# 1.1: Breakdown of Electromagnetic Radiation

Spectroscopy is the study of the interaction of radiation with matter. We know that radiation of frequency υ consists of photons whose energy is given by Planck’s law: $$E = hv$$. Where, $$h$$ is Planck’s constant = $$6.626068 \times 10^{-34} \;m^2 kg/s$$. The speed of the electromagnetic radiation in vacuum is $$c$$, which is equal to 299,792,458 m/s. Since $$c = \lambda{v}$$, the original equation can be written in the following two alternate forms:

$$E = \dfrac{hc}{\lambda} = hcv$$ or $$v = \dfrac{1}{\lambda}$$.

Where, $$1/\lambda$$ is the inverse wavelength or wavenumber (cm-1). The effect that a photon will have on matter or molecule will depend on $$E$$, and thus on $$v$$.

• For $$v$$ < 10-2 cm-1 (λ ~ 1m), we have radio frequencies. These are too low an energy photons for anything except to affect the magnetic energy of a nucleus in an external magnetic field (NMR Spectroscopy)
• For 10-2 cm-1 < $$v$$ < 10 cm-1 (λ ~ 1 cm ), we have microwave frequencies. Photons have enough energy to be absorbed by unpaired electrons spins in an externally magnetic field (ESR) or to change the rotational energy of a molecule (microwave rotational spectroscopy)
• For 10 cm-1 < $$v$$ < 10 cm4 (λ ~ 5 μm ), we have infrared frequencies. Photons have sufficient energy to be absorbed in the rotational motion of the molecules. This is called vibrational spectroscopy.
• For 10-2 cm-1 < $$v$$ < 10 cm5 (λ < 1 μm ), we have visible and UV spectroscopy which involves excitations of electrons (valence) from stable orbits to higher energy orbits in the molecule. Electronic spectroscopy (UV-VIS)
• For 105 cm-1 < $$v$$ < 10 cm6, we have vacuum UV, where the photons have enough energy that if absorbed by a valence electron, the electron can be “knocked” out of the molecule. This is called photoelectron spectroscopy
• For 106 cm-1 < $$v$$ < 10 cm8, these are X-rays and have enough energy to ionize not only valence electrons, but also core electrons. This spectroscopy is call X-ray Photo-electron spectroscopy (XPS) and also Extended X-ray absorption fine structure (EXAFS) and X-ray Absorption Near Edge Structure (XANES).
• For $$v$$ < 10 cm8. These are very energetic gamma rays and are not used extensitvely for spectroscopy with chemists. One key exception is Mössbauer spectroscopy which is enough energy to promote changes in the nuclei of the atoms.