The atomic number of an element tells you the number of electrons and protons in a neutral atom. Ions are forms of an element with different numbers of electrons. Isotopes are forms of an element with different numbers of neutrons.
The "and" may easily be misinterpreted. An atomic number (the Z number) was introduced into chemistry by Rutherford, Moseley, and Chadwick. Their work helped explain the repeating patterns seen with the elements, and helped along the organization of the most commonly discussed modern periodic table (organized by atomic number). An atomic number is a whole number representing the number of protons.
To make matters a little more interesting, in a neutral atom, an atom without charge, the number of protons equals the number of electrons. Therefore, while the Z is the number of protons, this number equals the number of electrons in a neutral atom. For example, hydrogen has 1 proton and 1 electron. It has a Z number of 1.
Note: "Experimentally the 'atomic number' of an element was established by Chadwick in 1920 from beta particle scattering experiments (an atoms electrons deflecting the bombarding beta particle electrons) and from the X-ray spectra results of Moseley in 1913. " --
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