Absorption and emission spectrum

Question

I was wondering how do you see a spectrum when light is passed through a substance. Like most of the substances we use are opaque, so how does light pass through them without being reflected? Also why do we see a spectrum and not a single colour?

Answer 1

If the substance is opaque you need a very tiny amount of it to get an absorption spectrum in its absorbing region. Otherwise we would just block the detector from the light completely and see nothing. Typically, however, materials will have regions they strongly absorb in and regions where they do not. For instance, using plastic cuvettes to do UV-Vis spectroscopy can cause issues when the interesting absorption bands of the plastic match those of the sample. In that case, a quartz cuvette is often employed instead to avoid this overlap. Of course, different samples can also overlap with each other, which can make disentangling a spectrum more difficult.

The details of exactly what bands of frequencies are absorbed is the purview of quantum mechanics. The first factor is the presence of quantized energy levels that are found by solving the Schrödinger equation. This can range from relatively easy for, e.g. the harmonic approximation of the vibrational bands of a diatomic molecular gas, to incredibly complex, like disordered solids and complex materials with many constituents. The second part is the intensity. The intensity of radiation absorption is directly related to the probability that a transition can actually occur. This is most often treated using Fermi’s Golden Rule of time dependent perturbation theory. The rule simply states that the transition probability is proportional to the square of the transition dipole moment integral. This leads to what are called selection rules, or rules for what quantum transitions are intense enough to be observed. It is these intense absorbing bands that we observe in a spectrum. Fermi’s Golden Rule also shows why the only frequencies of light that cause transitions are those that match the gaps between quantized energy states in matter. The process of modeling spectroscopy can become extremely involved for complicated systems, and many elaborate models and approximations have been developed depending on the types of systems you are interested in. Without more details, I can only speak this generally.