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I
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
outennost shell is related to the position of the element in the periodic table, and therefore
is an important factor in detennining 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: lonization (^) Energies and Energy Levels
From the Coulombic Potential Energy expression, we know that an electron in a given shell will require a ceftain 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 parlicular 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.
Each of the two^ electrons^ at^ this energy'
level is harder to remove^ than the
electron that is^ faither from^ the nucleus.
nucleus
ChemActivity I^ Photoelectron^ Spectroscopy^33
Critical Thinking^ Question
- Suppose that the values for the two energy levels^ for^ the atom^ in^ Model^ I^ are^ -0. MJ/mole and 6.26 MJ/mole.
c)
How much energy, in MJ, is required to remove electron "cx," in Model I
from one mole of neutral atoms?
What is (^) the potential energy of each of the three electrons in Model (^) 1?
(Hint: see CA3.)
Determine the ionization enersies 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.
Gritical Thinking (^) Question
- 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-mys,^ are^ used^ initris^ experiment.^ The^ gas^ phase atoms^ are^ irradiated^ wittr^ photons ofa particular energy. Ifthe energy ofthe 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, tr*r',^ 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
a)
b)
ChemActivity 8 Photoelectron Spectroscopy 35
Figure 2: A simulated photoelectron spectrum of the hypothetical^ atom in Figure 1.
a oH (J r r'l (ts O
Z C)
C)
Critical Thinking Questions
- 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?
- What is^ the numerical value at the position^ of the hatch mark in^ the photoelectron
spectrum of Figure^ 2?
- What energy is associated with the energy level^ of the electron in Figure^ 2?
Ionization Energy (MJ/mole)
- What determines the height (or intensity) of each peak^ in a photoelectron^ spectrum?
(^36) ChemActivity 8 Photoelectron Spectroscopy
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^ enersv level^ as shown in^ the^ enersv level diasram below:
t El
I (energy level)
ooa
oo
I lm t (ionization (^) energy)
Critical Thinking Questions
- How many peaks (1,2,3,4,5) (^) will appear in (^) a photoelectron spectrum of a sample of
this hypothetical atom? Why?
- Describe the relative height of the peaks in the photoelectron spectrum of a sample ' (^) of this hl.pothetical atom.
- 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.
38 GhemActivity 8 Photoelectron Spectroscopy
Model 5: The Neon Atom.
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 inthe n:l 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 MJimole, because that is the first ionization energy of Ne as determinedpreviously.
The second peak should be at a signifrcantly 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 eleclron (^) at
random from each of the atoms in the sample. Thus, of the 10 electrons in Ne, we would
expect that2ll0 (^) 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 deterrnined 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 comesponds 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 energt of 2.
MJ/mole and one at much higher energy, and the relative sizes of these two peaks should
be 4:1.
Critical Thinking Questions
- 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?
t5. Why is it expected that2ll0 of the ejected electrons will come from^ the^ n:^1 shell, and 8/10 ofthe electrons from the n:2 shell?
ChemActivity 8 Photoelectron^ Spectroscopy^39
- 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
- In a photoelectron spectrum, photons of 165.7 MJ/mole impinge on atoms of a certain element. If the kinetic energy of the ejected electrons is 25.4 MJimole, what
is the ionization energv of the element?
- The ionization energy of an electron from the^ first^ shell^ of lithium^ is^ 6.26 MJ/mble. The ionization energy of an electron from the second shell of lithium^ is^ 0. 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.
- An atom has the electrons in the energv levels^ as^ shown^ below:
El
'-*
Make a sketch of the PES of this element.
