Spectroscopy is, in general terms, the study of the interaction of electromagnetic radiation with matter.
Since the energy of individual particles is quantised (restricted to discrete values), it follows that the energies of the molecules which make up matter are also quantised. This means that there must be fixed separations between the energy levels of a molecule.
Transitions between energy levels separated by an energy ΔE can be made to occur if the molecule absorbs a photon of equal energy. i.e. absorption of a photon can excite a molecule from its current quantum state to one of higher energy, providing that the energy separation between the states is exactly equal to the energy of the photon. The energy of a photon is given by E = hν, so the requirement for a transition to occur is:
Thus a molecule will only absorb radiation of certain discrete frequencies that correspond to the energies of transitions between different quantum states of the molecule.
This acts as a kind of fingerprint for the molecule, as the energy levels in a molecule (and hence the differences between them) depend upon the molecule. The frequency that corresponds to the energy of a given transition is called the frequency of that transition or the transition frequency.
The process described above, of observing the frequencies at which absorption occurs, is absorption spectroscopy. Another process which is effectively the reverse of this is emission spectroscopy, in which a sample is irradiated to excite all the molecules. As the molecules fall back down in energy to their ground state, they emit photons of frequencies corresponding to the differences between energy levels.
This form of spectroscopy is widely used in studies of rotational and vibrational energy levels, but may well be unfamiliar.
It relies upon the inelastic scattering of photons when they interact with the molecules of a substance.
The incident photons may lose some of their energy when they collide with the atoms or molecules of the sample, in which case they will emerge with a lower frequency than that of the incident radiation. This is called the Stokes radiation from the sample.
Alternatively, assuming that some of the molecules in the sample are in an excited state, they may give up some of their energy to the photons in a collision. Such photons would emerge with a higher energy (higher frequency) than the incident radiation. This is known as the anti-Stokes radiation.
Naturally, some radiation passes through the sample without being scattered at all – this is called Rayleigh radiation, and emerges at the same frequency as the incident radiation.