Group Members: Your Name In Class Exercise #6. Photon A. Energy B

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1 Group Members: Your Name In Class Exercise #6 Shell Structure of Atoms Part II Photoelectron Spectroscopy Photoelectron spectroscopy is closely related to the photoelectric effect. When high energy photons hit an atom, molecule, or solid surface an electron can be emitted if the energy of the photon is greater than the ionization energy of the matter. By conservation of energy Ephoton = KE + IE Where KE is the kinetic energy of the electron and IE is the ionization energy (this would be the work function in the photoelectric effect). There are several modes for running the photoelectron spectrum; throughout this exercise we will consider the photoelectron experiment in which a high energy X-ray photon is used as the source and both the kinetic energy and the number of electrons emitted are measured. Because we know the energy of the photon and measure the the KEs of emitted electrons we can determine the IE. IE = Ephoton KE 1. Let s say that a hypothetical atom with one electron in its ground state is irradiated with photons that have energy of MJ/mole. On the drawing below, the large arrow represents the photon energy and the circle represents the electron in the lowest energy level of the atom. Which energy (A or B) represents the KE of the electron emitted and which represents the IE? Photon A Energy B

2 Upon ionization the emitted electrons all have energy of 40.8 MJ/mole. What is the ionization energy for atom in the ground state? What is the energy of the electron in the n=1 level (be sure to use the proper sign)? If the atom were in an excited state, would the kinetic energy of the emitted electron be greater or less? Explain. Consider the hypothetical atom to be in the first excited state (i.e. the electron is in the n=2 level). Knowing that the energy of a level is proportional to 1/n 2 and knowing the energy for n=1, what is the energy for the n=2 level? What will be the IE and KE for the atom in the excited state if a photon with 144.0MJ/mole energy is used? Photon Energy The axes shown below represent the photoelectron experiment results: the number of electrons emitted is the vertical scale and the horizontal axis represents the KE of the electron. Now imagine that the photoelectron spectrum of a sample in which 50% of the atoms were in the ground state and 50% were in the first excited state was measured using 144.0MJ/mole photons. Place labeled peaks on the graph below at appropriate places. No. of Electrons Typical peak shape Kinetic Energy of Electron (MJ/mole) 2

3 More commonly, the results of photoelectron spectrum are plotted with the horizontal axis as the Ionization Energy. Using this axis, plot the photoelectron spectrum of the sample with 50% atoms in the ground state and 50% of the atoms in the first excited state. No. of Electrons Ionization Energy (MJ/mole) 50 In most measurements of photoelectron spectra, the atoms are in their ground state. However multiple peaks may be seen in the spectra if there are multiple shells of electrons. For example, Li has two shells of electrons and exhibits the photoelectron spectrum shown below. Li Z=3 q core 1 No. of Electrons Ionization Energy (MJ/mole) Note that there are two peaks one at low energy that is about ½ the size of the peak at high energy. This spectrum illustrates important general features of the photoelectron spectrum: electrons are emitted from each shell and the size of the peak is proportional to the number of electrons in the shell. 2. For the photoelectron spectrum of Li, from what shell are electrons being ionized to give the the peak at 0.5 MJ/mole? Why is the peak at 6.3 MJ/mole twice as large as the peak at 0.5MJ/mole? 3

4 Low values of the ionization energy indicate that the electron is very easy to remove from the atom. Which electrons are closer to the nucleus, those in the inner shell or the outer shell? Which peaks correspond to ionization from the inner shell and outer shell? Orbitals and the Shell Model The shell structure and the experimental photoelectron spectrum of Ne are shown below. No. of Electrons Ne Z=10 q core Ionization Energy (MJ/mole) Note that three peaks are observed with IEs of 84.0 MJ/mole, 4.68 MJ/mole, and 2.08 MJ/mole. Also note that the peak at 2.08 MJ/mole is abut three times larger than either of the other two peaks. We must give up the notion that only the shell number (that is, the principal quantum number, n) determines the IE. We know from the mathematical description of the hydrogen atom that the n=2 shell has two different kinds of orbitals: s- (l=0) and p-orbitals (l=1). The p-orbitals comprise three types: p x, p y, and p z (m l =-1,0,1). Each orbital can hold two electrons so a more detailed description of the Ne atom is given by the electron configuration: 4

5 1s 2 2s 2 2p 6. The photoelectron spectrum of Ne exhibits three peaks, suggesting that the ionization of electrons may come from either the 1s, 2s, or 2p orbitals and that the energies of these ionization processes are different. 3. Which peak corresponds to ionization from the 1s orbital? Explain your reasoning, paying close attention to the ionization energy. Which peak corresponds to ionization from the 2s shell? Explain. Why are the peaks for ionization from the 2s and 2p shells of different size? Label the spectrum shown above with the names of the orbitals from which ionization occurred. Use the radial distribution curves shown below to rationalize why the IE for the 2s orbital is greater than the IE for the 2p orbital. Your rationalization must use the terms shielding and effective nuclear charge. (Hint: for which orbital can the electrons best get between the 1s shell and the nucleus). Ionization Energies and Electron Configurations The table below gives the orbital ionization energies for the first 18 elements. Table 1. Orbital Ionization Energies (MJ/mole) and Some Electron Configurations Element IE 1s IE 2s IE 2p IE 3s IE 3p Configuration 5

6 H s 1 He s 2 Li s 2 2s 1 Be s 2 2s 2 B s 2 2s 2 2p 1 C N O F Ne s 2 2s 2 2p 6 Na Mg s 2 2s 2 2p 6 3s 2 Al Si P S Cl Ar Compare the photoelectron spectrum of Ne with the energies listed above to verify the table. Another way of illustrating the electron configuration and orbital energies of Ne is given to the right. 2p Neon What is the electron configuration for N? For P? Fill in the rest of the table. 1s Draw the photoelectron spectra that you would expect for Na and Ar. 6

7 The first ionization energy is the energy to remove an electron from the highest energy filled orbital. Based on the shell model why do you think that the first ionization energy of Li is less than that of H? 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. 7