Photoelectron Spectroscopy

Transcription

1 32 ChemActivity 8 Photoelectron Spectroscopy (What Is Photoelectron Spectroscopy?) From our previous examination of the ionization energies of the atoms, we proposed a shell model of the atom, and noted that the number of valence electrons in the outermost shell is related to the position of the element in the periodic table, and therefore is an important factor in determining the physical and chemical properties of the element. Within this model, the electrons in an atom are arranged in shells about the nucleus, with the successive shells being farther and farther from the nucleus. The ionization energy described previously is the minimum energy needed to remove an electron from the atom. The most easily removed electron always resides in the valence shell, since that is the shell that is the farthest from the nucleus. For atoms with many electrons, we would expect that the energy needed to remove an electron from an inner shell would be greater than that needed to remove an electron from the valence shell, because an inner shell is closer to the nucleus and is not as fully shielded as the outer valence electrons. Thus, less energy is needed to remove an electron from an n = 2 shell than from an n = 1 shell, and even less is needed to remove an electron from an n = 3 shell. But do all electrons in a given shell require precisely the same energy to be removed? In order to answer this question, we must consider ionization energies in greater detail. Model 1: Ionization Energies and Energy Levels From the Coulombic Potential Energy expression, we know that an electron in a given shell will require a certain energy to be separated from the atom. Thus, an electron can be said to occupy an energy level in an atom. Within our model, each electron must be in a shell at a particular distance from the nucleus, and the energy levels corresponding to these shells are quantized that is, only certain discrete energy levels should be found. The electron at this energy level is easier to remove than electrons closer to the nucleus. γ α β Each of the two electrons at this energy level is harder to remove than the electron that is farther from the nucleus. nucleus

2 ChemActivity 8 Photoelectron Spectroscopy 33 Critical Thinking Question 1. Suppose that the values for the two energy levels for the atom in Model 1 are 0.52 MJ/mole and 6.26 MJ/mole. a) How much energy, in MJ, is required to remove electron "α" in Model 1 from one mole of neutral atoms? b) What is the potential energy of each of the three electrons in Model 1? (Hint: see CA3.) c) Determine the ionization energies of each of the three electrons in Model 1. Information When comparing the energy level of two different electrons, the electron with the higher ionization energy is said to occupy the lower energy level. Critical Thinking Question 2. Provide a statement, similar to the Information statement, that uses the potential energies of the electrons rather than the ionization energies. Model 2: Photoelectron Spectroscopy. Ionization energies may be measured by the electron impact method, in which atoms in the gas phase are bombarded with fast-moving electrons. These experiments give a value for the ionization energy of the electron that is most easily removed from the atom in other words, the ionization energy for an electron in the highest occupied energy level. An alternative, and generally more accurate, method that provides information on all the occupied energy levels of an atom (that is, the ionization energies of all electrons in the atom) is known as photoelectron spectroscopy; this method uses a photon (a packet of light energy) to knock an electron out of an atom. Electrons obtained in this way are called photoelectrons. Very high energy photons, such as very-short-wavelength ultraviolet radiation, or even x-rays, are used in this experiment. The gas phase atoms are irradiated with photons of a particular energy. If the energy of the photon is greater than the energy necessary to remove an electron from the atom, an electron is ejected with the excess energy appearing as kinetic energy, 1 2 mν 2, where v is the velocity of the ejected electron. In other words, the speed of the ejected electron depends on how much excess energy it has

