
3791:
3788:
3787:
3781:
3778:
3774:
3763:
3760:
3757:
3754:
3751:
3748:
3745:
3742:
3739:
3737:
3734:
3733:
3729:
3726:
3723:
3720:
3717:
3714:
3711:
3708:
3705:
3703:
3700:
3699:
3695:
3692:
3689:
3686:
3683:
3680:
3677:
3674:
3671:
3669:
3666:
3665:
3661:
3659:0.0000136 MeV
3658:
3655:
3652:
3649:
3646:
3643:
3640:
3637:
3635:
3632:
3631:
3627:
3624:
3621:
3618:
3615:
3612:
3609:
3606:
3603:
3601:
3598:
3597:
3594:
3590:
3587:
3584:
3582:
3578:
3576:
3573:total mass /
3572:
3569:
3566:
3564:
3561:
3559:
3556:
3553:
3552:
3546:
3543:
3539:
3535:
3531:
3520:
3517:
3514:
3511:
3508:
3505:
3502:
3499:
3496:
3494:
3491:
3490:
3486:
3483:
3480:
3477:
3474:
3471:
3468:
3465:
3462:
3459:
3458:
3454:
3451:
3448:
3445:
3442:
3439:
3436:
3433:
3430:
3427:
3426:
3422:
3419:
3416:
3413:
3410:
3407:
3404:
3401:
3398:
3396:
3393:
3392:
3389:
3385:
3382:
3379:
3377:
3373:
3371:
3368:total mass /
3367:
3364:
3361:
3359:
3356:
3354:
3351:
3348:
3347:
3341:
3339:
3335:
3328:
3321:
3317:
3314: +
3313:
3309:
3305:
3301:
3297:
3294:. The letter
3291:
3278:
3271:
3255:
3248:
3235:
3230:
3226:
3219:
3212:
3208:
3201:
3198: +
3194:
3190:
3185:
3176: =
3175:
3160:
3155:
3151:
3147:
3146:atomic number
3143:
3139:
3134:
3130:
3128:
3124:
3106:
3102:
3098:
3094:
3089:
3085:
3082:
3059:
3055:
3050:
3044:
3036:
3033:
3030:
3024:
3021:
3001:
2979:
2975:
2971:
2967:
2962:
2956:
2952:
2948:
2945:
2923:
2919:
2915:
2911:
2906:
2902:
2899:
2879:
2870:
2856:
2853:
2850:
2830:
2827:
2824:
2804:
2801:
2798:
2778:
2775:
2772:
2752:
2749:
2746:
2722:
2718:
2714:
2710:
2706:
2701:
2694:
2690:
2683:
2678:
2674:
2671:
2668:
2664:
2659:
2653:
2646:
2642:
2638:
2634:
2627:
2623:
2619:
2613:
2606:
2602:
2598:
2594:
2590:
2585:
2582:
2579:
2568:
2565:
2555:
2541:
2537:
2533:
2529:
2525:
2519:
2509:
2507:
2502:
2499:
2495:
2490:
2484:
2482:
2478:
2474:
2469:
2467:
2463:
2459:
2455:
2451:
2447:
2443:
2439:
2437:
2425:
2422:
2414:
2404:
2400:
2396:
2390:
2389:
2385:
2380:This section
2378:
2374:
2369:
2368:
2360:
2358:
2354:
2350:
2345:
2338:Q = 5.467 MeV
2334:Ni + C → Se
2333:
2332:
2331:
2328:
2324:
2317:
2311:
2306:
2302:
2298:
2294:
2290:
2285:
2281:
2279:
2278:atomic number
2273:
2271:
2266:
2262:
2258:
2254:
2245:
2236:
2233:
2232:nuclear decay
2228:
2226:
2222:
2218:
2214:
2210:
2204:
2202:
2198:
2193:
2192:
2185:
2182:
2178:
2159:
2156:
2155:
2151:
2148:
2147:
2143:
2140:
2139:
2135:
2132:
2131:
2127:
2124:
2123:
2119:
2116:
2115:
2111:
2108:
2107:
2094:
2091:
2090:
2086:
2083:
2082:
2078:
2075:
2074:
2070:
2067:
2066:
2062:
2059:
2058:
2054:
2051:
2050:
2046:
2043:
2042:
2038:
2035:
2034:
2030:
2027:
2026:
2019:
2016:
2011:
2004:
2001:
1998:
1995:
1992:
1988:
1984:
1980:
1976:
1973:
1972:
1971:
1970:) processes:
1969:
1965:
1960:
1958:
1954:
1950:
1946:
