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Spectroscopy is a general term used within analytical chemistry and some branches of physics that encompasses a wide range of analytical techniques involving probing atoms and molecules with radiation and seeing how they interact. In general, a molecule, part of a molecule or an individual atom can absorb, emit or transmit certain frequencies of radiation within the electromagnetic spectrum. The frequencies that are absorbed or transmitted can then give information on the structure and identity of sample being examined. This is important as it is impossible to "see" atoms and molecules with the light visible to the human eye.
The scale and use of spectroscopic techniques is huge and can be even used to obtain the chemical composition of stars and planets that are light years away and with more accurate, powerful and high resolution equipment it can be used in aspects of molecular biology.
 How it works
Atoms and molecules, which follow the laws of quantum mechanics, are restricted to only certain energy levels. Almost like bookshelves where each shelf is an energy level and each molecule is a book; you can only place books on the shelves rather than between them and some shelves can hold only a certain number of books. A particular amount of energy is required to lift an atom or molecule from one energy level to another, this is known as a transition. If there is too much or too little energy, the transition does not occur, but with just the right amount of energy, the transition will occur.
 Types of Spectroscopy by energy level
The electromagnetic spectrum stretches from low energy (low frequency) radio waves to high energy (high frequency) X-rays or gamma rays. Different levels of energy have different effects on atoms and molecules, for example lower energies affect only molecular vibrations, higher energies directly affect electrons. As such, types of spectroscopy can be ordered according to the energy levels that they probe. That's not to say that higher is better, of course, thorough chemical analysis requires the full range of the spectrum to be used.
 Radio waves
Radio waves are very low in energy when compared to the rest of the electromagnetic spectrum. In spectroscopy, this energy level is used in nuclear magnetic resonance (NMR) to cause transitions between magnetic energy levels within the nucleus of the atom. This type of spectroscopy is very useful to organic chemists.
Rotational energy levels are caused by the molecule under examination rotating at specific energies — giving a molecule a small amount of energy causes it to rotate faster, although there are a few added complications due to quantum mechanics. Microwaves have energy that corresponds to these rotational energy levels. This can give information about a molecule's structure, such as its rotational constant, which can give some information about mass. While microwave energy can be used directly to observe this, in practice these levels are most often viewed as part of rotational fine structure within Infrared spectroscopy. This is where IR radiation is applied but has just enough energy to boost the molecule into a higher rotational state too, because it probes vibrations and rotations it is sometimes referred to as rovibrational spectroscopy.
 Infrared radiation
The chemical bonds within molecules vibrate at certain energy levels — analogous to balls attached by springs vibrating. As a molecule takes in energy, it vibrates faster and moves up to a higher energy level. Transitions between these levels require similar energy to that found in the infrared region of the electromagnetic spectrum. IR spectroscopy is therefore most frequently used to determine information on the nature of chemical bonds such as their strength and length. Because these properties are related to mass, vibrational spectroscopy can be used to identify different atomic isotopes; the rovibrational spectrum of HCl, for example, contains two bands that overlap, but are distinct and high enough resolution, one corresponding to 35Cl and the other to the heavier 37Cl. Exchanging the proton (1H) for deuterium (2H) has a more pronounced effect as deuterium is twice as heavy.
Raman spectroscopy is a common variant on normal infrared spectroscopy which is also used to study the vibrations within molecules. It is used in conjunction with IR spectroscopy as the absorption peaks that don't appear in one method will appear in the other, however its mechanism is different. In Raman spectroscopy, the sample is irradiated with a laser in the IR region of the electromagnetic spectrum and the scattering of the light is detected.
 Visible light
The visible region of the electromagnetic spectrum is a minute range that overlaps the vibrational (infrared) and the electronic (ultraviolet) energy levels. Light absorbed in this region is responsible for giving colour to items in the real world. Single atoms in the gas phase often absorb finely in this region. This has an important application in astronomy where fine absorption lines in the spectrum of star light are used to identify the composition of the star. Because these lines are fine (atomic absorption is perhaps the least complex) they shift due to the Doppler Effect — the resulting information can be used to calculate the distance to the star, among other properties such as its wobble, which can be used to detect exoplanets.
 Ultraviolet light
UV light is high in energy, high enough to excite the electrons within a molecule, moving them from one molecular or atomic orbital to another. This method generally produces very broad absorption peaks but is very useful for determining concentrations. If the light in this region is strong enough, it may kick electrons out of the molecule entirely, ionising it or turning it into a highly reactive radical. When done deliberately, it is known as photo-initiation, kick-starting a chemical reaction using light rather than heat.
X-Rays are primarily used in diffraction experiments to determine the crystal structure (crystallography) but absorption techniques do exist. In the case of x-ray energy, core electrons, rather than valence electrons as in UV spectroscopy, are excited.
 Gamma rays
The impressively sci-fi sounding gamma rays are very high energy electromagnetic waves. This is a slightly more complex form of spectroscopy that involves nuclear transitions. Because it is most efficient for the source and target of the gamma rays to be the same, only a few substances can be successfully used with this method.