30.8 Quantum Numbers and Rules Physical characteristics that are quantized -such as energy, charge, and angular momentum are of such importance that names and symbols are given to them. The values of quantized entities are expressed in terms of quantum numbers, and the rules governing them are of the utmost importance in determining what nature is and does. This section covers some of the more mportant quantum numbers and rules-all of which apply in chemistry, material science, and far beyond the realm of atomic physics, where they were first discovered. Once again, we see how physics makes discoveries which enable other fields to grow. The energy states of bound systems are quantized, because the particle wavelength can fit into the bounds of the system in only certain ways. This was elaborated for the hydrogen atom, for which the allowed energies are expressed as E, x 1/n² , where n = 1, 2, 3, .. We define n to be the principal quantum number that labels the basic states of a system. The lowest-energy 1, the first excited state has n = 2, and so on. Thus the allowed values for the principal quantum number are n = 1, 2, 3, . state has n = (30.41)

30.8 Quantum Numbers and Rules Physical characteristics that are quantized -such as energy, charge, and angular momentum are of such importance that names and symbols are given to them. The values of quantized entities are expressed in terms of quantum numbers, and the rules governing them are of the utmost importance in determining what nature is and does. This section covers some of the more mportant quantum numbers and rules-all of which apply in chemistry, material science, and far beyond the realm of atomic physics, where they were first discovered. Once again, we see how physics makes discoveries which enable other fields to grow. The energy states of bound systems are quantized, because the particle wavelength can fit into the bounds of the system in only certain ways. This was elaborated for the hydrogen atom, for which the allowed energies are expressed as E, x 1/n² , where n = 1, 2, 3, .. We define n to be the principal quantum number that labels the basic states of a system. The lowest-energy 1, the first excited state has n = 2, and so on. Thus the allowed values for the principal quantum number are n = 1, 2, 3, . state has n = (30.41)