3 34 ChemActivity 8 Photoelectron Spectroscopy received. So, if IE is the ionization energy of the electron and KE is the kinetic energy with which it leaves the atom, we have Ephoton = IE + KE or, upon rearranging the equation, IE = Ephoton KE Thus, we can find the ionization energy, IE, if we know the energy of the photon and we can measure the kinetic energy of the photoelectron. The kinetic energy of the electrons is measured in a photoelectron spectrometer. Figure 1: Photoelectron spectroscopy of a hypothetical atom. Before Photon Interaction After Photon Interaction photon energy = MJ/mole (for example) Atom Atom + e kinetic energy of ionized electron = MJ/mole If photons of sufficient energy are used, an electron may be ejected from any of the energy levels of an atom. Each atom will eject only one electron, but every electron in each atom has an (approximately) equal chance of being ejected. Thus, for a large group of identical atoms, the electrons ejected will come from all possible energy levels of the atom. Also, because the photons used all have the same energy, electrons ejected from a given energy level will all have the same energy. Only a few different energies of ejected electrons will be obtained, corresponding to the number of energy levels in the atom. The results of a photoelectron spectroscopy experiment are conveniently presented in a photoelectron spectrum. This is essentially a plot of the number of ejected electrons (along the vertical axis) vs. the corresponding ionization energy for the ejected electrons (along the horizontal axis). It is actually the kinetic energy of the ejected electrons that is measured by the photoelectron spectrometer. However, as shown in the equation above, we can obtain the ionization energies of the electrons in the atom from the kinetic energies of the ejected electrons. Because these ionization energies are of most interest to us, a photoelectron spectrum uses the ionization energy as the horizontal axis.

4 ChemActivity 8 Photoelectron Spectroscopy 35 Figure 2: A simulated photoelectron spectrum of the hypothetical atom in Figure 1. Critical Thinking Questions 3. Use the data presented in Figure 1 to verify that the IE of the ejected electron is 28.6 MJ/mole. 4. What determines the position of each peak (where along the horizontal axis the peak is positioned) in a photoelectron spectrum? 5. What is the numerical value at the position of the hatch mark in the photoelectron spectrum of Figure 2? 6. What energy is associated with the energy level of the electron in Figure 2? 7. What determines the height (or intensity) of each peak in a photoelectron spectrum?

5 36 ChemActivity 8 Photoelectron Spectroscopy 8. Explain why it is not possible to determine the number of electrons in an individual hypothetical atom from the photoelectron spectrum in Figure 2. Model 3: The Energy Level Diagram of Another Hypothetical Atom. A hypothetical atom in a galaxy far, far away has 2 electrons at one energy level and 3 electrons at another energy level as shown in the energy level diagram below: E IE (energy level) (ionization energy) Critical Thinking Questions 9. How many peaks (1,2,3,4,5) will appear in a photoelectron spectrum of a sample of this hypothetical atom? Why? 10. Describe the relative height of the peaks in the photoelectron spectrum of a sample of this hypothetical atom. 11. Suppose that the two energy levels are 0.85 MJ/mole and 4.25 MJ/mole. On the axes below, make a sketch of the photoelectron spectrum of a sample of this hypothetical atom. Make sure to label the axes appropriately

6 ChemActivity 8 Photoelectron Spectroscopy 37 Model 4: A Simulated Photoelectron Spectrum of an Unknown Atom. Critical Thinking Questions 12. Based on the number of peaks (one), the intensity of the peak, and your understanding of the shell model: a) Explain why it is not possible to determine if the unknown atom is H or He? b) Explain why the unknown atom cannot be Li. 13. Based on the value of the IE given in Model 4 and on the values given in Table 1 of CA 4, identify the unknown atom.

