Electron Configurations

Electron
Configurations
Curtis Musser
Cate School
Carpinteria, California
Periodic Nature of the Elements
Electron configurations determine the properties of the atoms.

What Determines the Electron
Configuration?
• Energy of the electron
• Available orbitals
To find the electron arrangements,
one needs to know the relative energies of the orbitals.
What factors determine the energies, however?

The Three Energy Factors
• Effective nuclear charge (Z*)
• Distance
• Electron-electron electron repulsion
The first is the attraction of the nucleus for the electron, which is directly related to the
effective nuclear charge Z*.
A second factor is the distance the electron is from the nucleus, I.e., the “orbital radius.”
Finally, the close proximities of electrons can disturb nuclear-electron attractions. In the latter
electron-electron repulsion is intraorbital (or intrashell) as opposed to shielding in Z* which is
interorbital (or intershell).

Effective Nuclear Charge
• Z* = Z - Shielding by
electrons
A Simple Approximation:
• Z* = Z - core electrons.
The effective nuclear charge is the
charge “seen” by the electron. It is
the charge of the positive nucleus
minus the repulsions of the other
electrons in the atom. In a simple
Bohr atom you might simplify this
to the charge of the nucleus (Z)
minus the number of core
electrons. This of course assumes
perfect shielding from the core
electrons and none by the other
valence electrons.

Z* and the 1st and 2nd Ionization
• 1st I.E. of Na = 495 kJ/mol
Z* 3rd shell = 11 - 10 = 1
Energy of Sodium
• 2nd I.E. of Na = 4560 kJ/mol
Z* 2nd shell = 11 - 2 = 9
Z* 2nd shell
9(495) = 4455
To illustrate the simple calculation of Z*, look at the
ionization energies of sodium. The first electron to be
removed is in the third shell. The charge of the nucleus is
+11 and there are ten core electrons. This gives a Z* of
+1. The second electron must come from the second
shell, there are now only two core electrons, those of the
first shell. The Z* for this electron is +9. Notice that the
second ionization energy is about nine times that of the
first. This type of calculation is an over-simplification, but
it gives a good approximation.
11+

Z* Trend:
Increases going to the right on the periodic table
12+ • Z* 3rd shell Mg = 12 - 10 = 2
Z* 3rd shell Al = 13 - 10 = 3
13+
• If one continues this approximation
going across the periodic table, in
this case- the third period, one sees
that Z* increases incrementally.

Z* Trend:
Little change going down the periodic table
3+
11+
• Z* 2nd shell Li = 3 - 2 = 1
• Z* 3rd shell Na = 11 - 10 = 1
Z* 3rd shell Na
However, going down, the Z* remains the same.
Again, this is using the Bohr model, and it assumes
perfect shielding by the core electrons. ectrons.

Radial Probability
The radial probability is the “density”
of the electron cloud as you travel
out from the nucleus.
e.g., the 1s1
orbital
In reality the electrons of orbitals can
be found at varying distances from the
nucleus. That distance depends upon
the charge of the nucleus, the principle
quantum number of the orbital, and
shape of the orbital. This plot shows
the electron cloud of the 1s orbital with
a plot of the radial probability above--
the radial probability is the likelihood of
the electron to be at that distance from
the nucleus. In this case the spherical
orbital is hollow, which cannot be
discerned from the three-dimensional
model.

Radial Probability and Higher Order Orbitals
As you get to higher order
orbitals, , the average
distance the electron is
from the nucleus
increases, but there is
some overlap.
Here is the radial probability
of the 3p3
x orbital
Notice that at certain times the electrons of
higher order orbitals could be inside (I.e.,
closer to the nucleus) than lower order
orbitals.

Orbital Overlap
Here is an illustration of the overlap possible for the 2p and 3p orbitals.
The y-axis is the radial probability.

