Article Cite This: J. Chem. Educ. 2019, 96, 1424−1430
pubs.acs.org/jchemeduc
Moseley and X‑ray Spectra Rafaela T. P. Sant’Anna,‡ Emily V. Monteiro,† Romulo O. Pires,† Rosa C. D. Peres,† and Roberto B. Faria*,† †
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Departamento de Química Inorgânica, Instituto de Química, Universidade Federal do Rio de Janeiro, 21941-909 Rio de Janeiro, Rio de Janeiro, Brazil ‡ Instituto Federal de Educaçaõ , Ciência e Tecnologia do Rio de Janeiro, 20270-021 Rio de Janeiro, Rio de Janeiro, Brazil ABSTRACT: As 2019 is the 150th anniversary of the Mendeleev’s Periodic Table, UNESCO has proclaimed this year the International Year of the Periodic Table (IYPT2019). One of the most important steps in the evolution of the Periodic Table is the concept of atomic number, established by Moseley. In this article, his work is commented on, and the emission of X-ray lines is interpreted on the basis of a one-electron transition using Bohr’s theory. The agreement is very good for the Kα and Kβ lines, which can be used in classes to reinforce the quantized model of atoms. It is also shown that inner-electron-screening effects play a significant role, especially in the L-series lines. In addition to the discussion based on Bohr’s theory, the several different X-ray lines that are known for each element are also explained using LS spin−orbit-coupling spectroscopic terms. The presentation of X-ray data and discussion of the data using these two theoretical approaches in both undergraduate and graduate classes resulted in significant grade improvements on the topic of atomic theory. KEYWORDS: Second-Year Undergraduate, Upper-Division Undergraduate, Graduate Education/Research, Physical Chemistry, Inorganic Chemistry, Inquiry-Based/Discovery Learning, Atomic Properties/Structure, Atomic Spectroscopy, Periodicity/Periodic Table, Quantum Chemistry
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INTRODUCTION
Moseley moved to the University of Oxford, where he obtained the data for his seminal articles.2,3 X-rays were discovered by the mechanical engineer and physicist Wilhelm Conrad Röntgen (1845−1923) in 18956 and have a great number of applications today. One of the most visible applications to the general public is related to their use in tomography for medical diagnostics. In the field of chemistry, there are several techniques that use X-rays, such as the X-ray absorption spectroscopy (XAS), X-ray photoelectron spectroscopy (XPS), X-ray fluorescence elemental analysis (XRF), energy-dispersive analysis of X-rays (EDAX), powder X-ray diffraction, and single-crystal X-ray diffraction, which allow the determination of the structures of chemical compounds, including very-high-molecular-weight proteins. As a consequence of Moseley’s work on X-rays, the ordering principle for the chemical elements, based on the atomic weights, could be definitively abandoned in favor of the atomic number.2 As proposed initially by Dmitri Mendeleev (1834− 1907), the chemical properties of the elements must be considered more important than the atomic weights for positioning the elements in the periodic table, producing the so-called pair reversals cases (Ar and K, Co and Ni, Tl and I),
The United Nations General Assembly and United Nations Educational, Scientific and Cultural Organization (UNESCO) have proclaimed 2019 to be the International Year of the Periodic Table of Chemical Elements (IYPT2019);1 thus, it is a good time to emphasize the role of the work of Moseley, which allowed for the determination of the atomic numbers of chemical elements. Henry G. J. Moseley, who died on August 10, 1915, in one of the battles of World War I at the age of 27, published his seminal articles in 1913 and 1914.2,3 Moseley also published one additional article in which he refuted some criticisms of his work, specifically the interpretation of X-ray spectra by the use of Bohr’s theory.4 Henry G. J. Moseley was born in Weymouth, in southern England, on November 23, 1887. Moseley obtained his bachelor’s degree in physics at the Trinity College of the University of Oxford in 1906 and started working with radioactive isotopes at the University of Manchester in 1910, under the guidance of the physicist Ernest Rutherford (1871− 1937). In 1912, Moseley worked for a month in the laboratory of the physicist, chemist, and mathematician William Henry Bragg (1862−1942) at the University of Leeds to learn how to work with X-rays. When Moseley returned to the University of Manchester, he worked with the mathematician Charles Darwin (1887−1962) on X-ray measurements.5 In 1913, © 2019 American Chemical Society and Division of Chemical Education, Inc.
