Spectroscopy and the structure of matter

The observation of atomic spectra stimulated physicists in the early 19th century to develop the theory of quantum mechanics. This theory sets out to explain all physical phenomena at an atomic scale and atomic spectroscopy is an important validation. Quantum mechanics is flawed, however, notably in the description of gravity, but it is the best theory at present (although super string theory promises well) for the description of the structure of nuclei, atoms and molecules. 

Astrochemistry from astronomy to astrobiology. Andrew M. Shaw 2006 John Wiley Sons, Ltd 

The absorption of the radiation has been found empirically to increase so that a longer sample absorbs more light, as does a more concentrated sample, and it is found to vary exponentially  

Some simple rearrangement of Equation 3.1 leads to the concepts of transmission T = Io/1 and absorbance A = — log T, with the quantity s c l called the optical density. The choice of units here for the extinction coefficient (M-1 cm-1) is appropriate for measurement of the absorbance of a solution in the laboratory but not so appropriate for a distance Z of astronomical proportions. The two terms and c are contracted to form the absorption per centimetre, a, or, more conveniently (confusingly) in astronomy, per parsec. The intrinsic ability of a molecule or atom to absorb light is described by the extinction coefficient s, and this can be calculated directly from the wavefunction using quantum mechanics, although the calculation is hard. 

The extinction towards a star at 450 nm is 0.24 and is attributed to an interstellar cloud containing dust particles with an extinction coefficient of 0.0032 pc-1. Calculate the diameter of the intervening molecular cloud, expressing your answer in light-years. 

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