- An atom is a kind of object
- Structure is a property of an object
- Therefore, structure of an atom is a property of the atom

- Structure of an atom is a property of the atom
- Organizing is sorting things in order by their properties
- Therefore, structure of atoms can be used to organize atoms in order

- Structure of atoms can be used to organize atoms in order
- Atoms of different elements have different structures
- So, structure of atoms of different elements can be used to organize atoms of different elements

Therefore, structure of atoms of different elements can be used to organize atoms of different elements
The periodic table of the elements is systematically organized according to the
- An atom is a kind of object 
- Atoms of different elements have different structures 
- Organizing is sorting things in order by their properties 
- Structure is a property of an object