Quantum mechanics explains the physical stability of the atom by predicting its allowed discrete energy levels and defining the wave functions (also … - David W. Oxtoby

The central idea of quantum theory is that energy, like matter, is not continuous but it exists only in discrete packets. Discreteness of matter and charge on the microscopic scale seems entirely reasonable and familiar to us, based on the modern picture of atomic structure. But, the idea that energy also exists only in discrete chunks is contrary to our experience of the macroscopic world. The motions of a soccer ball rolling up and down the sides of a gully involve arbitrary amounts of kinetic and potential energy; nothing in ordinary human experience suggests that the energy of a system should change abruptly by “jumps.” Understanding quantum mechanics requires that we develop a new kind of physical intuition, based on the results of experiments that are impossible to understand using classical mechanics. These results are completely divorced from ordinary human experience in the macroscopic world around us, and our physical intuition from the macroscopic world cannot be transferred to the quantum domain. We must resist the urge to interpret these quantum results in terms of ordinary experience.

Laboratory or industrial chemical reactions are carried out with quantities that range from milligrams to tons, so we must be able to relate the relative atomic mass scale to the macroscopic scales used in practice. The link between the two scales is provided by Avogadro’s number (N_A).

Chemists think in the highly visual nanoscopic world of atoms and molecules, but they work in the tangible world of macroscopic laboratory apparatus. These two approaches to the chemical sciences cannot be divorced.