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Physical atoms refer to the bits and pieces which make up the atom (like protons and neutrons), the forces which hold or change their positions in space (like covalent bonding) and the bulk properties which follow (such as melting point). Chemical atoms refers to the manner in which different elements relate and the new substances formed by their union.
The distinction between these two ideas is due to Jean-Baptiste Dumas, who, in 1837, wrote:
"I find in Lewis the story of a demon who abducts a young lady and who, hoping to win her good graces, pledges to obey her first three orders: 'Show me,' said she, 'the most sincere of all lovers.' He complied promptly. 'Very well,' she continued, 'but now show me an even more sincere one.' The demon was taken aback. 'What would have happened had the lady been under the control of he who can show us an atom, and then divide it into two? He would have experienced no qualm producing the most sincere lover, followed by a more sincere still.' Mr. Griffins failed to understand that I had carefully distinguished between atoms relative to physical forces and atoms relative to chemical forces; that is to say, indivisible masses for the former, and other indivisible masses for the latter. It is thus possible to divide with one type of force that which resists the other type. In the case of chlorine and hydrogen, chemistry dissociated atoms that physics could not dissociate. That sums it all up."
Alan J. Rocke (in modern times) defines the chemical atomic theory thus (his original is in italics):
". . . there exists for each element a unique 'atomic weight', a chemically indivisible unit, that enters into combination with similar units of other element in small integral multiples."
Please note two points:
1) the concept of isotopes is ignored. Obviously, isotopes are important, but not to this discussion.
2) "chemically indivisible unit." A atom of oxygen will remain as an atom of oxygen throughout its chemical reactions. Sure, you can blow it apart, destoying the atom of oxygen, but the point, chemically, is that it then becomes something else.
In our era, "chemical atomism" means we study how and why atoms unite together to form molecules. The subject of how much an atom weighs is also the province of chemical atomism. "Physical atomism" studies the structure of individual atoms and how atoms stay together.
In Dumas' day there was confusion about the term "atom" and "molecule." Today, we associate "atom" with "element," but in the early 1800's, "atom" could also mean the basic unit of a "compound," whereas today we associate only the word "molecule" with "compound."
Dalton's theory is ultimately one of chemical atoms, joining together in small integer ratios. He says nothing worthwhile about the inside structure of the atom or the forces binding them. These discussions of physical atomism commenced in a modern way in 1897, well after Dalton had passed away.
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