Single-frequency absorption

In this section we will discuss more conventional spectroscopies absorption, emission and resonance Raman scattering. These spectroscopies are generally measured under single frequency conditions, and therefore our... 

From the description thus far, you might expect all 1H nuclei in a molecule to absorb energy at the same frequency and all 13C nuclei to absorb at the same frequency. If so, we would observe only a single NMR absorption band in the H or 13C spectrum of a molecule, a situation that would be of little use. In fact, the absorption frequency is not the same for all 4H or all 13C nuclei. 

Except in simple cases, it is very difficult to predict the infrared absorption spectrum of a polyatomic molecule, because each of the modes has its characteristic absorption frequency rather than just the single frequency of a diatomic molecule. However, certain groups, such as a benzene ring or a carbonyl group, have characteristic frequencies, and their presence can often be detected in a spectrum. Thus, an infrared spectrum can be used to identify the species present in a sample by looking for the characteristic absorption bands associated with various groups. An example and its analysis is shown in Fig. 3. 

The four structures with three double bonds (third row) and the one with four double bonds are the most plausible Lewis structures, (b) The structure with four double bonds fits these observations best, (c) +7 the structure with all single bonds fits this criterion best, (d) Approaches (a) and (b) are consistent but approach (c) is not. This result is reasonable because oxidation numbers are assigned by assuming ionic bonding. 2.109 The alkyne group has the stiffer C—H bond because a large force constant, k, results in a higher-frequency absorption. 

Let the effective loss coefficient now include, in addition to intrinsic loss, a contribution due to absorption (and scattering) by the analyte contained in the evanescent fraction/of the WGM y = yx +/xa. The effect of the analyte on the resonant (single-frequency) drop signal D0a, when analyte absorption is a small fraction of the total loss, can be written in terms of an approximate effective absorption path length Leff as defined below ... 

Let us consider a laser oscillating at a single frequency (single-mode operation) and gas molecules inside the laser resonator which have absorption transitions at this frequency. Some of the molecules will be pumped by the laser-light into an excited state. If the relaxation processes (spontaneous emission and collisional relaxation) are slower than the excitation rate, the ground state will be partly depleted and the absorption therefore decreases with increasing laser intensity. 

Therefore, neglecting the first term, the probability of absorption per unit time is given by the product dtn(t)am t) and fora single frequency we obtain... 

Equation (8.23) is for gN positive for gN negative, a minus sign must be added.] Although there are 2/+1 nuclear-spin energy levels, they are equally spaced, and the selection rule allows only transitions between adjacent levels hence we get a single NMR absorption frequency. 

Most measurements of the optical rotation are carried out at a single frequency, usually corresponding to the sodium D-line. However, studies of the variation of the optical rotation with the frequency of the incident light are also known, and are referred to as optical rotatory dispersion (ORD) [7], Historically, this was an important method for the determination of excitation energies in chiral molecules, but was later superseded by CD. We note that the calculation of ORD through regions of electronic absorption requires special care [27,28],... 

---