The number of atoms of each kind in any closed system remains constant

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The number of atoms of each kind in any closed system remains constant is scientific consept, formulated some around centuries 15–17, that explained the failure of the attempts of alchemy to convert some chemical elements (for example, led or silver) to another element (usually, gold), performing the chemical reactions.

This concept is good approximation in the description of the most of processes happening at the surface of the Earth, including the growth and being of living objects and the most of human activity. In such a way, the area of applicability of such a concept is wide.

The applicability of the concept is limited by the nuclear reactions, when the nuclei of atoms change their mass and, often, also the charge. In addition, it is possible to distinguish the metastable states of nuclei, and treat the nuclear isomers as atoms of different kind; then the transitions between the isomers should also be interpreted as variation of number of atoms of certain kind.

The examples of processes, that violate of the conservation mentioned are the $\alpha$-decay, $\beta$-decay, nuclear fusion, nuclear fission, creation of protons, alpha-particles and other compounds with high-energy beams of elementary particles or atomic nuclei. In some of these cases, even the total number of atoms does not conserve. In particular, the phenomenon of the Decay heat cannot be described within the concept in the title of the article.

References

http://en.wikipedia.org/wiki/Closed_system .. the total number of atoms of element $i$ in the system, which remains constant, since the system is closed.

http://en.wikipedia.org/wiki/Thermodynamic_system the fact that the system is closed is expressed by stating that the total number of each elemental atom is conserved..