Subshell energies

We compare our observed spectra with Tanabe-Sugano diagrams, such as Fig. 1 for octahedral d3 and tetrahedral d7 and Fig. 2 for octahedral d8 (and tetrahedral d2). The variable in this diagram is not an energy but the ratio A/B between the subshell energy difference A (called (Ei — E2) or 10 Dq by certain authors) and the Racah parameter of in-terelectronic repulsion B. Hence, a higher value of A/B does not necessarily mean a blue-shift of the absorption spectrum if B decreases, it may sometimes correspond to a red-shift. 

Fig. 6.1. Orbital subshell energy levels allow the chemist to figure out bonding of elements.

Note that in the scandium atom, unlike the hydrogen atom, the subshells for each n are spread apart in energy.Thus,the 2p energy is above the 2s. Similarly, the n = 3 subshells are spread to give the order 3s < 3p < 3d.The 3d subshell energy is now just below the 4s. (Values for this figure were calculated from theory by Charlotte F. Fischer, Vanderbilt University.)... 

Go to http //now.brookscole.com/ cracolice3e and click Chemistry Interactive for the module Atomic Subshell Energies. 

Fig. B.2. Schematic interpretation of electron configurations for d- and f-block atoms in the ground state, allowing for the intra-orbital repulsions and the trends in subshell energies... 

Absorption and emission of Cr(III) arises from the parity-forbidden electronic transitions in the 3d electronic shell. Crystal field split states of Cr(III) in octahedral symmetry are illustrated in the Tanabe-Sugano diagrams. The relative positions of the excited T2 and states depend on the crystal field strength (the subshell energy difference A = 10 Dq). In cases where DqIB <2.3 (low-field cases) Tj is the low state and the emission arises from the T2 to A2 spin-allowed transition. In the case of Dq/B > 2.3 (high field cases), the lowest state is E and the luminescence arises from the spin-forbidden transition from E to A2 characteristic for the R-line emission of ruby. The spin-allowed transitions are characterized by broad emission spectra and short lifetimes, contrary to the spin-forbidden emission from the E state (which sometimes is mixed with T, levels) with narrow band and long lifetimes. 

Filling up the 4/ orbital is a feature of the lanthanides. The 4/ and 5d orbitals are of similar energy so that occasionally, as in La, Ce and Gd, one electron goes into 5d rather than 4f. Similarly, in the actinides, Ac to No, the 5/ subshell is filled in competition with 6d. 

For atoms having an atomic number greater than 10, the electron filling the inner shell vacancy may come from one of several possible subshells, each at a different energy, resulting in families of characteristic X-ray energies, e.g., the Ka, P family, the La, P, y family, etc. 

The X-ray spectrum observed in PIXE depends on the occurrence of several processes in the specimen. An ion is slowed by small inelastic scatterings with the electrons of the material, and it s energy is continuously reduced as a frmction of depth (see also the articles on RBS and ERS, where this part of the process is identical). The probability of ionizii an atomic shell of an element at a given depth of the material is proportional to the product of the cross section for subshell ionization by the ion at the reduced energy, the fluorescence yield, and the concentration of the element at the depth. The probability for X-ray emission from the ionized subshell is given by the fluorescence yield. The escape of X rays from the specimen and their detection by the spectrometer are controlled by the photoelectric absorption processes in the material and the energy-dependent efficiency of the spectrometer. 

Consider now the solutions of the spherical potential well with a barrier at the center. Figure 14 shows how the energies of the subshells vary as a function of the ratio between the radius of the C o barrier Rc and the outer radius of the metal layer R ui- The subshells are labeled with n and /, where n is the principal quantum number used in nuclear physics denoting the number of extrema in the radial wave function, and / is the angular momentum quantum number. 

These are shown in Fig. 2.3 and illustrate most convincingly the various quantum shells and subshells described in the preceding section. The energy required to remove the I electron from an atom of hydrogen is 13.606 eV (i.e. 1312 kJ per mole of H atoms). This rises to 2372 kJ mol for He (Is-) since the positive charge on the helium nucleus is twice that of the... 

FIGURE 1.41 The relative energies of the shells, subshells, and orbitals in a many-electron atom. Each of the boxes can hold at most two electrons. Note the change in the order of energies of the 3d- and 4s-orbitals after Z = 20. 

We need to make another decision at carbon (Z = 6) does the sixth electron join the one already in the 2p-orbital or does it enter a different 2p-orbital (Remember, there are three p-orbitals in the subshell, all of the same energy.) To answer this question, we note that electrons are farther from each other and repel each other less when they occupy different p-orbitals than when they occupy the same orbital. So... 

Answer Boron loses an electron from a higher-energy subshell than beryllium does.]... 

In the d block, the energies of the (n — l )d-orbitals lie below those of the ns-orbitals. Therefore, the ws-electrons are lost first, followed by a variable number of (n — 1 )d-electrons. For example, to obtain the configuration of the Fe3+ ion, we start from the configuration of the Fe atom, which is [Ar]3d 64s2, and remove three electrons from it. The first two electrons removed are 4s-electrons. The third electron comes from the Id-subshell, giving [Ar 3d5. 

The second quantum number is called the angular momentum quantum number. It is designated by the letter f and can be thought of as representing a subshell within a principal energy... 

Energy Level, n Type of Subshell Number of Subshells... 

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