Received: December 8, 2018 Revised: May 2, 2019 Published: May 23, 2019 1424
DOI: 10.1021/acs.jchemed.8b01012 J. Chem. Educ. 2019, 96, 1424−1430
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where the order by atomic weight is reversed.7 The X-ray frequencies determined by Moseley for several elements allowed him to determine a new property of the elements, namely, the atomic number. Ordering the elements following this new property definitively settled the position proposed by Mendeleev for the elements Ar, K, Co, Ni, Tl, and I. The explanation for these pair reversals would be fully explained later by the discovery of isotopes. The atomic-number ordering principle had been anticipated by Antonius van den Broek (1870−1926), a Dutch amateur physicist, who proposed the existence of the alphon particle. This particle should have a charge of +1 and half of the mass of the α particle and corresponds to hydrogen. Then, each element would be some aggregation of alphon particles, which is in line with the fact that for many pairs of consecutive elements, the atomic weight increases by approximately two units. On the basis of his ideas, van den Broek produced periodic tables in which the elements were ordered by the number of alphons in each atom, which was the same as the sequence position of the elements in the periodic table.7,8 Moseley also indicated that the atomic numbers, calculated by the X-ray-frequency values for each element, should be a very reliable tool for finding the missing elements in the periodic table. These missing elements were proposed by Mendeleev mostly on the basis of the chemical properties of the elements and using the ordering principle by atomic weight.2 In this way, Moseley’s results indicated that seven elements were waiting to be discovered (elements with atomic numbers 43, 61, 72, 75, 85, 87, and 91).9 All of these elements were later discovered, confirming the correctness of Moseley’s method to determine the atomic number of the elements. Three of these elements were discovered by women (alone or in collaboration with other researchers), showing a more significant participation by women in science in more recent years. Even though the use of X-rays is very common and pervasive in our lives, we observed that most undergraduate and even graduate chemistry students do not understand of the electronic processes that occur in the production of X-rays. This lack of understanding may be a consequence of most general-chemistry and inorganic-chemistry textbooks not giving much attention to the techniques developed by historical actors; these textbooks do not present a description of the processes by which X-rays are produced or an interpretation of X-ray experimental data. Only the consequences of Moseley’s results for the periodic law, based on atomic numbers, are presented.10−16 Because of this, we included this topic in the atomic-structure discussions presented in our undergraduate and graduate inorganicchemistry classes. We noticed that the presentation of X-rayelectronic-production processes improved the students’ comprehension of atomic structure, electronic transitions, and spectroscopic terms. Despite the relevance of Moseley’s work for the building of chemistry, it has not been recognized with the naming of a chemical element, although the name mosleyum has been previously suggested.7 The following sections will present the most recent experimental X-ray data and their interpretation, initially using Bohr’s theory and later using LS-spectroscopic terms. The level of discussion is intended to be used in both, undergraduate and graduate inorganic classes, in which atomic
structure, Bohr’s theory, electronic transitions, and LSspectroscopic terms are presented.
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ELECTRONIC TRANSITIONS FOR X-RAY PRODUCTION AND BOHR’S THEORY As seen in the Moseley article,3 a plot of the square root of the emitted X-ray frequency versus the atomic number gives a straight line. For the elements ranging from Al to Au, Moseley reported two series of lines. These series were called the K series and L series. He reported two lines in the K series: the more intense line (longest wavelength) was designated α, and the weaker line was designated β. For the L series, Moseley showed that it only starts at Zr and has four lines for La and the heavier elements. Again, the line with the longest wavelength is the most intense, similar to that observed in the line spectra of hydrogen. The letters K and L are associated with the first (K) and second (L) shells of the atoms. This notation can be extended to other shells using the letters M, N, and O and so on, corresponding to the third, fourth, and fifth shells and so on. The up-to-date experimental values of the X-ray emission lines from neon (Z = 10) to fermium (Z = 100) have been given by Deslattes et al., who present many more X-ray lines than were observed by Moseley.17 Figure 1 shows some of the
Figure 1. Energy of the X-ray lines of the K series versus Z2 in the range of Z = 10 to Z = 100.
