The supplied energy is a kinetic energy which appears during exothermic chemical reactions.

Many reactions appearing in a spontaneous way in nature are exothermic; i.e. the products of the reactions have part of their energy in the form of kinetic energy, which will take part in the balance leading to the local Température, energy which one can hope for to recover.

General information

In Nuclear physics, this energy kinetic is named supplied energy and its evaluation can be done easily by considering energies of the particles or entering cores and those of the particles or outgoing cores. It is of course necessary to consider the exact mass of the cores, taking into account the nature of the states (fundamental or excited) of the products.

One can of course be interested in the supplied energy for each stage of a feedback path, or be interested in the unit of the energy which one can recover. The evaluations are then different for nuclear reactions of explosions, where only the few milliseconds of the initial chain reaction will intervene (before fast dispersion), which the hours, or month of the whole of the reactions in the heart of a power station where the same reactions will intervene but where the energy recovered in the desired form (of the thermal energy of the coolant) integrates a good portion of all the reactions available of each stage of the chain.

Certain kinetic energies of products for the reader who does not have that its has to make are practically irremediable, because of weakness of the cross Section of the reactions which could bring them to a Thermalization; there is thus Neutrino S or antineutrinos which takes along part of the energy of the reactions béta, energy remaining in practice inalienable.

Particular cases

The reactions of Radioactivité reveal a characteristic due to the fact that these reactions, nuclear, very generally utilize of the neutral atoms, or very slightly ionized. It follows that the energy balances can take account of the electrons of the atom; this makes it possible to express the supplied energies according to the masses of the neutral atoms, rather than according to the binding energies of the nucleons of the cores. This comes owing to the fact that one can regard as negligible the binding energies of the outer-shell electrons compared to all other energies intervening: energy of mass of the cores and the electrons.

In the equations which follow one will note $\backslash \; mathcal\; \{M\}\; (has,\; Z)$ the mass of an atom of atomic number Z and of mass number has .

*radioactivité α : noting $X\_\; \{Z\}\; ^\; \{\}$ the core father has, entering, and $Y\_\; \{Z-2\}\; ^\; \{A-4\}$ the core wire, the supplied energy in the reference mark of the core father is:

$Q\_\; \{\backslash \; alpha\}\; =\; \backslash \; mathcal\; \{M\}\; (X)\; c^\; \{2\}\; -\; \backslash \; mathcal\; \{M\}\; (Y)\; c^\; \{2\}\; -\; \backslash \; mathcal\; \{M\}\; (He\_\; \{2\}\; ^\; \{4\})\; c^\; \{2\}$

remarque: the weakness of the binding energies of the electrons allows the use of the mass of the atom He, in the place of that of the particle α even if the corresponding electrons are, still temporarily, on the core fils.

*radioactivité β : it is known that two kinds of transitions β meet; the β^- where an ejected particle is an electron, and the β⁺ for which it is about a positon. In each case another particle is created, the antineutrino and the neutrino, respectively, which carry part of the energy released by the reaction. A reaction known as of orbital electron capture is related to the transition β⁺: an outer-shell electron interacts with a proton to give a neutron.

With regard to the reaction β^- the supplied energy is:

$Q\_\; \{\backslash \; beta^\; \{-\}\}\; =\; \backslash \; mathcal\; \{M\}\; (has,\; Z)\; c^\; \{2\}\; -\; \backslash \; mathcal\; \{M\}\; (has,\; Z+1)\; c^\; \{2\}\; -\; E\; (\backslash \; naked\; bar\; \{\backslash \})$.

remarque: there too the mass of the electron created is hidden in the mass of the atom sortant.

For the reaction β⁺, it comes:

$Q\_\; \{\backslash \; beta^\; \{+\}\}\; =\; \backslash \; mathcal\; \{M\}\; (has,\; Z)\; c^\; \{2\}\; -\; \backslash \; mathcal\; \{M\}\; (has,\; Z-1)\; c^\; \{2\}\; -\; 2m\_\; \{E\}\; c^\; \{2\}\; -\; E\; (\backslash \; naked)$,

and for the orbital electron capture:

$Q\_\; \{THIS\}\; =\; \backslash \; mathcal\; \{M\}\; (has,\; Z)\; c^\; \{2\}\; -\; \backslash \; mathcal\; \{M\}\; (has,\; Z-1)\; c^\; \{2\}\; -\; E\; (\backslash \; naked)$.

One will recall here that the statistical study of the supplied energy of the transitions β revealed nature continues spectrum of the particles β and was an argument at the origin of the invention of the neutrino.

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