7 38 ChemActivity 8 Photoelectron Spectroscopy Model 5: The Neon Atom. +10 Let us now predict what the photoelectron spectrum of Ne will look like, based on our current model of the Ne atom. In this model, there are 2 electrons in the n =1 shell, and 8 electrons in the n = 2 shell of a Ne atom. Assuming that all of the electrons in each of the shells has the same energy, we would expect two peaks in the photoelectron spectrum. One peak, from the electrons in the n = 2 shell, should appear at an energy of 2.08 MJ/mole, because that is the first ionization energy of Ne as determined previously. The second peak should be at a significantly higher energy, because it corresponds to the ejection of electrons from the n = 1 shell, which is significantly closer to the nucleus. At this point we do not have any good way of estimating what that energy is, but we know that it will be a lot higher than 2.08 MJ/mole. Finally, we also can predict the relative sizes of the two peaks that is, the relative areas under the two curves on the spectrum. Recall that in photoelectron spectroscopy, the bombarding photon ejects an electron at random from each of the atoms in the sample. Thus, of the 10 electrons in Ne, we would expect that 2/10 of the time the electron is ejected from the n = 1 shell, and 8/10 of the time it is ejected from the n = 2 shell. The size of the peak in the spectrum is determined by the relative number of electrons with a given IE. Thus, the peak at 2.08 MJ/mole should be 4 times as large as the peak at a much higher energy, which corresponds to the ejection of electrons from the n = 1 shell. To summarize, our prediction is that the photoelectron spectrum of Ne should consist of two peaks, one at an energy of 2.08 MJ/mole and one at much higher energy, and the relative sizes of these two peaks should be 4:1. Critical Thinking Questions 14. The peak due to the n = 1 shell is predicted to be at a much higher ionization energy than the n = 2 peak because the n = 1 shell is "significantly closer to the nucleus." Why is the distance of the shell from the nucleus important in determining the corresponding peak position in the photoelectron spectrum? 15. Why is it expected that 2/10 of the ejected electrons will come from the n = 1 shell, and 8/10 of the electrons from the n = 2 shell?

8 ChemActivity 8 Photoelectron Spectroscopy Make a sketch of the predicted photoelectron spectrum of Ne based on the description given above. Indicate the relative intensity (peak size) and positions of the two peaks. Exercises 1. In a photoelectron spectrum, photons of MJ/mole impinge on atoms of a certain element. If the kinetic energy of the ejected electrons is 25.4 MJ/mole, what is the ionization energy of the element? 2. The ionization energy of an electron from the first shell of lithium is 6.26 MJ/mole. The ionization energy of an electron from the second shell of lithium is 0.52 MJ/mole. a) Prepare an energy level diagram (similar to the one in Model 3) for lithium; include numerical values for the energy levels. b) Sketch the photoelectron spectrum for lithium; include the values of the ionization energies. 3. An atom has the electrons in the energy levels as shown below: E Make a sketch of the PES of this element.

9 40 ChemActivity 9 The Shell Model (III) (How Many Peaks Are There in a Photoelectron Spectrum?) Model 1. Simulated Experimental Photoelectron Spectrum of Neon. Critical Thinking Questions 1. a) Is the photoelectron spectrum for Ne shown in Model 1 consistent with our model of the structure of atoms? b) Describe the ways (if any) in which our prediction was correct and the ways (if any) in which it was not correct. 2. Why is it not important to place numbers along the vertical axis of photoelectron spectra? 3. Based on the spectrum in Model 1, estimate the number of electrons at each of the three energy levels in Ne. Explain your reasoning clearly. (Hint: Recall that the total number of electrons should equal the number of electrons in a Ne atom.)

10 ChemActivity 9 The Shell Model (III) 41 Information: The Neon Atom Revisited. Contrary to our predictions, there are three peaks in the spectrum, not two! It appears that we must now modify our model to remain consistent with these new experimental results. We note that there is a peak at 2.08 MJ/mole (as expected) and one at a much higher energy in this case, 84.0 MJ/mole. We can safely assume that this higher energy peak corresponds to the electrons in the n = 1 shell, and that the electrons in that shell have an energy of 84.0 MJ/mole. Thus, the other two peaks must both arise from electrons in the n = 2 shell. This suggests that there are electrons with two different energies in the n = 2 shell, some with an energy of 4.68 MJ/mole, and others with the expected energy of 2.08 MJ/mole. In other words, there are two different energy levels associated with the n = 2 shell. To differentiate between them, we label them the 2s and 2p levels (or subshells), with the s designation corresponding to the lower energy level (and higher ionization energy) of the two (IE = 4.68 MJ/mole). (The labels s and p are used for historic reasons. They do not have any particular significance in the context of our model, but are used to be consistent with the designations used by contemporary practicing scientists.) The lowest energy level of a given shell is always designated as an s level, and so the electrons in the n = 1 shell are considered to be in a 1s energy level. Note that the 2s peak is approximately equal in size to that of the 1s peak, whereas the 2p peak is about three times as big. Thus, we can conclude that there are two electrons (of the eight total) in the 2s level of Ne, and six electrons in the 2p level. Our refined shell model of the Ne atom has the 10 electrons distributed in three different energy levels: 2 electrons in a 1s level, 2 electrons in a 2s level, and 6 electrons in a 2p level. At this point we will not be concerned about the details of the differences between the 2s and 2p levels. The important point is that the 2s level is slightly lower in energy than the 2p, but not by a large amount. This suggests that the electrons in both levels of the n = 2 shell are at nearly the same distance from the nucleus, and are clearly much farther from the nucleus than the electrons in the n = 1 shell. Also, we have found that there appears to be a limit of 2 on the number of electrons that can be placed in an s subshell. Critical Thinking Question 4. What is the reasoning behind the assumption that the peak at 84.0 MJ/mole (for neon; Model 1) corresponds to the electrons in the n = 1 shell? 5. Based on the information provided by the photoelectron spectrum in Model 1, why are two of the three peaks in the spectrum of neon assigned to the n = 2 shell, rather than to the n = 1 shell?