lines of the K series, named KL2, KM2, and KN2 (also called Kα2, Kβ3, and Kβ2II). This kind of notation will be made clearer later, but for now, it is sufficient to say that this notation indicates the shells involved in the electronic transitions that produce the X-rays. For example, KL2 indicates an electronic transition between the first and second shells (K and L). When observed at high resolution, the X-ray lines are indeed multiple lines very close to each other. In this way, the Roman numeral indicates which of these multiple lines we are referring to. For the very radioactive elements (i.e., Tc, Po, At, Rn, Fr, and Ac), there are no reliable experimental values, and for some heavy radioactive elements, only the value of the most stable isotope has been considered to produce Figure 1.17 As shown by Moseley,2,3 the plot of X-ray energy (eV) versus the square of the atomic number shows almost linear behavior, especially for the first half of the elements. The plot in Figure 1 is equivalent to that of the square root of the X-ray frequency (cm−1) versus the atomic number in Moseley’s 1425
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Table 1. Comparison between the Theoretical and Calculated Values for the Slopes of the E versus Z2 Plots for Three Lines in the K Series X-ray Line
Equation
Theoretical, eVa
Experimental, eV
Deviation from the Theoretical Value, %
R2
KL2 KM2 KN2
1 2 3
10.204268 12.093948 12.755335
10.066 ± 0.023 11.475 ± 0.037 12.156 ± 0.031
1.35 5.12 4.70
0.99981 0.99961 0.99988
a
Calculated for elements up to Z = 50.
article.3 The KM2 and KN2 lines depart from the linear behavior more than the KL2 line does. Moseley’s explanation for this almost linear behavior was based on Bohr’s theory for the hydrogen atom, which was still being developed18,19 (a more complete article by Bohr only appeared in 191520). For an atom to produce X-rays, it is necessary for a high-energy electron beam to strike the atom (irradiation by γ-rays is also an alternative21). The collision of these high-energy electrons can remove inner electrons from the target atom. In the case of the K series, one electron is removed from the first shell (K shell), producing a vacancy in the atom. An X-ray photon is then emitted when one electron in any other shell of the atom moves to occupy the vacancy in the K shell. This phenomenon is a one-electron inner-shell transition, which in the case of the KL2 line corresponds to the decay of an electron from the second shell (L shell) to the first shell (K shell), and the energy of this transition can be calculated by eq 1, which is derived from Bohr’s theory.20 Thus, a plot of the X-ray energy versus Z2 should produce a straight line with a slope equal to [e4m/(8h2ε02)](3/4) = 10.204268 eV, where e is the electron charge, m is the electron mass (as indicated in Bohr’s 1915 article,20 the reduced mass should be used, but this is an unnecessary complication at this level), h is the Planck constant, and ε0 is the electric constant. Linear fitting using the KL2 experimental data17 for elements Z = 10 through Z = 50 gives a slope equal to 10.066 ± 0.023 eV, which is very close to the theoretical value. e mZ ij 1 1y jj − 2 zzz 8h2ε0 2 k 12 2 { 4
E=
Figure 2. Energy of some of the X-ray lines of the K and L series versus Z2, in the range of Z = 10 up to Z = 50.