Z* versus Z
The black line represents the simple approximation of Z* base upon the Bohr model.
The red line is based upon empirical measurements in the gas phase. There are several things to notice
here. H, Li, and Na have similar Z* values. Also, B, which now has 2s and 2p orbitals in the valence shell,
has a slightly lower Z* than Be. The 2p electron on average is a bit farther from the nucleus; thus it is
shielded slightly more. Finally, in atoms with doubly occupied orbitals, there is some electron-electron
repulsion within the orbitals. (For more, see page 319 of Zumdahl)

First Ionization Energy vs Z
2500
2000
Z* increases going ->
1500
1000
500
0
3 4 5 6 7 8 9 10
Atomic Number (Z)
Note, the first ionization energy of B is less than that of Be because the 2p is
shielded more than the 2s. Notice the similarity of the pattern of Z* to that of the
ionization energy of the atoms. Again, those atoms with doubly occupied orbitals
have slightly less than expected ionization energies due to electron-electron
repulsions within the orbitals.

Ionization Energy and Distance:
1st Ionization Energy in kJ/mol
Group 1 Group 2
Li 520 Be 900
Na 495 Mg 738
K 419 Ca 590
Rb 409 Sr 550
Cs 382
Ba 503
Going down a group, Z* remains fairly constant--if anything it increases slightly due to incomplete shielding by
core electrons. However, the ionization energies decrease due to the greater distance the electron is from the
nucleus.

Rules for Arranging Electrons
• Aufbau Principle
• Hund’s Rule
• Pauli Exclusion Principle
To take a closer look at the electron configurations, one needs to know the three basic rules for
arranging the electrons. The aufbau principle (or aufbauprinzip), introduced by Bohr (1920) tells
us to fill the orbitals form lowest energy to highest for atoms in the ground state--aufbau is German
for building-up. Hund’s rule tells us that we fill degenerate orbitals singularly with electron spins
parallel before pairing. This minimizes electron-electron repulsions while allowing for favorable
magnetic interactions. Finally, the Pauli exclusion principle reminds us that no two electrons in an
atom can occupy the same space with similar spin to its partner. This is because the electrostatic
and magnetic repulsions would be too great.

“Normal” Electron Configurations
1s 2s 2p 3s 3p 4s 3d 4p 5s . . . .
5s 5p 5d 5f 5g
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
To find “normal” electron configurations, one can use the periodic table
or the simple chart above. To satisfy the aufbau principle, the “normal”
order of the energy levels can be found by drawing diagonal lines up and
to the left. By the way, the symbols for the types of orbitals come from
spectroscopy: s - sharp; p - principle; d - diffuse; f - fundamental.

In reality, the order of lowest to
highest energy orbitals changes
greatly for NEUTRAL atoms as the
nuclear charge increases and the
shielding of the core electrons
changes. Note that for the single
electron atom H, there are no
differences in the sublevels of the
shells. This becomes nearly true
again for the inner most core shells of
larger atoms as the subshells
coalesce. Also, note that energy
levels cross over each other as the
nuclear charge changes and orbitals
shrink in size. (For more, see page 39
Cotton and Wilkinson, Basic Inorganic
Chemistry)

Exceptions to “Normal” Electron
Configurations Due to Electron-Electron
Repulsions
[Ar]4s 1 3d 5
For example, Cr
not [Ar]4s 2 3d 4
3d ___ ___ ___ ___ ___
4s ___
3d ___ ___ ___ ___ ___
4s ___
• The energy of repulsion is greater than the energy
difference between the energy levels
For Cr (Z=24), the 3d sublevel is only slightly higher in energy than the 4s sublevel. The electronelectron
repulsions of paired electrons in the 4s is enough to cause the electron to jump to the sightly
higher 3d sublevel.

Other Exceptions Due to
Electron-Electron Repulsions
Nb [Kr]5s 1 4d 4
[Kr]5s__ 4d __ __ __ __ __
Mo [Kr]5s 1 4d 5
[Kr]5s__ 4d __ __ __ __ __
Gd [Xe]6s 2 4f 7 5d 1
2
[Xe]6s 4f __ __ __ __ __ __ __ 5d __ __ __ __ __
Cm [Rn]7s 2 5f 7 6d 1
2
[Xe]7s 5f __ __ __ __ __ __ __ 6d __ __ __ __ __
This phenomenon can be seen with several other elements of the periodic table. All of these
elements can exhibit ferromagnetism due to their large number of unpaired electrons. In fact Gd(III)
([Xe]4f7) is used as an MRI contrast agent due to its high number (seven) of unpaired electrons.