11 42 ChemActivity 9 The Shell Model (III) Model 2. Energy Level Diagrams for Helium, Neon, and Argon. Helium Neon Argon 1s p 2s p 3s p s s 84.0 Energy levels are not to scale. Energies are given in MJ/mole. 1s 309 Critical Thinking Questions 6. Based on the energy level diagram in Model 2, sketch a photoelectron spectrum for Ar. Make sure to indicate the relative intensities and positions of all peaks.

12 ChemActivity 9 The Shell Model (III) 43 Exercises 1. a) Based on our revised shell model, how many peaks would be expected in a photoelectron spectrum of lithium? b) What would you expect the relative sizes of the peaks to be? c) The 1s ionization energies for H, He, and Li are 1.31, 2.37, and 6.26 MJ/mole, respectively. Explain this trend. d) The first ionization energies for H and Li are 1.31 and 0.52 MJ/mole, respectively. Explain why the Li first ionization energy is lower. 2. Answer Ex. 1a and 1b for beryllium and for carbon. 3. Sketch the energy level diagram (as in Model 2) for Be and for C. 4. What element do you think would give rise to the photoelectron spectrum shown below? Explain your reasoning. Problems 1. Indicate whether each of the following statements is true or false and explain your reasoning: a) The photoelectron spectrum of Mg 2+ is expected to be identical to the photoelectron spectrum of Ne. b) The photoelectron spectrum of 35 Cl is identical to the photoelectron spectrum of 37 Cl. 2. The energy required to remove a 1s electron from F is 67.2 MJ/mole. The energy required to remove a 1s electron from Cl is: a) 54 MJ/mole; b) 67.2 MJ/mole; c) 273 MJ/mole; d) a 1s electron cannot be removed from Cl. Explain.

13 44 ChemActivity 10 Electron Configurations ChemActivity 10 Electron Configurations (How Are Electrons Arranged?) Model: Ionization Energies and Electron Configurations. Table 1. Ionization energies (MJ/mole) for the first 18 elements. Element 1s 2s 2p 3s 3p H 1.31 He 2.37 Li Be B C N O F Ne Na Mg Al Si P S Cl Ar Table 2. Electron configurations of selected elements. Element Configuration H 1s 1 He 1s 2 Be 1s 2 2s 2 C 1s 2 2s 2 2p 2 Ne 1s 2 2s 2 2p 6 Mg 1s 2 2s 2 2p 6 3s 2

14 ChemActivity 10 Electron Configurations 45 Critical Thinking Questions 1. What is the first ionization energy of: a) N? b) Ar? 2. Give an experimental method for obtaining the data in Table What information is provided by an electron configuration? 4. What is the relationship between the data in Tables 1 and 2? 5. Is it possible to deduce the electron configuration for an atom from its photoelectron spectrum? If so, describe how. If not, describe why not. 6. We will now construct two possibilities for the photoelectron spectrum of K. a) First, consider the first 18 electrons of K, in shells n = 1, 2, and 3. For these 18 electrons, estimate the IEs [Hint: compare to Ar.] and indicate their relative intensities. b) If the 19 th electron of K is found in the n = 4 shell, would the ionization energy be closest to 0.42, 1.4, or 2.0 MJ/mole? Explain. [Hint: compare to Na and Li.] Show a predicted photoelectron spectrum based on this assumption.