1942:
1940:
1936:
1932:
1928:
1923:
1921:
1917:
1913:
1905:
1901:
1897:
1894:
1890:
1889:
1888:
1882:
1878:
1874:
1870:
1869:
1868:
1866:
1862:
1858:
1854:
1850:
1840:
1838:
1829:
1825:
1822:
1819:
1811:
1808:
1800:
1797:
1793:
1790:
1789:proton number
1786:
1785:
1784:
1767:
1764:
1759:
1755:
1751:
1748:
1743:
1739:
1735:
1732:
1729:
1726:
1721:
1717:
1710:
1707:
1704:
1698:
1693:
1689:
1685:
1682:
1679:
1669:
1668:
1667:
1665:
1655:
1653:
1643:
1641:
1637:
1631:
1629:
1625:
1619:
1617:
1612:
1608:
1603:
1601:
1595:
1592:
1588:
1582:
1579:
1569:
1567:
1563:
1559:
1554:
1551:
1545:
1543:
1538:
1529:
1526:
1522:
1517:
1511:
1508:
1507:nuclear force
1498:
1496:
1492:
1487:
1485:
1481:
1477:
1473:
1469:
1464:
1462:
1461:radioactivity
1458:
1454:
1449:
1447:
1442:
1433:
1431:
1430:
1427:the study of
1423:
1419:
1417:
1416:nuclear force
1411:
1409:
1405:
1401:
1391:
1389:
1384:
1379:
1377:
1372:
1368:
1366:
1362:
1358:
1353:
1351:
1347:
1343:
1339:
1338:
1335: =
1334:
1329:
1322:
1318:
1308:
1306:
1301:
1299:
1295:
1291:
1287:
1283:
1279:
1275:
1269:
1259:
1257:
1253:
1249:
1245:
1241:
1237:
1232:
1227:
1223:
1221:
1217:
1213:
1209:
1208:
1207:nuclear force
1202:
1200:
1196:
1192:
1187:
1181:
1177:
1173:
1169:
1164:
1162:
1158:
1157:chemical bond
1154:
1150:
1146:
1142:
1133:
1130:
1127:
1123:
1119:
1115:
1110:
1108:
1104:
1100:
1096:
1081:
1079:
1075:
1070:
1068:
1064:
1060:
1056:
1055:nuclear power
1052:
1048:
1044:
1040:
1035:
1033:
1029:
1025:
1020:
1016:
1011:
1007:
1003:
998:
996:
992:
988:
984:
980:
976:
972:
968:
964:
953:
948:
946:
941:
939:
934:
933:
931:
930:
924:
914:
911:
906:
900:
899:
898:
897:
890:
887:
885:
882:
880:
877:
875:
872:
870:
867:
865:
862:
860:
857:
855:
852:
850:
847:
845:
842:
840:
837:
835:
832:
830:
827:
825:
822:
820:
817:
815:
812:
810:
807:
805:
802:
800:
797:
795:
792:
790:
787:
785:
782:
780:
777:
775:
772:
770:
767:
765:
762:
760:
757:
755:
752:
750:
747:
745:
742:
740:
737:
735:
732:
731:
728:
723:
722:
715:
712:
710:
707:
705:
702:
701:
698:
693:
692:
683:
680:
678:
675:
673:
670:
669:
667:
666:
661:
658:
656:
653:
651:
648:
647:
643:
642:
639:
636:
635:
632:
627:
622:
621:
614:
611:
607:
606:by cosmic ray
604:
603:
602:
599:
598:
592:
591:
582:
579:
577:
574:
573:
572:
569:
565:
562:
560:
557:
556:
555:
552:
548:
545:
544:
543:
540:
539:
533:
532:
525:
522:
518:
517:pair breaking
515:
514:
513:
510:
508:
505:
504:
501:
496:
495:
488:
485:
483:
482:Decay product
480:
478:
475:
473:
470:
469:
466:
463:
461:
458:
456:
455:Cluster decay
453:
451:
448:
444:
441:
439:
436:
435:
434:
431:
429:
426:
422:
419:
415:
412:
411:
410:
407:
406:
405:
402:
400:
397:
396:
393:
388:
387:
380:
377:
375:
372:
370:
367:
365:
362:
360:
357:
355:
352:
351:
345:
344:
335:
332:
331:
330:
327:
325:
322:
