NAME _________________________________________ UNIT 6 (2): QUANTUM AND PES
I-VIII) Review -Electron Configuration and Magnetic Properties of Ions
The following section bridges our work on quantum mechanics with periodic trends due to its connection with ionization energy). It also connects
with spectroscopy. Spectroscopy is the study of the interaction of light with matter … Matter interacts differently with light of different energies and
hence there are a number of different methods. This is about one of those methods … PES, or photoelectron spectroscopy.
IX) The interaction between charged objects is a non-contact force that acts over some distance of separation.
Every electrical interaction involves a force that highlights the importance of the quantity of charge of
one object, charge, the quantity of charge on a second object and the distance between the two
objects.
The interaction can be between a balloon and your hair … it does not matter, there are always two charges
and a distance between them as the three critical variables that * influence the strength of the interaction.
http://www.physicsclassroom.com/Class/estatics/u8l3b.cfm
A) This interaction in classic physics has been expressed (popularly) as a relative of Newton’s Law of
universal gravitation
1) Coulomb’s Law: an estimate of the relative forces of attraction between two charged
particles such as a nucleus and an electron.
Check Out:
https://www.youtube.com/watch?v=yUPdtFqilXo&index=4&list=PLllVwaZQkS2op2kDuFifhStNsS49LAxkZ
a) Coulomb’s law states that the force of attraction between two charged particles is
related to the *magnitude of their charges and the distance between them.
F = kQ1Q2/d2
where k = 9.0 x 109 N∙m2/C2
Q = a charge in Coulombs
F = Force in Newton
d = distance in meters
A variation on the above is: Energy between particles = k Q1Q2/d
Thus Coulomb’s law & its variation tells us 2 things:
Coulomb’s law predicts that the force of
attraction for electrons by the nucleus is
proportional to the magnitude of the charges
which means:
The greater the charges of the particles, the
greater the coulombic forces between them.
The energy between the nuclear charge and the
electrons is inversely proportional to the
distance between them.
which means
The closer the particles are to each
other, the greater the attraction.
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b) Differences between Newton’s Law of universal gravitation and Coulomb's law:
i) The constant (k) is significantly greater than Newton's universal gravitation
constant (G) Thus a unit of charge will attract a second unit of charge with
significantly more force than a unit of mass will attract a unit of mass.
ii) Gravitational forces are only attractive; electrical forces can be either
attractive or repulsive
http://www.physicsclassroom.com/Class/estatics/u8l3b.cfm
c) Now really, Coulomb’s law does NOT apply to calculations for interactions between
electrons … but we can use it as a guide for our approach. And because of this
impact we call the interactions between charged particles coulombic forces
i) It does NOT apply to calculations for electrons because…Coulomb’s law is
from classical physics & electron behavior is governed by quantum mechanics
3) As written: The energy between particles can be expressed in a similar equation to
Coulomb’s law ….E = k Q1Q2/d
B) Ionization energy: The energy (in kJ/mol) required to remove 1 mol of electrons from the ground
state of 1 mol of atoms, in the gaseous phase.
C) Coulomb’s law & Ionization Energy: Put these two ideas together and we can infer that
1) *the farther an electron is from the nucleus, the lower the energy required to remove that
electron (the lower the ionization energy)
2) Electrons close to the nucleus are held with a * greater force
than those
that are more distant from the nucleus.
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3) Lastly, *higher positive nuclear charges draw electrons closer to the nucleus and hold them
with a greater force.
…. thus we come back around, full circle to this being about charge, a second charge and
distance
X) Photoelectron spectroscopy (PES): an experimental method used to measure the energies of electrons in
atoms. These energies, called binding energies or ionization energies,
give direct experimental evidence of the shell model of the atom
A) Recall: Light consists of photons, each of which has energy E= hν, where h is Planck’s constant and
ѵ is frequency of the light.
Recall: In the photoelectric effect, incident light ejects electrons from a material. This requires the
photon to have sufficient energy to eject the electron.
B) Photoelectron spectroscopy *determines the energy needed to eject electrons from the material
in the gas phase
1) Measurement of these energies provides a method to deduce the shell structure of an atom.
essentially, the 1s, 2s, 2p … sublevel and orbital notation
associated with quantum mechanics
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2) The intensity of the photoelectron signal at a given energy is a * measure of the number of
electrons in the energy level.
a) Thus: *The size of the spectrophotometric peaks relates to the # of electrons
\
in the subshell (sublevel).
C) PES provides information on all the occupied energy levels of an atom (the ionization energies
of all electrons in the atom) …. It uses photons (packets of light energy) to knock an electron or
electrons out of an atom.
1) PES works like the photoelectric effect except that the sample is in the gas phase.
When a very high-energy ultraviolet photon of a known energy bombards a gaseous atom in a
vacuum, the photon ejects an electron. The ionization energy (binding energy) of the electron
is calculated using:
Ionization energy = (energy of the photon) – (kinetic energy of the electrons)
2) A typical photoelectron spectrometer uses high-energy photons of about 12,000 kJ/mol.
a) Any ionization energy less than the bombarding photons can be read by the
spectrophotometer. …. For this reason, there are limits to PES …These
limitations deal with electrons, so tightly bound to their nucleus that their
ionization energies exceed 12,000 kJ/mol (more later)
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3) A photoelectron spectrum of an atom is a graph showing energy on the x-axis and relative
number of electrons on the y-axis. Below are 5 graphs of 5 different elements.
