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Comments re Chapter 21 Problems:

21-2	A short exercise involving wavelength, frequency, and wavenumber.
21-4	A set of true/false questions about spectroscopy. Levine's true/false questions are often not so easy, but they are always informative.
21-7	An short exercise based on the harmonic oscillator. There is (at most) one important line per vibration in the (low-resolution) vibrational spectrum of a molecule. If the molecule is diatomic there will be one line if the molecule has at least a small dipole moment and no line if the two atoms are the same.
21-8	A problem that demonstrates how the transition moment for a harmonic oscillator is calculated. The wave functions are given in Fig. 18.18 and the needed formulae for integrals are shown in Table 15-1. Two of the integrals are zero - one because it is odd around the middle of the integration interval, and the other because the terms cancel. When working out the integrals it will save time to leave the normalization constants as symbols (e.g., A0) until the end. This problem is not as short as some of the others, but it is very instructive.
21-9	A short exercise that demonstrates how wavelengths for two transitions should be combined to get the wavelength for a comination of the transitions. Straight addition doesn't work because it is energies that can be added and because wavelength is not directly proportional to energy.
21-10	A made-up problem that involves using a known frequency and the formula for the energies of the levels to determine the value of a related frequency.
21-11	Calculate frequencies for transitions of a particle in a 1-D box. For these transitions Dn (the change in the quantum number) must be odd. This problem (like many spectroscopy problems) is also an advanced exercise in cancelling units.
21-12	This problem emphasizes finding the difference in energy between two energy levels. This kind of problem occurs within lots of other problems.
21-13	Another problem in which finding the energy difference between two levels is important. The formula is then used in a ratio problem.
21-20	Another of Levine's true/false problems. It is important to understand that he makes very fine distinctions and uses language very exactly. Parts (e), (f), and (g) concern material that will not be covered in detail; these parts of problem 21-20 are therefore optional.
21-21	Yet another true/false problem.
21-25	Energy-level differences again. This time the formula is used to predict the wavelength of one transition given the wavelength of a different transition.
21-26	The wavelength of a pure rotational transition is used to calculate the moment of inertia of a diatomic molecule and then the bond length. Note the very great precision with which the wavelengths can be measured. Because the wavelengths are known so precisely it is necessary to use as many significant digits as are available for the fundamental constants and to treat molecules composed of different isotopes separately.

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