E=
E=
E=
e 4mZ2 ij 1 1y j − 2 zzz 2 2j 2 8h ε0 k 1 3 {
e 4mZ2 ij 1 1y j − 2 zzz 2 2j 2 8h ε0 k 1 4 {
e 4mZ2 ij 1 1y j − 2 zzz 2 2j 2 8h ε0 k 2 4 {
(4)
(5)
For the K series, the agreement between the theoretical (based on Bohr’s theory) and experimental values is very good. For the L series, the agreement is not as good but still reasonable, especially when considering the simplicity of Bohr’s theory. Moseley observed that for the K series, the square root of the X-ray frequency is a function of (N − k), where N is the atomic number and k = 1.2,3 This observation results in exchanging Z with (Z − 1) in eq 1. Using this correction in the atomic number, the linear fit for the KL2 Xray lines gives a slope equal to 10.403 ± 0.014 eV (R2 = 0.99993), which deviates by 1.94% from the theoretical value and is a little worse than the fit using Z2 (see Table 1 for comparison). However, in the case of the L series, the correction in the Z value is more significant. Moseley found that the square root of E was a function of (Z − 7.4),3 and we found that the best linear fit for the L2M1 lines was obtained using (Z − 9).2 Using this correction on the Z value, we obtained a slope equal to 1.8914 ± 0.0035 eV (R2 = 0.99989), which deviates by 0.092% from the theoretical value (see Table 2 for comparison). This finding suggests the substitution of Z with (Z − 9) in eq 4, and it is very impressive that reducing Z by a constant value produces a very good linear fit. To explain this correction on the Z value, we can suppose that the effective nuclear charge for the electrons beyond the L shell can be Z minus the screening produced by the two 1s electrons and the seven electrons still in the L shell, as one of these electrons was removed to produce a vacancy, which explains the value of 9
2
(1)
Equations 2 and 3 are the corresponding equations based on Bohr’s theory for the other X-ray lines shown in Figure 1 (KM2 and KN2, respectively). The results of the linear fitting of the experimental data for the elements up to Z = 50 are presented in Table 1, together with their theoretical values. E=
e 4mZ2 ij 1 1y j − 2 zzz 2 2j 2 8h ε0 k 2 3 {
(2)
(3)
Electronic transitions may also occur to a vacant position produced in the second shell (called the L series by Moseley), and two of these transitions are named L2M1 and L2N1. These X-ray lines correspond to the Balmer series in Bohr’s theory for the hydrogen atom, which considers that light is emitted when the electron moves from one external orbit (n > 2) to the second orbit (n = 2). Figure 2 shows these X-ray lines together with the KL2, KM2, and KN2 lines for comparison. In this figure, the abscissa axis only reaches Z2 = 2500 (Z = 50) to make the linear behavior more evident. The corresponding equations are given by eqs 4 and 5, and a comparison between the theoretical and experimental values is presented in Table 2. 1426
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Table 2. Comparison between the Theoretical and Calculated Values for the Slopes of the E versus Z2 Plots for Two Lines in the L Series X-ray Line
Equation
Theoretical, eVa
Experimental, eV
Deviation from the Theoretical Value, %
R2
L2M1 L2N1
4 5
1.889679 2.551068
1.386 ± 0.013 1.921 ± 0.011
26.7 24.7
0.9971 0.9996
a
Calculated for elements up to Z = 50.
we obtained. Lazzarini and Bettoni21 also explained the correction (Z − 1), employed by Moseley to fit the X-ray lines in the K series, as being due to the screening effect produced by the electron remaining in the first shell (K shell). As a last word on this section, it must be stated that it is not possible to rely on Bohr’s theory for the interpretation of the high-resolution X-ray spectral data.17 In addition, as shown in Figure 1, the linear behavior is lost for the heavier elements, and this can be explained only by modern quantum mechanics, including spin−orbit interactions (as will be shown in the next section) and other additional effects such as relativistic corrections. However, the corrections on Z that produce a better linear fit of the experimental data in eqs 1−5 enrich the class discussions on the electronic structures of atoms and significantly increase students’ comprehension of Bohr’s theory.
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Figure 3. Identification of the X-ray line Kα with the movement of one electron from the 2p orbital to the 1s orbital. At high resolution, this X-ray line is shown to be a doublet of two very close lines. As the transition 2s → 1s is forbidden, the doublet can be explained only by the use of spectroscopic terms (see Figure 4).
