Binding energy

Binding energy must be applied in order ( for example, a celestial body, a molecule, an atom, a nucleus ) to disassemble a bound system of two or more constituents which are held together by forces of attraction into its components. An equally large energy is released when the bound system forms from the individual parts. Sometimes under binding energy is understood not this amount of energy itself, but the change of the energy content of the system if its parts are coming together, they have the same amount, but is negative. For example, the commonly used in the chemistry of reaction is negative if, in the reaction energy is released.

The term binding energy is a common technical term, but linguistically somewhat unfortunate. It leads - especially with a following genitive, such as binding energy "of the uranium nucleus " or " the ATP molecule " - slightly to the misunderstanding, if it were an amount of energy that is present in the bound system and from can be released to him. It is true, as stated above, the opposite: the binding energy has been released and discharged already in the formation of the bound system, and is therefore no longer available.

Illustration

For example, if the distance between two permanent magnets is sufficiently low, they attract each other and move toward each other. Moments before the collision both magnets have their highest kinetic energy, which is then converted into sound energy and heat. Must be applied in order again to separate the magnets from each other, the binding energy, agrees in magnitude consistent with the released energy. So to the magnets separate, the binding energy must be introduced into the system. If this is not done, so the magnets stay united.

Chemistry

The chemical bond energy is a measure of the strength of a covalent bond. The molar binding energy of ionic crystals is described by lattice energy and lattice energy.

Binding energies between atoms in molecules lie between 200 and 700 kJ · mol -1 ( 2-7 eV per bond). Particularly low binding energy is observed for hydrogen bonds. You are only 17-167 kJ / mol ( 0.18 to 1.7 eV per bond) was significantly weaker than the bonding force within a molecule.

Atomic physics

In atomic physics, is as binding energy, the energy called that is necessary for decomposing an atom / ion in a (nother ) ion and an electron. They shall be established by the electrical attraction between the electron and the nucleus. At the capture of an electron of the same amount of energy is released. Sometimes with binding energy that of the atom as a whole is (not just a single electron ) meant.

Particularly low binding energies have the valence electrons of the first main group of 13.6 eV for the hydrogen atom via 5.14 eV for sodium to 3.9 eV for cesium. The higher loading an ion is, the higher the bonding energy of the residual electrons. Thus, the second and third ionization energy be already 47 and 72 eV for sodium.

To remove an electron from an uncharged solid, energy must be applied, which is referred to as the work function. It is often much lower than the binding energy of the isolated atoms and is, for example, when cesium only 2.14 eV. Its value can be reduced by the Schottky effect. The work is, for example, in Richardson Edison effect, the secondary electron multiplier, the secondary electron microscope and the photoelectric effect of importance.

Even when gleichrichtendem metal -semiconductor junction as in the Schottky diode electron to overcome the Schottky barrier, that is usually between 0.5 and 0.9 eV. The band gap in the band model of a semiconductor corresponds to the binding energy of an electron in the valence band.

Nuclear physics

In nuclear physics, the binding energy is the amount of energy that must be expended Conversely, to decompose the nucleus into its nucleons as great energy is released when nucleons combine to form a core.

The binding is due to the attractive force of the strong interaction between nucleons. You will be weakened by the mutual Coulomb repulsion of the positively charged protons in the nucleus. The maximum binding energy per nucleon is achieved with nickel -62. Lighter nuclei have relatively more nucleons at the surface, where they are less tightly bound. For heavier nuclei, the binding energy per nucleon increases then decreases, because the more protons are present, the stronger grows the repulsive Coulomb force between them on. Therefore, in the field of light nuclei by nuclear fusion ( fusion ), are obtained in the field of heavy nuclei by nuclear fission energy. The binding energy of atomic nuclei can be estimated within the framework of the droplet model with the Bethe- Weizsäcker formula. The spikes in the graph are related to the magic numbers.

The binding is connected to a mass defect because of the equivalence of mass and energy: The bound core has between 0.1 % ( deuteron ) and 0.9 % (Ni -62 ) less mass than all its nucleons together. For an accurate determination of the mass of an atom can therefore be the binding energy of the nucleus derived:

It is

The binding energy of short-lived nuclei can be determined for example by measuring the energies of their decay products.

Gravity

The gravitational binding energy is the energy that is needed (eg the Earth ) to disassemble a very held together by gravity bodies into many tiny components and remove them infinitely far apart. Conversely, the same amount of energy is released when these ingredients together to form a gravitationally bound body. This is done by the collapse of a gas cloud in a more compact celestial body, such as a rating (see also jeans criterion), leading to a warming of the cloud.

Calculation example

Idealized to a celestial body as a sphere of radius and homogeneous density, then the binding energy is obtained as follows:

It is allowed to fall first on a sphere with radius ( with ) and density from infinity more matter, so that a spherical shell of thickness forms on the surface and you get a new ball of radius and density.

The gravitational potential of the previous bullet is (with the outside of the ball)

In which

The mass of the previous sphere. The spherical shell of thickness be added to have the same density. So there must be a mass

Are brought from infinity to the surface of the sphere. The released energy is

To build up layer by layer so a sphere with radius together, so the following binding energy is a total free:

The binding energy is thus

A homogeneous sphere with the earth mass and radius possessed by this formula a gravitational binding energy of about 2.24 · 1032 J. However, the earth is not a sphere of homogeneous density: the Earth's core has an almost twice as high density as the Earth's mantle. According to the " Preliminary Reference Earth Model" ( PREM ) for the density distribution in the Earth's interior is better approximated calculated the binding energy of the earth numerically 2.489 · 1032 J.

Pictures of Binding energy

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