Electronic energy levels of atoms

Whereas the gas lasers described use energy levels characteristic of individual atoms or ions, laser operation can also employ molecular energy levels. Molecular levels may correspond to vibrations and rotations, in contrast to the electronic energy levels of atomic and ionic species. The energies associated with vibrations and rotations tend to be lower than those of electronic transitions thus the output wavelengths of the molecular lasers tend to He farther into the infrared. 

PES is also useful for studying the electron energy levels of atoms. Usually PES is used to analyze for the presence of specific elements in samples by identil g known binding energies. For example, the Oij electrons occur in the PES spectrum at 530 eV and Cij appears at 285 eV. However, we can imagine an idealized schematic PES spectrum of an element such as phosphorus shown in Fig. 9.50. Because the actual spectrum is very complex and hard for a non-expert to interpret, we have represented the data from the PES spectrum in a very simple manner. Note that the area of each peak is proportional to the number of electrons that have that particular energy. 

A typical x-ray photoelectron spectmm consists of a plot of the iatensity of photoelectrons as a function of electron E or Ej A sample is shown ia Figure 8 for Ag (21). In this spectmm, discrete photoelectron responses from the cote and valence electron energy levels of the Ag atoms ate observed. These electrons ate superimposed on a significant background from the Bremsstrahlung radiation inherent ia n onm on ochrom a tic x-ray sources (see below) which produces an increa sing number of photoelectrons as decreases. Also observed ia the spectmm ate lines due to x-ray excited Auger electrons. 

The lines of primary interest ia an xps spectmm ate those reflecting photoelectrons from cote electron energy levels of the surface atoms. These ate labeled ia Figure 8 for the Ag 3, 3p, and 3t7 electrons. The sensitivity of xps toward certain elements, and hence the surface sensitivity attainable for these elements, is dependent upon intrinsic properties of the photoelectron lines observed. The parameter governing the relative iatensities of these cote level peaks is the photoionization cross-section, (. This parameter describes the relative efficiency of the photoionization process for each cote electron as a function of element atomic number. Obviously, the photoionization efficiency is not the same for electrons from the same cote level of all elements. This difference results ia variable surface sensitivity for elements even though the same cote level electrons may be monitored. 

Figure 1 (a) Schematic representation of the electronic energy levels of a C atom and... 

Table 10.3 Electronic energy levels of some common molecules or atoms with unpaired...

Figure 10.5 Energy levels of atomic orbitals, n is the principal quantum number, and the 5, p, d notation indicates the azimuthal quantum number (/). For / = 1 and above the orbital is split into multiple suborbitals (indicated by the number of lines), corresponding to the values of the magnetic quantum number m Each of these lines can hold two electrons (corresponding to spin up and spin down ), giving rise to the rules for filling up the orbitals.

Erwin Schrodinger developed an equation to describe the electron in the hydrogen atom as having both wavelike and particle-like behaviour. Solution of the Schrodinger wave equation by application of the so-called quantum mechanics or wave mechanics shows that electronic energy levels within atoms are quantised that is, only certain specific electronic energy levels are allowed. 

In gases (atomic or ionic) the electronic energy levels of free atoms are narrow, since they are diluted systems and perturbation by the surroundings is very weak. An important fact derived from the discrete nature of the electronic levels in a gas is the high monochromaticity of the laser lines in this type of laser, compared to that of solid-medium based lasers. The high degree of coherence achievable with gas lasers is also a characteristic feature related to the narrow linewidth. 

According to quantum mechanics, electrons in atoms occupy the allowed energy levels of atomic orbitals that are described by four quantum numbers the principal, the azimuthal, the magnetic, and the spin quantum numbers. The orbitals are usually expressed by the principal quantum numbers 1, 2, 3, —increasing from the lowest level, and the azimuthal quantum numbers conventionally eiqiressed by s (sharp), p (principal), d (diffuse), f (fundamental), — in order. For instance, the atom of oxygen with 8 electrons is described by (Is) (2s) (2p), where the superscript indicates the munber of electrons occupying the orbitals, as shown in Fig. 2-1. 

Fig. 6-4. Electron energy levels of an adsorbate particle broadened by interaction with adsorbent metal crystal M adsorbent metal R = atomic adsorbate particle = adsorbed particle W= probability density of electron energy states x = distance to adsorbate particle, xq = distance to adsorbed particle.

Atomic emission spectroscopy is one of the oldest instrumental techniques used for chemical analysis. It is used to study the transitions between electronic energy levels in atoms or ions. These energy differences are usually in the visible region (400-700 nm) of the electromagnetic spectrum, but if the energy difference is larger, then the transitions may lie in the ultraviolet region. 

We have used the electronic energy levels for atomic hydrogen to serve as a model for other atoms. In a similar way, we can use the interaction of two hydrogen atoms giving the hydrogen molecule as a model for bonding between other atoms. In its simplest form, we can consider the bond between... 

As we have seen in Chapter 11, the energy levels of atoms and ions, depending on the relative role of various intra-atomic interactions, are classified with the quantum numbers of different coupling schemes (11.2)— (11.5) or their combinations. Therefore, when calculating electron transition quantities, the accuracy of the coupling scheme must be accounted for. The latter in some cases may be different for initial and final configurations. Then the selection rules for electronic transitions are also different. That is why in Part 6 we presented expressions for matrix elements of electric multipole (Ek) transitions for various coupling schemes. 

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