SPLITTING OF X-RAY LINES AND THE ENERGY LEVELS AS INDICATED BY SPECTROSCOPIC TERMS At present, many additional X-ray lines are known, when compared with those that were observed by Moseley.2,3,17 For example, the lines called Kα and Kβ by Moseley are now known to be multiple lines. In the case of Kα, it is a double line, indicated as Kα1 and Kα2. In the case of the line Kβ, it is indeed a set of four lines that are very close, indicated as Kβ3, Kβ1, Kβ5II, and Kβ5I. These multiple lines cannot be explained by Bohr’s theory.20 Quantum mechanics, together with spin− orbit interactions in the Russell−Saunders coupling scheme (LS coupling), describes the energies of the atoms using spectroscopic terms. The spectroscopic terms for several valence-shell electronic configurations can be found in almost all physical chemistry (in the introduction to quantum mechanics sections) and inorganic-chemistry (in the electronic spectroscopy of coordination compounds sections) textbooks. For a hydrogen atom with one electron in the 1s atomic orbital, it has only one possible energy level, which is indicated by the 2S1/2 term.22−24 If a high-energy electron beam reaches an atom with more than two electronic shells and removes one electron from the 1s orbital, this atom will also have only one energy level that is indicated by the 2S1/2 term symbol (ignoring the interactions between this inner-shell electron and any partially filled valence subshells).22 Then, an X-ray photon is produced when one electron moves from any other shell to fill the 1s vacancy. In addition to the emission of an X-ray photon, a new vacancy is formed, and the total energy of the atom is described by the spectroscopic term that is determined from the subshell containing a vacancy.22 Figure 3 presents the electronic transition, which produces the Kα X-ray line. This representation, however, does not explain the fact that this X-ray line is a double line, indicated as Kα1 and Kα2. To explain the doublet Kα1 and Kα2, we need to know the spectroscopic terms of the initial and final states and consider the selection rules for the allowed transitions. Considering that
all spectroscopic terms for an atom missing one electron in an inner shell are doublets (S = 2), all transitions will be allowed by the selection rule ΔS = 0, where S is the spin multiplicity of the atom. The other selection rules are ΔL = ±1 and ΔJ = 0, ±1. This means that there are two allowed transitions between the L and K shells, K2S1/2 → L2P1/2 and K2S1/2 → L2P3/2, as the transition K2S1/2 → L2S1/2 is forbidden by the ΔL = ±1 selection rule. These spectroscopic terms consider that if one electron is missing from the 2p subshell, the electronic configuration will be 2p5, which has the same spectroscopic terms as 2p1, which are 2P1/2 and 2P3/2, with the latter being the lowest-energy term given by Hund’s rules for a p5 electronic configuration.24 Indeed, the single Kα line observed by Moseley is a double line, and the spectroscopic terms of the energy levels involved in this transition are indicated in Figure 4. For example, calcium has the lines KL2 or Kα2 (K2S1/2 → L2P1/2) = 3688.128 eV and KL3 or Kα1 (K2S1/2 → L2P3/2) = 3691.719 eV. Moseley reported only one line at 3693 eV. It is worth noting that the atom with a vacancy in the K shell has a higher total energy than the atom with a vacancy in the L shell.22,25 This observation means that the K2S1/2 term is the highest-energy term for the atom, as shown in Figure 4. Note that the letters K and L indicate the shells where one electron is missing. This is called a normal X-ray energy-level diagram and shows a reversed energy scale when compared with more common spectroscopic-term diagrams for valence-shell electronic transitions.25 In addition to those lines involving the K and L shells, transitions between the K and M shells (labeled as Kβ X-ray lines by Moseley), the K and N shells, the L and M shells, and the L and N shells have also been observed for several elements.17 In the M shell, in addition to the s and p orbitals, there are d orbitals, which produce the terms 2D3/2 and 2D5/2. 1427
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Figure 4. Identification of the Kα X-ray lines using spectroscopic terms. These lines correspond to the transitions K2S1/2 → L2P1/2 (KL2 or Kα2) and K2S1/2 → L2P3/2 (KL3 or Kα1). The letters K and L indicate the principal quantum number, n, which is equal to 1 or 2, respectively, where there is a one-electron vacancy.
Figure 6. Identification of the multiple X-ray Kβ lines using spectroscopic terms. These lines correspond to the transitions K2S1/2 → M2P1/2 (KM2 or Kβ3), K2S1/2 → M2P3/2 (KM3 or Kβ1), K2S1/2 → M2D3/2 (KM4 or Kβ5II), and K2S1/2 → M2D5/2 (KM5 or Kβ5I). The letters K and M indicate the principal quantum number, n, which is equal to 1 or 3, respectively, where there is a one-electron vacancy.
