7 Quantum Mechanics: Concepts7must change sign. Thus, two electrons in the same atom cannot have an identical set of values for the four quantum numbers n, l, m, ms. The exclusion principle forms the basis of many properties of matter, including the periodic classiation of the elements, the nature of chemical bonds, and the behaviour of electrons in solids; the last determines in turn whether a solid is a metal, insulator, or semiconductor. For example, the Pauli exclusion principle leads to the simplid description of the structure of atoms that was st proposed by the physicists J. Hans D. Jensen and Maria Goeppert Mayer working independently in 1949. In this model, electrons in atoms are thought of as occupying diffuse shells in the space surrounding a dense, positively charged nucleus. The st shell is closest to the nucleus. The others extend outward from the nucleus and overlap one another. The shells are sometimes designated by capital letters beginning with K for the st shell, L for the second, M for the third, and so forth through Q for the seventh shell. The maximum number of electrons that can occupy shells one through seven are, in sequence, 2, 8, 18, 32, 50, 72, 98. The lightest element, hydrogen, has one electron in the st shell. The heaviest elements in their normal states have only the st four shells fully occupied with electrons and the next three shells partially occupied. In terms of a more reed, quantum-mechanical model, the K換 shells are subdivided into a set of orbitals, each of which can be occupied by no more than a pair of electrons. Atomic orbitals are commonly designated by a combination of numerals and letters that represent speci properties of the electrons associated with the orbitals�for example, 1s, 2p, 3d, 4f. The numerals, called principal quantum numbers, indicate energy levels as well as relative distance from the nucleus. A 1s electron occupies the energy level nearest the nucleus. A 2s electron, less71
