Photoelectron Spectroscopy of Multi-Electron Atoms

Author: John Hutchinson

The ionization energy of an atom tells us the energy of the electron or electrons which are at highest energy in the atom and are thus easiest to remove from the atom. To further analyze the energies of the electrons more tightly bound to the nucleus, we introduce a new experiment. The photoelectric effect can be applied to ionize atoms in a gas, in a process often called photoionization. We shine light on an atom and measure the minimum frequency of light, corresponding to a minimum energy, which will ionize an electron from an atom. When the frequency of light is too low, the photons in that light do not have enough energy to ionize electrons from an atom. As we increase the frequency of the light, we find a threshold at which electrons begin to ionize. Above this threshold, the energy hν of the light of frequency ν is greater than the energy required to ionize the atom, and the excess energy is retained by the ionized electron as kinetic energy.

In photoelectron spectroscopy, we measure the kinetic energy of the electrons which are ionized by light. This provides a means of measuring the ionization energy of the electrons. By conservation of energy, the energy of the light is equal to the ionization energy IE plus the kinetic energy KE of the ionized electron:

hν = IE + KE

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Thus, if we use a known frequency ν and measure KE, we can determine IE. The more tightly bound an electron is to the atom, the higher the ionization energy and the smaller the kinetic energy of the ionized electron. If an atom has more than one electron and these electrons have different energies, then for a given frequency of light, we can expect electrons to be ejected with different kinetic energies. The higher kinetic energies correspond to the weakly bound outer electrons, and the lower kinetic energies correspond to the tightly bound inner electrons.

The ionization energies for the first twenty elements are given in table 1. We note that there is a single ionization energy for hydrogen and helium. This is consistent with the shell model of these atoms since, in both of these atoms, the electron or electrons are in the innermost shell. The energies of these electrons correspond to the n=1 energy level of the hydrogen atom. In lithium and beryllium, there are two ionization energies. Again, this is consistent with the shell model, since now there are electrons in both of the first two shells. Note also that the ionization energy of the inner shell electrons increases as we go from hydrogen to lithium to beryllium, because of the increase in nuclear charge. The lower energy electrons correspond to the n=1 energy level of hydrogen and the higher energy electrons correspond to the n=2 energy level.

Element	Ionization Energy (MJ/mol)
H	1.31
He	2.37
Li	6.26	0.52
Be	11.5	0.90
B	19.3	1.36	0.80
C	28.6	1.72	1.09
N	39.6	2.45	1.40
O	52.6	3.12	1.31
F	67.2	3.88	1.68
Ne	84.0	4.68	2.08
Na	104	6.84	3.67	0.50
Mg	126	9.07	5.31	0.74
Al	151	12.1	7.79	1.09	0.58
Si	178	15.1	10.3	1.46	0.79
P	208	18.7	13.5	1.95	1.01
S	239	22.7	16.5	2.05	1.00
Cl	273	26.8	20.2	2.44	1.25
Ar	309	31.5	24.1	2.82	1.52
K	347	37.1	29.1	3.93	2.38	0.42
Ca	390	42.7	34.0	4.65	2.9	0.59

Surprisingly, though, boron has three ionization energies, which does not seem consistent with the shell model. From the hydrogen atom energy levels, we would have expected that all n=2 electrons would have the same energy. We can note that the two smaller ionization energies in boron are comparable in magnitude and smaller by more than a factor of ten than the ionization energy of the electrons in the inner shell. Thus, the electrons in the outer n=2 shell apparently have comparable energies, but they are not identical. The separation of the second shell into two groups of electrons with two comparable but different energies is apparent for elements boron to neon.

As such, we conclude from the experimental data that the second shell of electrons should be described as two subshells with slightly different energies. For historical reasons, these subshells are referred to as the as the "2s" and "2p" subshells, with 2s electrons slightly lower in energy than 2p electrons. The energies of the 2s and 2p electrons decrease from boron to neon, consistent with the increase in the nuclear charge.

Beginning with sodium, we observe four distinct ionization energies, and beginning with aluminum there are five. Note for these elements that the fourth and fifth ionization energies are again roughly a factor of ten smaller than the second and third ionization energies, which are in turn at least a factor of ten less than the first ionization energy. Thus, it appears that there are three shells of electrons for these atoms, consistent with our previous shell model. As with n=2, the n=3 shell is again divided into two subshells, now called the 3s and 3p subshells.

These data also reveal how many electrons can reside in each subshell. In each n level, there are two elements which have only the ionization energy for the s subshell. Hence, s subshells can hold two electrons. By contrast, there are 6 elements which have both the s and p subshell ionization energies, so the p subshell can hold 6 electrons.

The shell and subshell organization of electron energies can also be observed by measuring the "electron affinity" of the atoms. Electron affinity is the energy released when an electron is added to an atom:

A(g) + e-(g) A-(g)

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If there is a strong attraction between the atom A and the added electron, then a large amount of energy is released during this reaction, and the electron affinity is a large positive number. (As a note, this convention is the opposite of the one usually applied for energy changes in reactions: exothermic reactions, which give off energy, conventionally have negative energy changes.)

The electron affinities of the halogens are large positive values: the electron affinities of F, Cl, and Br are 328.0 kJ/mol, 348.8 kJ/mol, and 324.6 kJ/mol. Thus, the attached electrons are strongly attracted to the nucleus in each of these atoms. This is because there is room in the current subshell to add an additional electron, since each atom has 5 p electrons, and the core charge felt by the electron in that subshell is large.

By contrast, the electron affinities of the inert gases are negative: the addition of an electron to an inert gas atom actually requires the input of energy, in effect, to force the electron into place. This is because the added electron cannot fit in the current subshell and must be added to a new shell, farther from the nucleus. As such, the core charge felt by the added electron is very close to zero.

Similarly, the electron affinities of the elements Be, Mg, and Ca are all negative. This is again because the s subshell in these atoms already has two electrons, so the added electron must go into a higher energy subshell with a much smaller core charge.