The excitation of electrons to higher energy states through absorption of visible and ultraviolet light (usually covering the range of wavelengths from \(200 \: \text{nm}\) to \(780 \: \text{nm}\)) is discussed in Sections 9-9 and 28-1 . We now will consider what happens on absorption of much shorter wavelength, more energetic, photons. When radiation of wavelengths on the order of \(120 \: \text{nm}\) is absorbed by a molecule of ethene, the excited state has just sufficient energy (about \(250 \: \text{kcal mol}^{-1}\)) to cause the most loosely bound electron to be ejected. With radiation of still shorter wavelength, such as the \(58.4 \: \text{nm}\) \(\left( 490 \: \text{kcal mol}^{-1} \right)\) provided by a helium discharge tube, these electrons will have, by the Einstein law, a kinetic energy of \(\left( 490 - 250 \right) = 240 \: \text{kcal mol}^{-1}\). More tightly bound electrons also can be ejected by \(58.4 \: \text{nm}\) radiation, and they will have kinetic energies \(E = h \nu - I\), in which \(h \nu\) is the energy of the absorbed radiation \(\left( 490 \: \text{kcal mol}^{-1} \right)\) and \(I\) is the ionization energy. If we know \(h \nu\) and measure the number of ejected electrons as a function of their kinetic energies, we can derive a spectrum that shows how the probability of excitation correlates with the ionization energy. Such spectra, called photoelectron spectra , are shown in Figure 27-10 for gaseous ethene, ethyne, and benzene and are quite individualistic. Considerable fine structure is observed as the consequence of a considerable spread in the vibrational levels of the excited state. Substitution and conjugation have substantial effects on ionization energies. We have mentioned how methyl groups are able by their electron-donating power to stabilize carbon cations more than hydrogens do (Section 8-7B). The same effect is very prominent in the ionization of alkenes, the lowest energy required to eject an electron from 1-butene being about \(11 \: \text{kcal mol}^{-1}\) greater than from cis - or trans -2-butene. The corresponding differences for 1-hexene and 2,3-dimethyl-2-butene are about \(27 \: \text{kcal mol}^{-1}\). Conjugation produces similar effects. The lowest energy required to eject an electron from 1,4-pentadiene with isolated double bonds is \(21 \: \text{kcal mol}^{-1}\) greater than for the isomeric 1,3-pentadiene with conjugated double bonds. Photoelectron spectroscopy also can be carried on with x rays as the source of excitation and in this form often is called "ESCA" (Electron Spectroscopy for Chemical Analysis). The x rays used have wavelengths on the order of \(0.9 \: \text{nm}\) \(\left( 32,000 \: \text{kcal mol}^{-1} \right)\) and the energies involved are more than ample to cause ejection of electrons form inner shells as well as from valence shells. An x-ray photoelectron spectrum of the carbon \(1s\) electrons of ethyl trifluoroethanoate is shown in Figure 27-11. This spectrum is extremely significant in that it shows four different peaks - one for each chemically different carbon present. What this means is that the energy required to eject a \(1s\) electron of carbon depends on the chemical state of the carbon. The energy range for this compound is fully \(185 \: \text{kcal mol}^{-1}\) of the approximately \(6700 \: \text{kcal mol}^{-1}\) required to eject a \(1s\) electron. This form of spectroscopy is especially well suited to the study of solid surfaces and is being used widely for the characterization of solid catalysts.