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One cause of radioactive decay of atoms is the decrease in wavelength of the atomic wave structure; with distance from the atomic centre. In the case of atoms the Hall fraction (wavelength) decreases rapidly at the larger atomic numbers making it difficult to add and retain particles of a fixed wavelength (i.e. the wavelength of a free electron). The atom not only has to capture the electron but in order to retain the electron the atom has to compact the electron on one axis; so that the compacted electron wavelength fits the outer wavelength (Hall fraction) of the atomic structure.

The nucleus plays a different part in that it has to retain the proton that pairs with the electron to form a meson within the atomic structure.

However the number of protons a nucleus can hold is not limited by the Hall fractions of the atomic shells, but is dependent on the addition of neutrons which allow the nucleus to add protons without any proportional increase in the volume of the nucleus. The neutrons (and hence the nuclei) are natures form of Bose Einstein Condensate.

The narrowness of the outer wavelength of atoms of atomic No.84 and higher is why atoms of very high atomic numbers (created by experiment) have no stable electron shells.

The large width of the inner wavelength (large Hall fractions) explains why atoms of low atomic numbers are gaseous (plenty of room for an electron of minimum compaction to move around).

For the Hall fractions of atomic structure see:

http://69.5.17.59/hfas.pdf

http://69.5.17.59/hfps2.pdf

and the paper used as the reference work for Hall fractions:

arXiv:cond-mat/0510688 v2 20 Dec 2005

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