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Encyclopedia > Mass excess

Binding energy is the energy required to disassemble a whole into separate parts. A bound system has a lower potential energy than its constituent parts; this is what keeps the system together. The usual convention is that this corresponds to a positive binding energy. In the physical sciences, potential energy is energy which is captured within a physical system by virtue of the relative positions or configurations of objects, and which has the potential to be released when the system is allowed to attain a configuration with a lower energy state. ...

In general, binding energy represents the mechanical work which must be done in acting against the forces which hold an object together, while disassembling the object into component parts separated by such sufficient distance that further separation requires negligible additional work. Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. ...

Electron binding energy is a measure of the energy required to free electrons from their atomic orbits.

Nuclear binding energy is derived from the strong nuclear force and is the energy required to disassemble a nucleus into free unbound neutrons and protons. At the atomic level, the binding energy of the atom is derived from electromagnetic interaction and is the energy required to disassemble an atom into free electrons and a nucleus. In astrophysics, gravitational binding energy of a celestial body is the energy required to disassemble it into space debris (dust and gas). This quantity is not to be confused with the gravitational potential energy, which is the energy required to separate two bodies, such as a celestial body and a satellite, to infinite distance, keeping each intact (the latter energy is lower). The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ... A semi-accurate depiction of the helium atom. ... This article or section does not cite its references or sources. ... Properties  In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... Linus Pauling, as a pioneer of the valence bond theory, is one of the first quantum chemists. ... Electromagnetic interaction is a fundamental force of nature and is felt by charged leptons and quarks. ... Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature, and chemical composition) of celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... The gravitational binding energy of an object is the amount of energy required to accelerate every component of that object to the escape velocity of every other component. ... Potential energy (U, or Ep), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. ...

## Mass defect GA_googleFillSlot("encyclopedia_square");

Because a bound system is at a lower energy level than its unbound constituents, its mass must be less than the total mass of its unbound constituents. For systems with low binding energies, this "lost" mass after binding, may be fractionally small. For systems with high binding energies, however, the missing mass may be an easily measurable fraction.

Since all forms of energy in a system (which has no net momentum) have mass, the question of where the missing mass of the binding energy goes is of interest. The answer is that this mass does not "disappear" into energy (a common misconception); rather, transformed to heat or light, this mass may move away to another location. The "mass defect" from binding energy is therefore only mass which has moved. However, it remains mass, because mass is conserved in systems for any given single observer, so long as the system remains closed. Thus, if binding energy mass is transformed into heat, the system must be cooled (the heat removed) before the mass-deficit appears in the cooled system. In that case, the removed heat (which has mass itself when measured in the original inertial frame) represents exactly the mass "deficit." In classical mechanics, momentum (pl. ... In physics, heat, symbolized by Q, is defined as energy in transit. ...

For example, when two large objects (such as the earth and a meteor) are attracted by a gravitational field and collide, the energy for the heat of impact is extracted from the gravitational field of the objects. However, the system does not lose mass (which represents its binding energy) until this heat is radiated into space, and this space is no longer counted as part of the original system (equivalent to opening the original system). The gravitational field is a field (physics), generated by massive objects, that determines the magnitude and direction of gravitation experienced by other massive objects. ...

Closely analogous considerations apply in chemical and nuclear considerations. However, in nuclear reactions, the fraction of mass which may be removed as light or heat, and which then appears as binding energy, is often a much larger fraction of the system mass. This is because nuclear forces are comparatively stronger than other forces.

The energy given off during either nuclear fusion or nuclear fission is the difference between the binding energies of the fuel and the fusion or fission products. In practice, this energy may also be calculated from the substantial mass differences between the fuel and products, once evolved heat and radiation have been removed. The deuterium-tritium (D-T) fusion reaction is considered the most promising for producing fusion power. ... For the generation of electrical power by fission, see Nuclear power plant An induced nuclear fission event. ...

## Atomic binding energy

The binding energy for a single atom is given by:

Where:

c is the speed of light
ms is the mass of the separated nucleons
mb is the mass of the bound nucleus
Z is the atomic number of the bound nucleus
mp is the mass of one proton
N is the number of neutrons
mn is the mass of one neutron

The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation in a vacuum, not just visible light. ... In physics a nucleon is a collective name for two baryons: the neutron and the proton. ... A semi-accurate depiction of the helium atom. ... Properties  In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... This article or section does not cite its references or sources. ...

### Specific quantitative example: a deuteron

A deuteron is the nucleus of a deuterium atom, and consists of one proton and one neutron. The masses of the constituents are: Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of one atom in 6400 of hydrogen (see VSMOW; the abundance changes slightly from one kind of natural water to another). ... Properties  In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... This article or section does not cite its references or sources. ...

mproton = 1.007825 u (u is atomic mass unit)
mneutron= 1.008665 u
mproton + mneutron = 1.007825 + 1.008665 = 2.01649 u

The mass of the deuteron is: The unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic and molecular masses. ...

Atomic mass 2H = 2.014102 u

The mass difference = 2.01649 - 2.014102 = 0.002388 u. Since the conversion between rest mass and energy is 931.494MeV/u, therefore a deuteron's binding energy is The fuel value or relative energy density is the quantity of potential energy in fuel, food or other substance. ...