Exceptions to “Normal” Electron
Configurations Due to Energy Level
Inversions
e.g., ., Cu [Ar]4s 1 3d 10 or [Ar]3d 10 4s 1
4s ___
but not [Ar]4s 2 3d 9
3d ___ ___ ___ ___ ___
As the nuclear charge grows, the inner shells contract. This creates inversions of energy levels.
In the cases in which these inverted energy levels are only partially full, there will be exceptions
to the normal pattern on electron configurations. In the case of copper, the 4s is higher in energy
than the 3d. Note, that one might want to write the electron configuration with the 3d preceding
the 4s to abide by the aufbau principle. The loss of the 4s electron accounts for the Cu(I)
oxidation state.

Other Exceptions Due to Energy Level Inversions
Pd [Kr]5s 0 4d
Ag [Kr]5s 1 4d
Au [Xe]6s 1 4f
4d 10 or
4d 10 or
4f 14 5d 10 or
[Kr]4d 10 5s 0
[Kr]4d 10 5s 1
[Xe]4f 14
14 5d 10 6s
6s 1
La [Xe]6s 2 4f 0 5d 1
or
[Xe]6s 2 5d 1 4f 0
Ac [Rn]7s 2 5f 0 6d 1
or
[Rn]7s 2 6d 1 5f 0
Th [Rn]7s 2 5f 0 6d 2
or
[Rn]7s 2 6d 2 5f 0
Other exceptions to the normal trend of electron configurations can explain many of the
oxidation states of the respective atoms. Palladium, sometimes know as one of the
Noble metals can be often be found as Pd(0). Silver has a 1+ oxidation state. You may
also note that some periodic tables place lantium and actinium in the d-block.

Exceptions Due to Both Electron-
Electron Repulsions and Energy Level
Inversions
e.g.,
., Tc
[Kr]5s 1 4d 6 or [Kr]4d 6 5s 1
5s ___
4d ___ ___ ___ ___ ___
In some cases, both the energy level inversion and electron-electron
repulsion cause variations form the normal electron configurations. In this
example technetium’s 4d is slightly lower in energy than its 5s; however, an
electron gets promoted from the 4d to the 5s due to electron-electron
repulsion.

Other Exceptions Due to Both Electron-
Electron Repulsions and Energy Level
Inversions
Ru [Kr]5s 1 4d 7
or
[Kr]4d 7 5s 1
Rh [Kr]5s 1 4d 8
or
[Kr]4d 8 5s 1
Pt [Xe]6s 1 4f
4f 14
5d 9
14 5d
or
[Xe]4f 14 5d 9 6s 1
As was seen in technetium, the same thing happens to its neighboring fifth period
elements, ruthenium and rhodium. The energy level inversion is delayed until later in
the sixth period and only platinum is affected.

Fe [Ar]4s 2 3d 6
The Oxidation States of Iron
3d ___ ___ ___ ___ ___
4s ___
Fe 2+ [Ar]3d 6 4s 0
4s ___
3d ___ ___ ___ ___ ___
Fe 3+ [Ar]3d 5 4s 0
4s ___
3d ___ ___ ___ ___ ___
Most transition metals have a 2+ oxidation state although in the atom they often have more than two electrons in
their highest energy level, nd. The reason being is that the energy levels invert in the ion. Note, the inversion of
the 4s and 3d energy levels in Fe(II). Iron has the additional oxidation state of 3+ due to the loss of the electron
from the 3d that suffers electron-electron repulsion of its partner.

A Few More Examples of Periodic Properties
• Atomic radius
• Decreases going right due to increased Z*
• Increases going down due to added shells
• Electronegativity
• Increases going right due to increased Z*
• Decreases going down due to increased distance
• Electron Affinity
• Increases going to the right due to increased Z*
• Increases going down due to decreased electron-electron repulsion in the larger
valence orbitals
• Exceptions due to added subshells or shells
Almost all periodic properties as well as other unique atomic
properties can be explained by explain by using electron
configurations and the three factors effecting electron energy: Z*,
distance from the nucleus, and electron-electron repulsion. Having
students use and understand these factors gives the the tools to
make predictions of chemical and physical behavior of atoms.

Conclusion
Electron configurations along with
• Effective nuclear charge (Z*)
• Orbital radius (distance)
• Electron-electron electron repulsions
can explain most physical and chemical
properties and their periodic trends.

Thank you!