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 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 Energy of Sodium
1st I.E. of Na = 495 kJ/mol Z*3rd shell = 11 - 10 = 1
2nd I.E. of Na = 4560 kJ/mol Z*2nd shell = 11 - 2 = 9 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 overover-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+
Z*2nd shell Li = 3 - 2 = 1 Z*3rd shell Na = 11 - 10 = 1 However, going down, the Z* remains the same. Again, this is using the Bohr model, and it assumes perfect shielding by the core el ectrons. electrons.
11+
Radial Probability The radial probability is the “density” of the electron cloud as you travel out from the nucleus. e.g., the 1s 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 3px 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
Z* increases going -> 2000
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 For example, Cr [Ar]4s13d5
[Ar]4s23d4
not
3d ___ ___ ___ ___ ___
3d ___ ___ ___ ___ ___
4s ___
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]5s14d4
[Kr]5s__ 4d __ __ __ __ __
Mo [Kr]5s14d5
[Kr]5s__ 4d __ __ __ __ __
[Xe]6s24f75d1
[Xe]6s24f __ __ __ __ __ __ __ 5d __ __ __ __ __
Cm [Rn]7s25f76d1
[Xe]7s25f __ __ __ __ __ __ __ 6d __ __ __ __ __
Gd
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]4s13d10
or
[Ar]3d104s1
but not [Ar]4s23d9
4s ___ 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]5s04d10
or
[Kr]4d105s0
Ag [Kr]5s14d10
or
[Kr]4d105s1
Au [Xe]6s14f145d10
or
[Xe]4f145d106s1
La [Xe]6s24f05d1
or
[Xe]6s25d14f0
Ac [Rn]7s25f06d1
or
[Rn]7s26d15f0
Th [Rn]7s25f06d2
or
[Rn]7s26d25f0
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 ElectronElectron Repulsions and Energy Level Inversions e.g., Tc [Kr]5s14d6 or
[Kr]4d65s1
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 ElectronElectron Repulsions and Energy Level Inversions Ru [Kr]5s14d7
or
[Kr]4d75s1
Rh [Kr]5s14d8
or
[Kr]4d85s1
Pt [Xe]6s14f145d9
or
[Xe]4f145d96s1
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.
The Oxidation States of Iron Fe
[Ar]4s23d6
3d ___ ___ ___ ___ ___ 4s ___
4s ___
Fe2+ [Ar]3d64s0
3d ___ ___ ___ ___ ___
4s ___
Fe3+ [Ar]3d54s0
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 repulsions
can explain most physical and chemical properties and their periodic trends.
Thank you!
