PHOTOELECTRON SPECTROSCOPY PROBLEMS:
1. A hydrogen atom in its ground state is irradiated with 80 nm radiation. What is the kinetic
energy (in eV) of the ejected photoelectron?
Useful formulae:
ν = c/λ
E = hν
1 Joule = 6.2415×1018 eV
E=-R/n2
R = 2.1799 × 10-18 J
2. When 1 nm radiation is used to obtain the photoelectron spectrum of neon, electrons are
ejected with kinetic energies of 372, 1191, and 1218 eV. From what atomic orbitals do these
electrons originate? What is the orbital energy of each of these orbitals?
3. The orbital energies of the atomic orbitals in argon are: -3206, -326, -249, -29, and -16 eV.
Assuming that the intensity of the peaks in the photoelectron spectrum are proportional to the
number of electrons contained in the atomic orbital, sketch on the axis below the photoelectron
spectrum (as a function of electron kinetic energy, EKE) expected for argon that is subjected to
X-rays with an energy of 3500 eV:
4. Two 3d transition metal elements have been formed into an alloy. Shown below is the XPS
spectrum in the region corresponding to ejection of 3p electrons. Each peak shows an
unresolved doubling, which is due to the difference in energy between 3p electrons that have the
orbital angular momentum (ℓ 1 for p electrons) parallel to the spin, or antiparallel to the spin.
Estimate the binding energy of the electrons from the graph, and use that information in
conjunction with the table of core electron binding energies (next page) to deduce the two
elements that are present in the alloy. Based on the relative intensities of the two peaks, estimate
the percentage of each element in the alloy (a rough, eyeball estimate is good enough).
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Table of Core Electron Binding Energies of the Elements (eV)
Z
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Element
H
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar
K
Ca
S
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
1s
13.6
24.6
54.7
111.5
188
284.2
409.9
543.1
696.7
870.2
1070.8
1303
1559.6
1839
2145.5
2472
2822.4
3205.9
3608.4
4038.5
4492
4966
5465
5989
6539
7112
7709
8333
8979
9659
10367
11103
11867
12658
13474
14326
2s
2p1/2
2p3/2
3s
3p1/2
3p3/2
3d3/2
3d5/2
21.7
30.65
49.78
72.95
99.82
136
163.6
202
250.6
297.3
349.7
403.6
460.2
519.8
583.8
649.9
719.9
793.2
870
952.3
1044.9
1143.2
1248.1
1359.1
1474.3
1596
1730.9
21.6
30.81
49.5
72.55
99.42
135
162.5
200
248.4
294.6
346.2
398.7
453.8
512.1
574.1
638.7
706.8
778.1
852.7
932.7
1021.8
1116.4
1217
1323.6
1433.9
1550
1678.4
29.3
34.8
44.3
51.1
58.7
66.3
74.1
82.3
91.3
101
110.8
122.5
139.8
159.5
180.1
204.7
229.6
257
292.8
15.9
18.3
25.4
28.3
32.6
37.2
42.2
47.2
52.7
58.9
68
77.3
91.4
103.5
124.9
146.2
166.5
189
222.2
15.7
18.3
25.4
28.3
32.6
37.2
42.2
47.2
52.7
59.9
66.2
75.1
88.6
100
120.8
141.2
160.7
182
214.4
10.2
18.7
29.8
41.7
55.5
70
95
10.1
18.7
29.2
41.7
54.6
69
93.8
37.3
41.6
48.5
63.5
88.7
117.8
149.7
189
230.9
270
326.3
378.6
438.4
498
560.9
626.7
696
769.1
844.6
925.1
1008.6
1096.7
1196.2
1299
1414.6
1527
1652
1782
1921
5. Shown below is a the photoelectron spectrum of CO, plotted as a function of the electron
binding energy (EBE=hν – EKE). The peaks in the spectrum fall at the following electron
binding energies:
Peak #
1
2
3
5
6
7
8
9
10
11
12
13
14
15
Energy (eV)
14.01
14.28
16.54
16.73
16.92
17.11
17.29
17.46
17.64
17.81
17.97
19.67
19.88
20.08
Intensity
strong
weak
weak
medium
medium
medium
medium
weak
tiny
tiny
miniscule
weak
tiny
miniscule
Shown below is the CO molecular orbital diagram that is found in many textbooks:
Now, for the actual questions:
(a). From which molecular orbital is the electron ejected in the 14.01 eV EBE peak?
(b). From which molecular orbital is the electron ejected in the 16.54 eV EBE peak?
(c). From which molecular orbital is the electron ejected in the 19.67 eV EBE peak?
(d). What is the ionization potential of CO?
(e). What is the vibrational frequency (in units of eV and cm-1) of the ground state of CO+?
(f). What is the vibrational frequency (in units of eV and cm-1) of the first excited state of CO+?
(g). What is the orbital energy of the 5σ orbital of CO, in eV?
(h). What is the orbital energy of the 1π orbital of CO, in eV?
(i). What is the orbital energy of the 4σ orbital of CO, in eV?
6. The gold anion (also called auride) is rarely encountered, but salts with this anion have been
created. It can be produced in the gas phase and probed by photoelectron spectroscopy,
however.
(a). What do you expect will be the ground electronic configuration of Au−, which has 80
electrons?
(b). Which orbital lies highest in energy in the Au− anion?
(c). Shown below is the photoelectron spectrum of Au−. Based on the spectrum, what would you
estimate to be the electron affinity of gold?
For comparison, the electron affinities of some nonmetallic elements are:
C
1.263 eV
N
-0.07 eV
O
1.461 eV
F
Si
1.385 eV
P
0.746 eV
S
2.077 eV
Cl
As
0.81 eV
Se
2.021 eV
Br
Sb
1.07 eV
Te
1.971 eV
I
3.399 eV
3.617 eV
3.365 eV
3.059 eV
Note: Nitrogen has a negative electron affinity because the N− anion lies higher in energy than
an N atom plus an electron (in the gas phase); thus, the gas-phase N− anion will spontaneously
eject an electron very, very quickly. The triply charged N3− nitride anion is only stable when it is
surrounded by cations.
The photoelectron spectrum explains why, in some situations, gold can behave as a
pseudohalogen. It has a high electron affinity (higher than all of the typical nonmetals except for
the halogens).
7. A portion of the X-ray photoelectron spectrum (XPS) of ethylchloroformate is given below,
along with the structure of the compound:
The structure of the ethylchloroformate
molecule is given below:
CH3-CH2-C-Cl
║
O
You will notice that the 1s electrons on
carbon have a binding energy of roughly
290 eV, while the 2s electrons on chlorine
have a binding energy of roughly 273 eV.
However, there are three distinct carbon 1s
peaks, which correspond to carbons in
chemically different environments. The
three carbons in the molecule are the
methyl carbon (CH3), the methylene carbon
(CH2), and the carbonyl carbon (C=O).
(a). Which carbon atom gives the peak labeled (a) in the spectrum?
(b). Which carbon atom gives the peak labeled (b) in the spectrum?
(c). Which carbon atom gives the peak labeled (c) in the spectrum?
(d). Explain how you have assigned the peaks in this manner.