L-shell electrons

In these approximations for the K series the value 1 is subtracted from the atomic number Z to correct for the screening of the nuclei by the remaining K-shell electron. For the L series the screening effect of the two K-shell electrons and the seven remaining L-shell electrons must be taken into consideration by subtracting 7.4. 

Carbon has six electrons around the atomic core as shown in Fig. 2. Among them two electrons are in the K-shell being the closest position from the centre of atom, and the residual four electrons in the L-shell. TTie former is the Is state and the latter are divided into two states, 2s and 2p. The chemical bonding between neighbouring carbon atoms is undertaken by the L-shell electrons. Three types of chemical bonds in carbon are single bond contributed from one 2s electron and three 2p electrons to be cited as sp bonding, double bond as sp and triple bond as sp from the hybridised atomic-orbital model. 

Fig. 7.16. Binding energies of (a) K shell electrons and (b) L shell electrons as a function of atomic number. The graphs were constructed from data tabulated in Ref. [56].

Figure 5.1 The X-ray emission and Auger processes (Pollard and Heron 1996 37). An inner shell vacancy is created in the K shell by the photoelectric process (emitted photoelectron not shown), (a) shows the X-ray emission process, where an L shell electron drops down to fill the vacancy, and the excess energy (EK - EL) is carried away as an X-ray photon. In (b), an L shell electron drops down, but the excess energy is carried away by an Auger electron emitted from the M shell, with kinetic energy approximately equal to EK - EL — EM. Reproduced by permission of the Royal Society of Chemistry.

An important feature of SC AP is that in regions of level energies for which the condition e, -A. yo is fulfilled, the occupation numbers n,- 1 (5n,->0) and the contributions from these levels are practically negligible. Thus, when y=yS" the contribution from the K-shell electrons to 5 is averaged out and when y = y the same holds true for contributions from the K- and L-shell electrons. 

The layout of the periodic table (Fig. 2.5) reflects the shell structure of the electrons. Hydrogen and helium have only -shell electrons. The elements in row two have and L-shell electrons, with the Is orbitals always filled and the 2s and 2p orbitals filled in succession. Those in row three have and L-shell electrons, with Is, 2s, and 2p orbitals filled, and the 3 s and 3p orbitals are filled in succession. Elements in the fourth row have K, L, and M-shell electrons, with the Is, 2s, 3s, 2p, and 3p orbitals completely filled. After the 4s orbitals are filled, the 3d orbitals are filled, giving the transition metals. Then come the 4p orbitals. Row five is filled in an analogous fashion. In row six, the lanthanides, which fit between lanthanum and hafnium, reflect the appearance of the N-shell electrons, which fill the f orbitals. Row seven, which contains the actinides, also has K, L, M, and N-shell electrons. 

Figure 1.2 Schematic diagram to show X-ray emission to fill vacancy caused by nuclear decay. An L-shell electron (A) is shown filling a K-shell vacancy (B). In doing so, it emits a characteristic K X-ray.

The nomenclature for X-ray emission consists of the name of the shell in which the vacancy was created (K, L, M, N), and on the electronic shell that filled the vacancy. For instance, ejection of a K shell electron, filled with a L shell electron is denoted as K if filled with an M shell electron, then Kp is used, and so on. Due to electronic subshells, nomenclature becomes significantly complex, as shown in Figure 7.19. 

The energy of characteristic X-rays is the energy difference between two electrons in different shells. It is well defined and dependent on the atomic number of the atom. For example, the energy of the X-ray Ka line is the energy difference between a K shell electron and L shell electron. Thus, we can identify a chemical element from the characteristic X-rays that it emits. Moseley s Law defines the relationship between wavelength of characteristic X-rays (A.) and atomic number (Z). 

Fig. 5. Probability (per unit time) of Auger capture to the L shell of a Ne ion embedded in a FEG El as a function of the number of L-shell electrons bound to the ion before the capture. El is in atomic units. Two different values of the electronic density = 1.5 and 2 are shown.

Figure 1.2. 7-ray emission and internal conversion process. In internal conversion process, the excitation energy of the nucleus is transferred to a X-shell electron, which is then ejected, and the X-shell vacancy is filled by an electron from the L-shell. The energy difference between the L-shell and L-shell appears as the characteristic K X-ray. The characteristic K X-ray energy may be transferred to an L-shell electron, which is then ejected in the Auger process. 