320:
317:
315:
312:
311:
308:
304:
300:
299:Mirror nuclei
297:
296:
292:
289:
288:
285:
284:
281: −
280:
275:
272:
271:
268:
267:
262:
259:
258:
255:
254:
249:
246:
245:
241:
240:
235:
232:
231:
227:
222:
221:
214:
211:
209:
206:
204:
201:
199:
196:
195:
192:
187:
186:
181:
178:
176:
173:
171:
170:Nuclear force
168:
166:
163:
159:
156:
154:
151:
150:
149:
146:
144:
141:
140:
139:
138:
134:
130:
129:
126:
123:
122:
113:
110:
102:
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
4413:
4399:
4390:
4381:
4356:
4352:
4346:
4313:
4307:
4301:
4268:
4262:
4256:
4245:. Retrieved
4235:
4224:. Retrieved
4220:the original
4210:
4194:
4185:
4174:. Retrieved
4169:
4129:. Retrieved
4119:
4070:
4066:
4060:
4049:. Retrieved
4047:. 2016-03-11
4044:
4035:
4022:
4013:
4002:. Retrieved
3998:
3989:
3978:. Retrieved
3973:
3941:. Retrieved
3936:
3912:. Retrieved
3908:the original
3899:
3890:
3879:. Retrieved
3871:
3861:
3847:. Retrieved
3842:
3776:
3772:
3769:
3758:0.0082857 Da
3724:0.0091058 Da
3696:1.11226 MeV
3678:13.13572 MeV
3592:
3580:
3574:
3562:
3557:
3541:
3537:
3533:
3529:
3526:
3509:0.9988443 Da
3506:61.928345 Da
3475:0.9988464 Da
3443:0.9988496 Da
3440:57.932276 Da
3411:0.9988372 Da
3408:55.934937 Da
3387:
3375:
3369:
3357:
3352:
3337:
3333:
3326:
3319:
3315:
3311:
3307:
3303:
3299:
3295:
3289:
3276:
3269:
3253:
3246:
3233:
3228:
3224:
3217:
3210:
3206:
3199:
3192:
3188:
3183:
3171:
3158:
3149:
3141:
2871:
2539:
2534:neutrons, a
2531:
2530:protons and
2527:
2523:
2521:
2503:
2497:
2493:
2485:
2470:
2440:
2432:
2417:
2411:October 2014
2408:
2393:Please help
2381:
2341:
2329:
2322:
2315:
2286:
2282:
2274:
2270:doubly magic
2250:
2229:
2224:
2205:
2190:
2174:
2014:
2008:
1991:strontium-87
1989:decaying to
1964:exoenergetic
1963:
1961:
1943:
1924:
1911:
1909:
1899:
1892:
1886:
1880:
1876:
1872:
1846:
1833:
1782:
1664:nuclear mass
1661:
1651:
1649:
1632:
1620:
1604:
1596:
1583:
1576:In the main
1575:
1555:
1546:
1539:
1535:
1524:
1520:
1512:
1504:
1488:
1484:decay chains
1465:
1450:
1443:
1439:
1426:
1424:
1420:
1412:
1397:
1380:
1373:
1369:
1354:
1345:
1336:
1332:
1325:
1302:
1271:
1228:
1224:
1214:) holds the
1211:
1205:
1203:
1188:
1165:
1139:
1131:
1111:
1092:
1084:Introduction
1071:
1050:
1036:
1031:
1027:
1023:
1018:
1014:
999:
962:
961:
524:Photofission
472:Decay energy
399:Alpha α
353:
306:
302:
282:
278:
265:
252:
238:
105:
99:October 2014
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
3764:2.5727 MeV
3755:3.09433 MeV
3752:1.005343 Da
3749:3.016029 Da
3746:14.9312 MeV
3730:2.8273 MeV
3721:3.08815 MeV
3718:1.005350 Da
3715:3.016049 Da
3712:14.9498 MeV
3693:2.22452 MeV
3690:0.002388 Da
3687:1.50346 MeV
3684:1.007051 Da
3681:2.014102 Da
3650:1.007825 Da
3647:1.007825 Da
3616:1.008665 Da
3613:1.008665 Da
