Quantum mechanics explains the physical stability of the atom by predicting its allowed discrete energy levels and defining the wave functions (also called atomic orbitals) associated with each energy level. The orbitals determine the probability density for finding the electrons at particular locations in the atom when the electrons are in a specific quantum state.

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.

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The conservation of matter in a chemical change is represented in a balanced chemical equation for that process. The study of the relationships between the numbers of reactant and product mole­cules is called stoichiometry. Stoichiometry is fundamental to all as­pects of chemistry.

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<sub>A</sub>).

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The definite mass ratios involved in reactions suggested a convenient method for counting the number of atoms of each element participating in the reaction. These results, summarized as the laws of chemical combination,provided overwhelming, if indirect, evidence for the existence of atoms and molecules.

Investigating chemical reactions can be greatly complicated and often obscured by the presence of extraneous materials. So, the first step, therefore, is to learn how to analyze and classify materials to ensure that you are working with pure substances before initiating any reactions.

Upon encountering a new topic, try this: imagine that you are the first person ever to see the laboratory results on which it is based. Imagine that you must construct the new concepts and explanations to interpret these results, and that you will present and defend your conclusions before the scientific community. Be suspicious. Cross-check everything. Demand independent confirmations. Always remain, with Boyle, the “skeptical chemist.”