15 46 ChemActivity 10 Electron Configurations c) If the 19 th electron of K is found in the third subshell of n = 3, would the ionization energy be closest to 0.42, 1.4, or 2.0 MJ/mole? Explain. [Hint: compare to other cases in which a new subshell appears.] Show a predicted photoelectron spectrum based on this assumption. Exercises 1. Explain why more energy is required to remove an electron from the 1s orbital of Na (104 MJ/mole) than to remove an electron from the 1s orbital of Ne (84 MJ/mole). 2. According to the data in Table 1, would it require less than 0.50 MJ/mole, 0.50 MJ/mole, or more than 0.50 MJ/mole to remove a 3s electron from the Mg + ion? Explain.

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17 48 ChemActivity 10 Electron Configurations ChemActivity 11 Electron Configurations and the Periodic Table (How Many Subshells Are There?) Model 1. Simulated Photoelectron Spectrum of Potassium. Table 1. Ionization energies (MJ/mole) for selected elements. Element 1s 2s 2p 3s 3p 3d 4s K Ca Sc Critical Thinking Questions 1. Which of your predicted spectra from CTQ 6 of ChemActivity 10 provides the better match to the experimental spectrum, Model 1? Explain.

18 ChemActivity 11 Electron Configurations and the Periodic Table Based on the analysis we have used to assign peaks in photoelectron spectra to shells and subshells in atoms, why is the peak at 0.42 MJ/mole in the K spectrum assigned to the n = 4 shell (as opposed to being another subshell of n = 3)? Refer to the data in Table 1 of ChemActivity 10: Electron Configurations. Model 2. Simulated Photoelectron Spectrum of Scandium. (The 1s peak occurs at 433 MJ/mole and is not shown in this spectrum.) Critical Thinking Question 3. In the photoelectron spectrum of Sc, the peak at 0.63 MJ/mole is assigned to the 4s subshell. Why is the peak at 0.77 MJ/mole in the Sc spectrum assigned as a third subshell of n = 3 (named 3d) as opposed to being a second subshell of n = 4 (that is, 4p)?

19 50 ChemActivity 10 Electron Configurations Model 3: The Periodic Table. Note that the periodic table has an unusual form. The elements are arranged in "blocks" of columns a block of two columns on the left, six columns on the right, and ten columns in the middle. Critical Thinking Questions 4. What is the relationship between the form of the periodic table and the electron configurations of the elements? 5. Based on the form of the periodic table, how many electrons is the 3d subshell capable of holding? 6. Predict the electron configuration of Ga. 7. What is the common feature of the electron configurations of the elements in a given column of the periodic table?

20 ChemActivity 11 Electron Configurations and the Periodic Table 51 Exercises 1. Identify the element whose simulated photoelectron spectrum is shown below: IMPORTANT NOTE: In the above spectrum, the peak which arises from the 1s electrons has been omitted. 2. Place the following in order of increasing energy to remove an electron from the 1s energy level: C Pt Ba Ne Zn Gd 3. Make a rough sketch of the photoelectron spectrum of vanadium. Indicate the subshell that gives rise to each peak and the relative height of each peak. 4. Provide the electron configuration for: P, P 3, Ba, Ba 2+, S, S 2, Ni, Zn. 5. How many valence electrons does Ga have? Problems 1. As atomic orbitals are filled, the 6p orbitals are filled immediately after which of the following orbitals? 4f, 5d, 6s, 7s. 2. Provide the electron configuration for: Pd, Pd 2+, Gd, Gd 3+.