Now these are 2 different questions and will be answered thus in 2 parts.
Even before coming to the number of atoms, we first need to know WHAT atoms are in the compound. This was achieved by decomposing a compound into it’s constituent elements by extreme procedures such as – heating, burning, electrolysis etc. Once you know the constituent elements, finding the number is child’s play. You know the molar mass of the elements so find out the number of moles of elements found
eg. electrolysing 18 grams of water will give you 16 grams of oxygen and 2 grams of hydrogen. Since molar mass of oxygen atoms is 16 and hydrogen atoms is 1, we can
say there are 2 atoms of H for 1 atom of O, thus we reach H20
About the structure? I am sorry but I don’t think that’s ELI5-able. There is an entire branch of study for this known as ‘spectroscopy’. I had it as an elective in college. We had some 14-15 forms of spectroscopy in there and it was quite convoluted. It’s more technology than science. Let’s just say we use machines to observe them and draw conclusions from the findings. There is no unified spectroscopic method and which method to use depends totally on the properties of the compound – polar / non-polar , transparent / opaque , solid / liq / gas at room temperature , conductive/non-conductive etc.
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