From: Pearson Education Test Prep: Ap Chemistry p110
 Each signal or peak in a photoelectron spectrum *represents the energy of one or more
electrons in a given energy subshell (sublevel).
Translation: The # of peaks = # of subshells, with the subshell closer to the nucleus as
the peak farther to the right. …. Check out the graph of Li with a 1s2 2s1
electron configuration.
The *intensity
of each signal at a given energy is interpreted as the
relative number of electrons in that energy level.
e.g.) The 6260 kJ signal in the lithium photoelectron spectrum is twice the size as the
520 kJ peak. This means that there are

twice as many electrons in one subshell compared to the other.

The larger energy peak corresponds to 2 electrons in the 1s subshell because
they are close to the nucleus and held with a larger force than the one
electron in the 2s sublevel represented by the 520 kJ signal.
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4) Thus PES provides direct evidence for the shell model of the atom and is a useful means to
rationalize and explain periodic properties and trends.
5) Electron configurations of atoms with multiple electrons can be inferred from photoelectron
spectra. BUT!! PES has its limitations.
PES fails to isolate the 1s2 electrons from atomic numbers 4 and higher … and the 2s from
atomic number 13 and higher…
a) Essentially the respective electrons are bound so tightly to the nucleus that the
ionization energy required to remove the electrons exceeds the 12,000 kJ/mol
photons typically used the photoelectron spectrophotometers.
Thus often, the 1s or 2s electrons do not correspond to any signals in a reading.
A higher energy technique, called x-ray photoelectron spectroscopy (XPS) is used
to probe the inner-core electrons on solid surfaces.
Take a look at: http://www.chem.arizona.edu/chemt/Flash/photoelectron.html
TRY THIS!!!!
The photoelectron spectra shown here,
show the energy required to remove a 1s
electron from a nitrogen atom and from
an oxygen atom. Which of the following
statements best accounts for the peak in
the upper spectrum being to the right of the
peak in the lower spectrum?
A) Nitrogen atoms have a half-filled p subshell
B) There are more electron-electron repulsions in oxygen atoms than in nitrogen atoms.
C) Electrons in the p subshell of oxygen atoms provide more shielding than electrons in the p
subshell of nitrogen atoms
D) Nitrogen atoms have a smaller nuclear charge than oxygen atoms.
Think… the binding energy of the oxygen atom’s electron is greater than that of the nitrogen’s …
what would account for a greater binding energy? ans: *D
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TRY THIS!!!! Given:
1) Explain what each of the peaks in the photoelectron spectrum of boron signifies:
*Each peak in the spectrum represents the relative number of electrons and the energy they have.
2) For each signal in the photoelectron spectrum of boron, assign an orbital designation from the
electron configuration.
*The peak at 800 kJ/mol represents 1 electron in the 2p subshell, and the peak at 1360 kJ/mol represents
two electrons in the 2s subshell
3) Use Coulomb’s law to explain why the signal in the helium spectrum is at a higher energy than
the signal in the hydrogen spectrum.
*The electrons in the 1s subshell of helium are held more strongly by the nuclear charge than
the electron in the 1s subshell of hydrogen because the nuclear charge of helium is superior to that of
hydrogen. Coulomb’s law predicts that the force of attraction for electrons by the nucleus is
proportional to the magnitude of the charges
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TRY THIS!!!! For 1 -5 use the following table as a source of information and insight.
1) Why are the values for the 1s electrons missing? * The 1s electrons are held so tightly to the
nucleus for the elements with strong nuclear charges (as in this case, atomic number 11 – 21) that PES
will not measure the ionization energies, which must be superior to the normal 12,000 kJ/mol. Any
electron with a binding energy (ionization energy) greater than 12,000 kJ/mol, cannot be ejected by
the PES system.
2) Why are the values for the 2s electrons from aluminum through scandium missing, but do exist
for sodium and magnesium?
* Very similar to 1… The nuclear charges of aluminum through scandium are greater than that of
sodium and magnesium, so the ionization energies of the closely held electrons in the 2s subshell are
greater than the energy of the ionizing photons of the PES process.
3) How do the listed values for magnesium give evidence for the shell model of the atom? *In Mg, the
ionization energies decrease as the subshells increase from 2s, 2p, 3s etc… The data show that the
electron ioniziation energies fall into different energy levels or shells
KEEP GOING!!!!
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4) Use Coulomb’s law to explain why sodium’s 3s energy value is lower than its 2s subshell.
*The 2s e- is farther from the +11 nuclear charge than are the 2s electrons. Coulomb’s law states
the energy between the nuclear charge and the electrons is inversely proportional to the distance
between them. … The greater the distance from the nucleus, the higher the energy and thus the lower
the required ionization energy.
5) Determine the trend in energy values from left to right along the row corresponding to the 3s
subshell.
* From left to right, the orbital ionization values (binding energies) increase with increasing
nuclear charge.
For a different voice on the issue try: https://www.youtube.com/watch?v=NRIqXeY1R_I This is quite nice, as
the narrator cleanly aids you in understanding more complicated spectra (check it out, at 2 minutes 15 seconds)
You may also try: https://www.youtube.com/watch?v=tpNbBV7Hk6k This is a YouTube video, from LPS
Chemistry.
References and Annotated Reading
Waterman E. L.: Pearson Education: AP Chemistry 2015 p. 109-113
http://www.physicsclassroom.com/
http://www.chem.qmul.ac.uk/surfaces/scc/scat5_3.htm
http://www.tech-faq.com/photoelectron-spectroscopy.html
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