In the N shell, there are f orbitals, which produce the terms 2 F5/2 and 2F7/2. The Kβ transitions between the K and M shells are shown in Figures 5 and 6. Figure 5 shows the movement of
electronic configurations that contain one vacancy in one inner orbital of the atom. As seen, several of these transitions are forbidden by the selection rules, but violation of the selections rules is not uncommon, especially in the heavy elements, for which the jj spin−orbit coupling is better at describing the states of the atoms, and for this coupling scheme, the selection rules are less restrictive.26,27 In fact, the attribution of the X-ray-line transitions is made on the basis of quantum-mechanical theoretical calculations, which consider the relativistic effects but neglect the outershell structure of the atoms to reduce the calculation work. Additionally, coupling with the valence-shell electrons was also neglected, which means an average of all possible total-angularmomentum states was considered. Additional details of these calculations and the approximations that are used can be found in the literature.17,22
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IMPACT ON TEACHING After the presentation of the experimental data on the line spectra of the elements, Bohr’s theory, and the LSspectroscopic terms, the presentation of the electronic process involved in the production of X-rays gives the teacher a good opportunity to determine if the students have mastered the previous concepts. This opportunity is particularly significant for the LS-spectroscopic terms, which are more difficult for the students to understand because each spectroscopic term corresponds to a total energy level of the atom and not to any orbital energy level. In this way, we observed that the introduction of the X-ray-production processes and the associated LS-spectroscopic terms caused the students to ask new questions, which allowed the teacher to evaluate if the students understood the concepts of electronic transitions in one-electron atoms, Bohr’s theory, and LS-spectroscopic terms for multielectron atoms. One of the most significant aspects in the introduction of the X-ray subject was the presentation of the energy diagram showing the spectroscopic term K2S1/2, corresponding to an atom with one vacancy in the first shell in the highest-energy position, as shown in Figures 4 and 6. Comparison of these figures with the usual Gotrian diagrams
Figure 5. Identification of the X-ray line Kβ with the movement of one electron from the 3p orbital to the 1s orbital. At high resolution, this X-ray line is shown to be a multiplet of four or five very close lines, which can be explained only by the use of spectroscopic terms (see Figure 6 and Table 3).
one electron from the 3p orbital to the 1s orbital, corresponding to the X-ray line Kβ. However, this line is a multiplet and not a single line. This multiplet can be explained by the use of the spectroscopic terms, as shown in Figure 6. Considering the spectroscopic terms, both the transitions K2S1/2 → M2D3/2 and K2S1/2 → M2D5/2 are forbidden by the selection rule ΔL = ±1, and the latter is also forbidden by ΔJ = 0, ±1. However, some of these transitions are observed for many elements.17 Table 3 gives a complete list of the spectroscopic terms involved in the X-ray transitions K → L, K → M, K → N, and L → M and a partial list for the transition L → N. A more complete list can be found in the literature.17,22 In this table, the electronic transitions are described using the spectroscopic terms as determined for 1428
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Table 3. Identification of X-ray Lines Using Spectroscopic Terms Transitions Identified by the Use of Spectroscopic Terms
Application of Selection Rulesb
KL1
K2S1/2 → L2S1/2
FL
KL2 or Kα2
K2S1/2 → L2P1/2
A
KL3 or Kα1
K2S1/2 → L2P3/2
A
KM1
K2S1/2 → M2S1/2
FL
KM2 or Kβ3
K2S1/2 → M2P1/2
A
KM3 or Kβ1
K2S1/2 → M2P3/2
A
KM4 or Kβ5II
K2S1/2 → M2D3/2
FL
KM5 or Kβ5I
K2S1/2 → M2D5/2
FL
KN1 KN2 or Kβ2II
K2S1/2 → N2S1/2 K2S1/2 → N2P1/2
FL A
KN3 or Kβ2I
K2S1/2 → N2P3/2
A
KN4 or Kβ4II
K2S1/2 → N2D3/2
FL
KN5 or Kβ4II
K2S1/2 → N2D5/2
FL
KN6 KN7 L1M1
K2S1/2 → N2F5/2 K2S1/2 → N2F7/2 L2S1/2 → M2S1/2
FL FL FL
L1M2 or Lβ4
L2S1/2 → M2P1/2
A
L1M3 or Lβ3
L2S1/2 → M2P3/2