Table 3 Energy shifts of K- and L-shell electrons in hydrogen-like due to various collective excitations. Upper half The contributions fixim low-lying nuclear states are calculated using experimental energies and transition probabilities [69]. Lower half The contributions from giant resonance states. Excitation energies and corresponding reduced electric transition strengths are again estimated based on empirical formulae. Notations are the same as in Table 2.

X-ray absorption X-ray excitation of K and L shell electrons Good quantitative method for heavier elements in presence of light elements... 

Figure 36. Lead levels in bone can be measured in vivo using XRF spectroscopy, (a) y-rays or X-rays are used (source) to eject either L-shell electrons (L-XRF) or K-shell electrons (K-XRF) from lead in bone when outer-shell electrons fill this vacancy, photons are released (fluorescence) and are monitored by the detector (10, 523). A typical X-ray fluorescence spectrum [(b), e.g., of a 112 pg Pbg phantom ) provides the number of counts observed as a function of photon energy. Emissions characteristic of lead occur at 72.8 keV (PbKa2), 75.0 keV (PbKoti), and 84.9 keV (Pb Kpi) (436, 523). Measurements on actual samples are correlated with those obtained from standard phantoms made of plaster-of-paris and doped with a known amount of lead to obtain bone lead concentrations in micrograms of Pb per gram (pg Pbg bone). The bone lead levels obtained by this method correlate extremely well with independent measurements of BLL (c). [Parts (a) and (c) adapted from (524). Part ( ) adapted from (436).]...

Lead levels in bone can be measured in situ accurately and quantitatively using XRF spectroscopy (Fig. 36) (10, 436, 523). X-ray fluorescence spectrometers [Fig. 36(a)] use y-rays or X-rays to eject either L-shell electrons... 

The core orbitals in the third-row elements have been also examined by estimating core-excitation energies [52], The numerical assessment demonstrates that 70 and 50 % portions of HFx are appropriate for K-shell and L-shell electrons, which requires to modify CV-B3LYP so as to deal with three different HFx portions, 20, 50, and 70 % for valence, L-shell, and K-shell electrons. The following is the extension of CV-B3LYP. 

Photoelectric absorption can only occur if the energy of the photon E is equal or higher than the binding energy 4> of the electron. For example, an X-ray photon with an energy of 15 keV can eject a K-electron (0 = 7.112 keV) or an L3-electron [4 u = 0.706 keV) out of a Fe atom. However, a 5 keV electron can only eject L-shell electrons from such an atom. 

True surface analysis on the order of a few atomic layers can be done by a somewhat different mechanism, as illustrated in f igure 20.74. In this case, the characteristic x-ray photon illustrated in Figure 20.73 does not escape the vicinity of the atomic core but instead ejects one of the L shell electrons. The result is a nonradiating electron transition with a kinetic energy characteristic of the chemical element (carbon). 

Figure 2.9 The photoelectric interaction, (a) Before photoelectric interaction a photon of energy E encounters the atom, (b) In the photoelectric interaction the photon is absorbed by a K-shell electron, and the electron is ejected with an energy equal to the photon energy less the K-shell electron-binding energy, (c) the K-shell vacancy is filled by an L-shell electron, and the difference in binding energies is given off as either (c) a characteristic x-ray photon or (d) an Auger electron. (Reprinted by courtesy of EG G ORTEC.)...

The noninvasive technique of X-ray fluorescence is useful for in vivo lead determination, e.g., bones. X-ray fluorescence occurs when an inner shell electron vacancy is filled with an electron from the next shell. For lead the filling of a vacancy in the K shell with an L-shell electron results in characteristic X-ray lines at 72 and 75 keV. Excitation of the K-shell electron is accomplished by 7-rays, where Co (122 and 136 keV) or ° Cd is used as the 7-source [13,76,77]. 

The next two terms, Is and 2p refer to the four electrons in the L shell. The L shell, when filled, can never have more than eight electrons the element neon has a filled L shell. The L-shell electrons belong to two different subshells, the s and the p, and the 2s and the 2p electrons have different energy levels (the number 2 referring to the L or second shell, and the letters s and p to the orbitals or subshells). The two 2 electrons have opposite spin and the two 2p electrons parallel spin. This view of the carbon atom is represented schematically in Fig. 3.2. 

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