3585:mass defect
3567:mass excess
3521:8.7948 MeV
3518:545.281 MeV
3515:0.585383 Da
3487:8.7811 MeV
3484:526.864 MeV
3481:0.565612 Da
3472:59.93079 Da
3455:8.7925 MeV
3452:509.966 MeV
3449:0.547471 Da
3423:8.7906 MeV
3420:492.275 MeV
3417:0.528479 Da
3380:mass defect
3362:mass excess
2280:increases.
2265:atomic mass
1987:rubidium-87
1979:radioactive
1904:mass defect
1628:Beryllium-8
1321:mass defect
1317:mass excess
1311:Mass defect
1252:temperature
1103:endothermic
1069:products).
1006:constituent
829:Oppenheimer
507:Spontaneous
477:Decay chain
428:K/L capture
404:Beta β
274:Isodiaphers
198:Liquid drop
4447:Categories
4247:2006-04-10
4226:2010-05-04
4176:2010-07-11
4131:2022-12-24
4051:2019-11-05
4004:2019-11-05
3980:2010-07-11
3943:2010-07-11
3914:2010-07-10
3881:2010-07-11
3849:2010-07-10
3820:References
3761:7.7181 MeV
3727:8.4820 MeV
3653:0.7826 MeV
3644:7.2890 MeV
3619:0.0000 MeV
3610:8.0716 MeV
3570:total mass
3512:9.1481 MeV
3478:9.1462 MeV
3446:9.1432 MeV
3414:9.1538 MeV
3365:total mass
3125:and − for
2355:, such as
2301:supernovae
1968:exothermic
1929:physicist
1607:beta decay
1600:beta decay
1410:proposed.
1189:After the
1107:exothermic
1057:, or in a
859:Strassmann
849:Rutherford
727:Scientists
682:Artificial
677:Cosmogenic
672:Primordial
668:Nuclides:
645:Processes:
601:Spallation
69:newspapers
4243:. aip.org
4095:1879-1123
3083:±
3034:−
3022:−
2946:−
2900:−
2702:±
2672:−
2654:−
2614:−
2586:−
2569:⋅
2458:plutonium
2382:does not
2349:cobalt-56
2344:nickel-56
2289:nickel-62
2201:electrons
1945:Nickel-62
1867:formula:
1826:N is the
1794:A is the
1787:Z is the
1765:−
1727:−
1708:−
1677:Δ
1591:nickel-62
1558:deuterium
1408:Helmholtz
1184:(− + + −)
1141:Electrons
864:Świątecki
779:Pi. Curie
774:Fr. Curie
769:Ir. Curie
764:Cockcroft
739:Becquerel
660:Supernova
364:Drip line
359:p–n ratio
334:Borromean
213:Ab initio
4338:10062738
4293:10046415
4111:34178643
4103:28733967
3784:See also
3662:13.6 eV
3154:neutrons
3138:nuclides
2491:formula
2477:nucleons
2357:SN 1987A
2257:hydrogen
2177:isotopes
2109:Reaction
2104:Fission
2028:Reaction
1957:hydrogen
1611:positron
1578:isotopes
1404:hydrogen
1383:polonium
1294:isotopes
1290:neutrons
1274:elements
1248:pressure
1244:neutrons
1236:hydrogen
1216:nucleons
1199:verified
1195:measured
1176:neutrons
1126:hydrogen
1078:hydrogen
1022:, where
991:nucleons
987:neutrons
923:Category
824:Oliphant
809:Lawrence
789:Davisson
759:Chadwick
655:Big Bang
542:electron
512:Products
433:Isomeric
324:Even/odd
301: –
276:– equal
263:– equal
261:Isotones
250:– equal
236:– equal
234:Isotopes
226:Nuclides
148:Nucleons
4361:Bibcode
4318:Bibcode
4273:Bibcode
4075:Bibcode
3554:nuclide
3349:nuclide
3332:. The "
3330:nuclide
3318:)
3284:939.565
3241:938.272
3221:nuclide
3191: (
3178:931.494
3163:(iron).