A
L1M4 or Lβ10
L2S1/2 → M2D3/2
FL
L1M5 or Lβ9
L2S1/2 → M2D5/2
FL
Abbreviated Notationa
Transitions Identified by the Use of Spectroscopic Terms
Application of Selection Rulesb
L2M1 or Lη
L2P1/2 → M2S1/2
A
L2M2
L2P1/2 → M2P1/2
FL
L2M3 or Lβ17
L2P1/2 → M2P3/2
FL
L2M4 or Lβ1
L2P1/2 → M2D3/2
A
L2M5
L2P1/2 → M2D5/2
A
L3M1 or Ll
L2P3/2 → M2S1/2
A
L3M2 or Lt
L2P3/2 → M2P1/2
FL
L3M3 or Ls
L2P3/2 → M2P3/2
FL
L3M4 or Lα2
L2P3/2 → M2D3/2
A
L3M5 or Lα1
L2P3/2 → M2D5/2
A
L1N1
L2S1/2 → N2S1/2
FL
L1N2 or Lγ2
L2S1/2 → N2P1/2
A
L1N3 or Lγ3
L2S1/2 → N2P3/2
A
L1N4
L2S1/2 → N2D3/2
FL
L1N5 or Lγ11
L S1/2 → N D5/2
FL
L1N6
L2S1/2 → N2F5/2
FL
L1N7
L2S1/2 → N2F7/2
FL
Abbreviated Notationa
Observations Observed only for W, Au, Np, Bk, and Fm Observed for almost all elements Observed for almost all elements Observed for Ne to P, and S Observed for almost all elements Observed for almost all elements Observed for almost all elements Observed for almost all elements Not observed Observed, starting at Ga Observed, starting at Ga Observed, starting at Kr Observed, starting at Kr Not observed Not observed Observed, starting at Tm Observed, starting at Cr Observed, starting at Cr Observed, starting at Pd Observed, starting at Pd
2
2
Observations Observed, at S Observed, at Yb Observed, at Sm Observed, at Ca Observed, at Gd Observed, at S Observed, at Tm Observed, at Dy Observed, at Ca Observed, at Ca Observed, at Eu Observed, at Rb Observed, at Rb Observed, at Ln Observed, at Ln Observed, at Ln Observed, at Ln
starting starting starting starting starting starting starting starting starting starting starting starting starting starting starting starting starting
a
IUPAC notation.25 Some authors use Roman numerals, for example, KLI instead of KL1.21,22 bFL, forbidden by ΔL = ±1; A, allowed by ΔL = ±1.
students must master. The inclusion of the electronic transitions that produce X-rays in the course reinforced the students’ comprehension of the electronic structures of atoms and the meaning of the spectroscopic terms, significantly increasing the students’ grades on this topic.
containing the spectroscopic terms involved in the valenceshell electronic transitions has been shown to be very helpful in the classroom for highlighting comprehension of electronic transitions and spectroscopic terms by the students. Therefore, we observed that the students’ grades for questions related to electronic transitions, Bohr’s theory, and LS-spectroscopic terms involving valence-shell electronic transitions improved significantly after the introduction of the X-ray subject in the Atomic Structure part of the course. This grade increase was observed in both the undergraduate and graduate inorganic-chemistry classes and was practically identical. The additional amount of time to include this X-ray discussion was very small, between 5 and 10% of the time dedicated to discussing atomic structure.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Rafaela T. P. Sant’Anna: 0000-0002-7761-4831 Emily V. Monteiro: 0000-0003-0005-9590 Romulo O. Pires: 0000-0002-0913-7332 Rosa C. D. Peres: 0000-0002-1021-071X Roberto B. Faria: 0000-0001-9337-4324
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CONCLUSION A simpler understanding of X-ray emission by atoms can be given by the use of Bohr’s theory. The introduction of this topic allows explanation of the low-resolution X-ray spectra of atoms (such as the data obtained by Moseley) using the simple principles of the quantized Bohr atom. On the other hand, the use of LS spin−orbit-coupling spectroscopic terms allows the explanation of all the lines observed in high-resolution experiments. These LS-spectroscopic terms are an almost universal language that undergraduate and graduate chemistry
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank the financial support of Conselho Nacional de Desenvolvimento Cientı ́fico e Tecnológico-CNPq, Grant nos. 141.341/2014-9 (R.T.P.S.), 140.864/2016-4 (E.V.M.), and 306.050/2016-1(R.B.F.). This study was financed in part 1429
DOI: 10.1021/acs.jchemed.8b01012 J. Chem. Educ. 2019, 96, 1424−1430
Journal of Chemical Education
Article
by the Coordenaçaõ de Aperfeiçoamento de Pessoal de Nı ́vel Superior, Brasil (CAPES), Finance Code 001.
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