8.2 The Quantum-Mechanical Model and the Periodic Table
Key Information in the Periodic Table
-- Among the main group elements (A groups), the A number equals the number of outer electrons -- The period number is the n value of the outermost s and p sublevels. [period number - 1] is the n value of the outermost d sublevels. [period number - 2] is the n value of the outermost f sublevel. --For an energy level, the n value squared is the number of orbitals, and 2n^2 is maximum number of electrons.
First Rule for Electron Configurations of Transition Elements
1. EFFECTS OF SHIELDING ON SUBLEVEL ENERGY--In any period, the ns sublevel fills before the (n-1)d sublevel. The switch in filling order is due to shilding and penetration effects. Based on (n-1)d radial probability distribution, an electron in this orbital spends most of its time outside the filled inner (n-2), (n-3), etc. levels. Therefore, the (n-1)d electron is shielded very effectively from the nuclear charge, (it is therefore easier to remove and is said to be at a higher energy level than ns).
What are the two common ways to indicate the distribution of electrons in the sublevels?
1. Electron Configuration--consists of principle energy level (n value), the letter designation of the sublevel (l value), and the number of electrons in the sublevel, written as a superscript. 2. Orbital Diagram--a depiction of orbital occupancy in terms of electron number and spin shown by means of arrows (+1/2 is up arrow, -1/2 is down arrow) in a series of small boxes or on a series of short lines (nl designation shown beneath).
Summary
1. In applying the aufbau principle, one electron is added to an atom of each successive element in accord with the exclusion principle (no two electrons can have the same set of quantum numbers) and Hund's rule (orbitals of equal energy bcome half-filled, with electron spins parallel, before any pairing of spins occurs). 2. For the main-group elements, valence electrons (those involved in reactions) are in the outer (highest energy) level only. For transition elements, (n-1)d electrons are also considered valence electrons. 2. Because of shielding of d electrons by electrons in inner sublevels and penetration by the ns electron, the (n-1)d sublevel fills after the ns and before the np sublevels. 3. In Periods 6 and 7, (n-2)f orbitals fill between the first and second (n-1)d orbitals. 4. The elements of a group have similar outer electron configurations and similar chemical behavior.
Second Rule for Electron Configurations of Transition Elements
2. EFFECTS OF PENETRATION ON SUBLEVEL ENERGY--the outermost ns electron penetrates closer to the nucleus than the (n-1)d sublevel for part of the time. As a result, the ns orbital is slightly lower in energy than the (n-1)d orbital.
Inner Electrons
Core Electrons --Electrons that fill all the lower energy levels of an atom except the valence level; electrons also present in atoms of the previous noble gas and any completed transition series.
Outer Electrons
Electrons that occupy the highest energy level (highest n value) and are, on average, farthest from the nucleus.
Separation of Degenerate Orbitals at the n=3 energy level
Even though the n=3 level spits into 3s, 3p, and 3d sublevels, Period 3 only fills 3s and 3p; 3d is filled in Period 4.
Exceptions to Electron Configurations of Transition Elements (Period 4)
Filling of the 3d orbitals proceeds one electron at a time, as with the p orbitals, except in two cases, Chromium (Z=24) and Copper (Z=29)
Remark: Following Aufbau Principle: Boron
Keep in mind that the fifth electron of boron can go into any one of the 2p orbitals. But, by convention, we start on the left and place the fifth electron in the ml=-1 orbital.
Hund's Rule
Principle. States that when orbitals of equal energy are available, the electron configuration of lowest energy has the maximum number of unpaired electrons with parallel spins.
How is the periodic table built?
The periodic table is built "from the ground up." It is completed by determining the ground-state electron configuration of each element--the lowest energy distribution of electrons in the sublevels of its atoms.
What is the basis for recurring patterns in chemical behavior?
The recurring pattern in electorn configurations is the basis for recurring patterns in chemical behavior.
Transition Elements
Transition elements are elements that occupy the d block or the f block (inner transition element) of the periodic table.
Stability of Half-filled and Filled Sublevels (Period 4; Chromium)
Vanadium (Z=23) has three half-filled d orbitals ([Ar]4s^23d^3). However, the last electron of the next element, Chromium, does not enter a fourth empty d orbital to give [Ar]4s^23d^4. Instead, Cr has one electron in the 4s sublevel and five in the 3d sublevel, making both sublevels half-filled. This is a more stable state for Cr than completely filling the 4s sublevel. The next element, Manganese, returns to the original pattern and has a filled 4s sublevel.
Condensed Electron Configurations
contain the element symbol of the noble gas from the previous row in brackets, to represent its configuration, followed by the electron configuration of filled inner sublevels and the energy level being filled.
Partial Orbital Diagrams
show only the sublevels being filled for the period in question
Stability of Half-filled and Filled Sublevels (Period 4; Copper)
The 4s sublevel of Cu is half-filled with one electron, and the 3d sublevel is filled with 10. From the exceptions of Chromium and Copper, we can conclude that half-filled and filled sublevels are unexpectedly stable (low in energy).
Aufbau Principle
The conceptual approach for building up atoms by adding one proton at a time to the nucleus and one electron to the lowest energy sublevel that is available, to obtain the ground-state electron configurations of the elements. (of course, one or more neutrons are also added to the nucleus)
Valence Electrons
The electrons involved in compound formation; in main-group elements, the electrons in the valence (outer) level.