0.002388 × 931.494 MeV/u = 2.224 MeV

Thus, expressed in another way, the binding energy is [0.002388/2.01649] x 100% = about 0.1184 % of the total energy corresponding to the mass. This corresponds to 1.07 x 1014 J/kg = 107 TJ/kg.

## Nuclear binding energy curve

In the periodic table of elements, the series of light elements from hydrogen up to sodium is observed to exhibit generally increasing binding energy per nucleon as the atomic mass increases. This increase is generated by increasing forces per nucleon in the nucleus, as each additional nucleon is attracted by all of the other nucleons, and thus more tightly bound to the whole. The periodic table of the chemical elements, also called the Mendeleev periodic table, is a tabular display of the known chemical elements. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... General Name, Symbol, Number sodium, Na, 11 Chemical series alkali metals Group, Period, Block 1, 3, s Appearance silvery white Atomic mass 22. ... The atomic mass of a chemical element is the mass of an atom at rest, most often expressed in unified atomic mass units. ...

The region of increasing binding energy is followed by a region of relative stability (saturation) in the sequence from magnesium through xenon. In this region, the nucleus has become large enough that nuclear forces no longer completely extend efficiently across its width. Attractive nuclear forces in this region, as atomic mass increases, are nearly balanced by repellant electromagnetic forces between protons, as atomic number increases. General Name, Symbol, Number magnesium, Mg, 12 Chemical series alkaline earth metals Group, Period, Block 2, 3, s Appearance silvery white Atomic mass 24. ... General Name, Symbol, Number xenon, Xe, 54 Chemical series noble gases Group, Period, Block 18, 5, p Appearance colorless Atomic mass 131. ... In chemistry and physics, the atomic number (Z) is the number of protons found in the nucleus of an atom. ...

Finally, in elements heavier than xenon, there is a decrease in binding energy per nucleon as atomic number increases. In this region of nuclear size, electromagnetic repulsive forces are beginning to gain against the strong nuclear force.

At the peak of binding energy, nickel-62 is the most tightly-bound nucleus, followed by iron-58 and iron-56. (This is the basic reason why iron and nickel are very common metals in planetary cores, since they are produced profusely as end products in supernovae). Multiwavelength X-ray image of the remnant of Keplers Supernova, SN 1604. ...

The existence of a maximum in binding energy in medium-sized nuclei is a consequence of the trade-off in the effects of two opposing forces which have different range characteristics. The attractive nuclear force (strong nuclear force), 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 which results between further added nucleons as a result of additional strong force interactions; such nuclei become less and 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. The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ...

Fusion produces energy by combining the very lightest elements into more tightly-bound elements (such as hydrogen into helium), and fission produces energy by splitting the heaviest elements (such as uranium and plutonium) into more tightly-bound elements (such as barium and krypton). Both processes produce energy, because middle-sized nuclei are the most tightly bound of all. General Name, Symbol, Number helium, He, 2 Chemical series noble gases Group, Period, Block 18, 1, s Appearance colorless Atomic mass 4. ... General Name, Symbol, Number uranium, U, 92 Chemical series actinides Group, Period, Block n/a, 7, f Appearance silvery gray metallic; corrodes to a spalling black oxide coat in air Atomic mass 238. ... General Name, Symbol, Number plutonium, Pu, 94 Chemical series actinides Group, Period, Block n/a, 7, f Appearance silvery white Atomic mass (244) g/mol Electron configuration [Rn] 5f6 7s2 Electrons per shell 2, 8, 18, 32, 24, 8, 2 Physical properties Phase solid Density (near r. ... General Name, Symbol, Number barium, Ba, 56 Chemical series alkaline earth metals Group, Period, Block 2, 6, s Appearance silvery white Atomic mass 137. ... General Name, Symbol, Number krypton, Kr, 36 Chemical series noble gases Group, Period, Block 18, 4, p Appearance colorless Atomic mass 83. ...

### Measuring the binding energy

As seen above in the example of deuterium, nuclear binding energies are large enough that they may be easily measured as fractional mass 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 nucleons are joined together to form a nucleus. All nuclei which last long enough to be weighed, are measurably lighter than a corresponding collection of free protons and neutrons. Unsolved problems in physics: What causes anything to have mass? Mass is a property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... Nucleon is the common name used in nuclear chemistry to refer to a neutron or a proton, the components of an atoms nucleus. ... A semi-accurate depiction of the helium atom. ...

Nuclear binding energy can be easily computed from the easily measurable 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 formula E=mc² can be used to compute the binding energy of any nucleus. (As a historical note, early nuclear physicists used to refer to computing this value as a "packing fraction" calculation). A display of the famous equation on Taipei 101 during the event of the World Year of Physics 2005. ...

For example, the atomic mass unit (1.000000 u) is defined to be 1/12 of the mass of a 12C atom – but the atomic mass of a 1H atom (which is a proton plus electron) is 1.007825 u, so each nucleon in 12C has lost, on average, about 0.8% percent of its mass in the form of binding energy. The unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic and molecular masses. ...

Image File history File linksMetadata AvgBindingEnergyPerNucleon. ... Image File history File linksMetadata AvgBindingEnergyPerNucleon. ...

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