The arrangment and location of what subatomic particles determine the chemical properties of an atom?

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I don't know that the location is as much a determining factor as is the number of subatomic particles available.  The subatomic particle, of course, is the electron, which orbit the nucleus of the atom by traveling in energy levels, two in the first, 6 in the second, and 10 in the third.  It is the number of electrons available in the outer energy level that determine the atoms chemical properties.  For example, hydrogen has the simplest atomic structure on the periodic chart of elements, with one proton in the nucleus and one electron circling in the first energy level about the nucleus.  One of the chemical properties used to classify atoms is their ability to combust, to combine chemically with oxygen.  Oxygen has 6 electrons in its outer energy level, with room for two electrons.  Hydrogen will combine quickly and explosively with oxygen to form water, as the lone electron from each of two hydrogen atoms joing together chemically with one oxygen atom to form one molecule of water, H2O.  It is this number of electrons available, or number of vacancies available, that determine both the ability and rate of an atom to combine chemically with other atoms.

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