Sodium atom energy levels

For atomic (gas) sodium (Na), the electronic configuration is ls 2s 2p 3s, leading to filled electronic energy levels Is, 2s and 2p, while the 3s level is half-filled. The other excited levels, 3p, 4s..., are empty. In the solid state (the left-hand side in Figure 4.6), these atomic energy levels are shifted and split into energy bands bands Is, 2s and 2p are fully occupied, while the 3s (/ = 0) band, the conduction band, is half-filled, so that a large number N 21 + l)/2 = N/2) of empty 3s excited levels is still available. As a result, electrons are easily excited into empty levels by an applied electric field, and so become free electrons. This aspect confers the typical metallic character to solid sodium. 

Secondly, we examined the mechanism of element-selective corrosion of austenitic stainless steels in liquid sodium. We performed calculations for a system where an 0 impurity atom accompanying Na atom approaches Or atom at an Fe(OOl) surface exposed to liquid sodium. The energy levels attributed to the Cr 3d orbitals are located above the Fermi level, while the energy levels originated from the 0 2p orbitals are below the Fermi level. Furthermore, the level for the Na 3s orbital is above the Fermi level. By the energy differences of these orbitals, the Cr atom is charged positively, while an 0 atom accompa-... 

Fig. 1. Atomic energy level diagram for the sodium atom. (Reprinted with permission from Ref. [3].)...

The list is not yet complete. Spectrum lines may exhibit what is termed fine structure. They consist not always of singlets , but of doublets , triplets , and higher multiplets . The fairly close pair represented by the yellow D lines of sodium is the most familiar example. Evidently, then, there exists some further factor, variation in which causes the rather delicate shifts in the atomic energy levels. Different values of this unknown factor will be denoted by different values of a quantum number r. 

In two and three dimensions a similar process occurs. The atomic energy levels of each of the atoms of, for example, elemental sodium are broadened into bands in the solid. The width of these bands depends upon the magnitude of the corresponding interaction integrals (the equivalent of the Hiickel for the pn one-dimensional chain above) between the orbitals concerned. Figure 13.1 shows how... 

The saturation of the absorption. Roughly speaking, saturation of the absorption occurs when each of the sodium atoms in a column of section equal to the cross section of the D2 transition have absorbed a photon per time interval equal to the hfetime of the upper energy level. There is not so much sodium in the mesosphere ( 1 metric ton all around the Earth). Thus, in spite of the relatively high cross section of the 3S i/2 3P3/2 transition, saturation occurs at a quite low level, ... 

Figure 20. Energy levels of neutral sodium atom mostly involved in the resonant incoherent 2-photon excitation for the polychromatic LGS. Wavelengths (nm), lifetimes (ns) and homogeneous widths (MHz).

The colors of fireworks displays are produced by emission from atomic ions as described in Chapter 7. The explosions of fireworks promote electrons to excited states. The energy level scheme of every element is different, so fireworks manufacturers can change colors by incorporating different elements. Sodium ions emit... 

Atomic spectra are much simpler than the corresponding molecular spectra, because there are no vibrational and rotational states. Moreover, spectral transitions in absorption or emission are not possible between all the numerous energy levels of an atom, but only according to selection rules. As a result, emission spectra are rather simple, with up to a few hundred lines. For example, absorption and emission spectra for sodium consist of some 40 peaks for elements with several outer electrons, absorption spectra may be much more complex and consist of hundreds of peaks. 

Unfortunately, the Schrodinger equation for multi-electron atoms and, for that matter, all molecules cannot be solved exactly and does not lead to an analogous expression to Equation 4.5 for the quantised energy levels. Even for simple atoms such as sodium the number of interactions between the particles increases rapidly. Sodium contains 11 electrons and so the correct quantum mechanical description of the atom has to include 11 nucleus-electron interactions, 55 electron-electron repulsion interactions and the correct description of the kinetic energy of the nucleus and the electrons - a further 12 terms in the Hamiltonian. The analysis of many-electron atomic spectra is complicated and beyond the scope of this book, but it was one such analysis performed by Sir Norman Lockyer that led to the discovery of helium on the Sun before it was discovered on the Earth. 

Energy level diagram of the sodium atom. The energy levels are denoted by the values for the principal quantum number , the orbital quantum number/, and the spin quantum number s. Levels with 1 = 0 are not split for / = 1 two separate levels are drawn (s = 1/2) for/> 1 the splitting is too small to be shown in the figure. Wavelengths of a few special transitions are given in nanometers. 

Energy level diagrams for the easily excited atomic lines of lithium, sodium, potassium and rubidium. Wavelengths are given in nanometres for the spectral lines produced by transitions between the different levels. The ionization potential is indicated by the dashed line above the respective diagrams. 

The most commonly observed line emission arises from excitation of atomic electrons to higher level by an energy source. The energy emitted by excited atoms of this kind occurs at wavelengths corresponding to the energy level difference. Since these levels are characteristic for the element involved, the emission wavelength can be characteristic for the element involved. Sodium and potassium produce different line spectra. 

If an electron is removed from an inner energy level of one of the heavier elements (in practice, with an atomic number greater than sodium), a vacancy or hole is produced in the electronic structure. This is an unstable arrangement, and two competing processes act to rectify this ... 

Ions, like atoms, have size. For ions, the term is ionic radii. For cations, the loss of electrons results in a decrease in size, since (for the representative metals) an entire energy level is usually lost. A sodium ion, Na+, is smaller than a sodium atom. The greater the number of electrons removed, the greater the decrease in radius. This applies to any element and its cations as illustrated by the trend in radii of Fe > Fe2+ > Fe3+. 

A sodium atom with only one electron in its outermost energy level would achieve a lower energy state if this electron were released to the chlorine atom, which would also achieve a lower energy state as a result. Both atoms would become ions (Na+ and Cl ), and each would have a stable, filled outermost energy level identical with those of the noble gases, neon in the case of sodium and argon in the case of chlorine. Thus, the electron transfer does take place and sodium chloride, NaCl, is formed. 

FIGURE 7.9 The electronic energy transitions for gaseous sodium atoms. There are two slightly different transitions between the same two levels because of the effect of two spin states that differ slightly in energy. 

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