2481:nucleus
2466:krypton
2454:uranium
2448:), and
2403:removed
2388:sources
2325:= 1 atm
2318:= 298 K
2297:iron-56
2293:iron-58
2251:In the
2221:orbital
2181:neutral
2023:Fusion
2003:Fission
1953:isotope
1951:of any
1949:nucleon
1935:uranium
1816:is the
1805:is the
1783:where:
1587:Iron-56
1566:lithium
1562:tritium
1491:iron-56
1476:uranium
1472:thorium
1468:bismuth
1286:protons
1282:nucleus
1231:gravity
1229:Unlike
1172:protons
983:protons
975:nucleus
879:Thomson
869:Szilárd
839:Purcell
819:Meitner
754:N. Bohr
749:A. Bohr
734:Alvarez
650:Stellar
554:neutron
438:Gamma γ
291:Isomers
248:Isobars
143:Nucleus
83:scholar
4336:
4291:
4127:. 1854
4109:
4101:
4093:
3855:Guides
3628:0 MeV
3223:where
3209:
3144:, the
2506:dalton
2462:barium
2446:helium
2336:
2261:sodium
2259:up to
2197:ionize
2152:15.11
2144:17.34
2128:11.18
2095:22.36
2087:12.85
2079:18.34
2071:17.53
1997:Fusion
1927:French
1920:vacuum
1914:= the
1887:where
1879:
1861:energy
1849:nuclei
1474:, and
1361:nickel
1240:helium
1122:nuclei
1063:splits
977:of an
971:energy
921:
889:Wigner
884:Walton
874:Teller
804:Jensen
571:proton
314:Stable
85:
78:
71:
64:
56:
4107:S2CID
3625:0 MeV
3334:total
3261:0.510
2805:0.585
2225:orbit
2184:atoms
2160:8.68
2136:0.94
2120:4.02
2063:3.27
2055:4.08
2047:5.52
2039:1.44
1939:X-ray
1278:atoms
1193:were
1124:like
854:Soddy
834:Proca
814:Mayer
794:Fermi
744:Bethe
319:Magic
90:JSTOR
76:books
4334:PMID
4289:PMID
4099:PMID
4091:ISSN
3775:and
3622:0 Da
3302:and
3286:4133
3274:and
3266:9461
3243:0813
3161:= 26
2831:19.3
2779:13.0
2753:14.0
2473:mass
2464:and
2456:and
2386:any
2384:cite
2320:and
2295:and
2189:MeV/
1966:(or
1910:and
1857:mass
1853:atom
1497:do.
1453:lead
1446:iron
1398:The
1357:iron
1256:star
1250:and
1210:(or
1197:and
1166:The
1116:and
1002:mass
1000:The
985:and
979:atom
844:Rabi
799:Hahn
709:RHIC
329:Halo
62:news
4398:at
4369:doi
4326:doi
4281:doi
4200:doi
4083:doi
3263:998
3180:028
2573:MeV
2397:by
2213:GSI
1918:in
1851:of
1097:or
965:in
714:LHC
628:and
45:by
4449::
4404:,
4367:.
