Well we knew about the chemical properties first and tried to come to a solution as why they behave a certain way. This allowed insight into the electrons in the outer shell.
After ordering the elements into a table we found patterns. We discovered the period system of basically 8 classes of elements behaving chemically similar. But what made them different?
One day we were able to measure the mass of individual Atoms. And it weirdly were all multiples of the mass of hydrogen, so we ended with a theory that they were built from the same elements in different numbers.
And from this its pretty obvious to come to the conclusion that each element is defined by the number of Protons (to bind X Electrons) and the extra mass comes from some additional neutral parts.
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