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At the beginning there was hydrogen. Hydrogen atom that is for which the Schrรถdinger equation can be solved exactly and from which we know the shapes and energies of atomic orbitals, at least  for atoms and ions with exactly one electron. Unfortunately, most of the interesting chemistry involve atoms with multiple electrons. Fortunately, atomic orbitals of other atoms (or ions) generally "look" like those of hydrogen atom. 

Take for example into consideration the case of carbon atom. It has 1s orbital filled with 2 "core" electrons and additional 4 valence electrons, two of them in 2s oribital and one each in two 2p orbitals (perpendicular to each other). It also has +6 positive charge in the nucleus  (6 protons).  All electrons are attracted by the nucleus, although not equally (see below), and all electron repel each other, trying to minimize that repulsion by staying as far from each other as possible within the confines of their orbitals.

Lets start with the nuclear charge. In the first very crude approximation, each electrons is attracted to the nucleus six time stronger than an electron with the same quantum numbers in the hydrogen atom.  Its most probable separation and orbital size would have diminished about 6 times and its energy would dropped even more drastically (the energy is proportional to the square of the nuclear charge and inversely proportional to separation distance).  However, that "shrinkage: has to be corrected by the fact that bringing electrons closer to the nucleus increases electron-electron repulsion as their separation decreases in the small orbitals. Thus, the shrinking is somewhat less that the number given in the previous sentence would suggests. 

But even that adjusted picture is not correct for all electrons.  The core electrons are attracted by the full +6 charge and indeed their energy is lowered so much that they do not participate in any bonding interactions (that is why they ale called core electrons).  They "wrap" around the nucleolus in a spherical orbital screening (shielding) the 2s and 2p electron from the full charge. In a slightly better approximation, these valence electrons will feel the diminished nuclear charge of about +4. Thus the 2s and 2p orbitals will "shrink" less and have their energy lowered less than the effects observed on the core orbital. 

There is a simple set of rules (Slater rules)  that allows one to estimate the effective nuclear charge felt by electrons in a given shell, but even that set does not take into account shielding  within the same shell.  In our carbon example, the 2s electrons are on average a bit closer  the nucleus than 2p electrons and shield them as well. The 2p electrons are in perpendicular orbitals and do not shield each significantly,   Based on even more sophisticated calculations, the effective charge, Zeff, for different electrons in carbon atom are: 5.67 for 1s electrons, 3.22 for 2s electrons, and 3.14 for 2p electrons.

The picture is worth a 1000 words (and a few hundred numbers). We have used these sophisticated calculations to generate models of atomic orbitals (valence s and p only) for several elements of interest to organic chemists. The models are to scale, just click and compare! Remember that within each type (s or p) the energy of the orbital is related to the average separation between electrons and nucleus (i.e. orbital size); with larger orbitals having higher energies.  Notice also how orbital sizes follow the electronegativity trends.

 
s orbitals
         
 
 
         
         
 
       
       
p orbitals
s orbitals
         
 
 
         
         
 
       
       
p orbitals
 
 
Molecular Gallery Last updated 08/31/11 Copyright 1997-2013
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