4357:63
4355:.
4332:.
4324:.
4314:77
4312:.
4287:.
4279:.
4269:69
4267:.
4168:.
4140:^
4105:.
4097:.
4089:.
4081:.
4071:28
4069:.
4043:.
3997:.
3972:.
3952:^
3935:.
3923:^
3902:.
3898:.
3874:.
3870:.
3841:.
3828:^
3736:He
3500:34
3497:28
3493:Ni
3466:32
3463:28
3460:Ni
3434:32
3431:26
3428:Fe
3402:30
3399:26
3395:Fe
3340:.
3282:=
3259:=
3251:,
3239:=
3174:Da
2869:.
2857:33
2843:;
2817:;
2791:;
2765:;
2498:mc
2496:=
2483:.
2230:A
2203:.
1922:.
1902:=
1525:mc
1523:=
1470:,
1337:mc
1163:.
1080:.
1019:mc
1017:=
1012:,
581:rp
547:2×
414:0v
409:2β
305:↔
4408:.
4375:.
4371::
4363::
4340:.
4328::
4320::
4295:.
4283::
4275::
4250:.
4229:.
4202::
4179:.
4134:.
4113:.
4085::
4077::
4054:.
4007:.
3983:.
3946:.
3917:.
3884:.
3852:.
3777:Z
3773:N
3743:1
3740:2
3709:2
3706:1
3702:H
3675:1
3672:1
3668:H
3641:0
3638:1
3634:H
3607:1
3604:0
3600:n
3593:A
3581:A
3575:A
3563:N
3558:Z
3542:A
3538:A
3534:A
3530:Z
3388:A
3376:A
3370:A
3358:N
3353:Z
3338:A
3327:m
3323:n
3320:m
3316:N
3312:Z
3308:A
3304:N
3300:Z
3296:A
3290:c
3280:n
3277:m
3270:c
3257:e
3254:m
3247:c
3237:p
3234:m
3229:N
3225:Z
3218:m
3214:n
3211:m
3207:N
3203:e
3200:m
3196:p
3193:m
3189:Z
3184:c
3159:Z
3150:N
3142:Z
3107:4
3103:/
3099:7
3095:A
3090:/
3086:e
3060:2
3056:A
3051:/
3045:2
3041:)
3037:Z
3031:N
3028:(
3025:d
3002:Z
2980:3
2976:/
2972:4
2968:A
2963:/
2957:2
2953:Z
2949:c
2924:3
2920:/
2916:1
2912:A
2907:/
2903:b
2880:a
2854:=
2851:e
2828:=
2825:d
2802:=
2799:c
2776:=
2773:b
2750:=
2747:a
2723:4
2719:/
2715:7
2711:A
2707:e
2695:2
2691:A
2684:2
2679:)
2675:Z
2669:N
2665:(
2660:d
2647:3
2643:/
2639:4
2635:A
2628:2
2624:Z
2620:c
2607:3
2603:/
2599:1
2595:A
2591:b
2583:a
2580:=
2566:A
2560:B
2556:E
2543:B
2540:E
2532:N
2528:Z
2524:A
2494:E
2434:(
2424:)
2418:(
2413:)
2409:(
2405:.
2391:.
2323:p
2316:T
2191:c
1912:c
1906:,
1900:m
1898:Δ
1893:E
1891:Δ
1883:,
1881:c
1877:m
1873:E
1871:Δ
1859:–
1830:.
1820:.
1814:n
1812:m
1809:.
1803:p
1801:m
1768:M
1760:n
1756:m
1752:N
1749:+
1744:p
1740:m
1736:Z
1733:=
1730:M
1722:n
1718:m
1714:)
1711:Z
1705:A
1702:(
1699:+
1694:p
1690:m
1686:Z
1683:=
1680:m
1521:E
1359:/
1346:c
1333:E
1032:m
1028:c
1024:E
1015:E
951:e
944:t
937:v
576:p
564:r
559:s
421:β
307:N
303:Z
283:Z
279:N
266:N
253:A
239:Z
158:n
153:p
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
