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From left to right and from top to bottom the elements gain in mass, and by columns they have specific chemical properties. The numbers in brackets denote the number of protons contained in the nucleus of that element. There are usually a number of isotopes of a given element, which are characterized by the number of neutrons in the nucleus (neutrons are electrically neutral particles of about the same mass as the proton). We shall discuss isotopes and the generic structure of the nucleus in the next chapter.
Since atoms are electrically neutral, for a specific element there must be an equal number of electrons as there are protons. Everything else being equal, we might expect these electrons to all occupy the lowest possible energy level. However, that turns out not to be the case.