Abstract
Matter is composed of electrons and nuclei. Their movements, governed by quantum mechanics, involves typicallength scales in the order of 100 pm, and typical energies in the order of \(10^{-18}\,\text {J}\). Electrons tend to lump around nuclei, and keep them bound together. The quite fast movements of electrons and the slower ones of the nuclei can be probed by letting them interact with electromagnetic fields, through spectroscopies.
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Notes
- 1.
The transmitted intensity \(I(\omega )\) can be converted into an absorption coefficient \(\alpha (\omega )\) by inverting the Beer-Lambert attenuation law \(I/I_0 = \exp (-\alpha \, l\, N/V)\). Here \(I_0\) is the original radiation intensity, \(l\) is the probed sample thickness, and \(N/V\) is the number density of absorbing atoms/molecules.
- 2.
The total decay rate \(\gamma \) is the sum of the rates of decay to all lower-lying states. For example, as described in Sect. 2.1.9, the 3p state of H decays at a rate \(\gamma _{\mathrm{3p}\rightarrow \mathrm{1s}} = 1.67\times 10^8\) s\(^{-1}\) to the ground state, and at a rate \(\gamma _{\mathrm{3p}\rightarrow \mathrm{2s}} = 2.25\times 10^7\) s\(^{-1}\) to the 2s state (decay to state 2p is dipole-forbidden, thus occurs at a negligible rate). Therefore the 3p state empties at a total rate \(\gamma _\mathrm{3p} = \gamma _{\mathrm{3p}\rightarrow \mathrm{1s}} + \gamma _{\mathrm{3p}\rightarrow \mathrm{2s}} = 1.90\times 10^8\) s\(^{-1}\).
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Manini, N. (2014). Introductory Concepts. In: Introduction to the Physics of Matter. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-14382-8_1
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DOI: https://doi.org/10.1007/978-3-319-14382-8_1
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