Humboldt State University ® Department of Chemistry

Richard A. Paselk


Atomic Orbitals*

Richard A. Paselk

Atomic Structure: a short review

Atomic structure is characterized/determined by the Atomic number, Z, which tells us how many electrons and protons the free atom has.

Quantum mechanics is necessary to provide a more detailed picture of atomic structure. To explore the electronic substructure of atoms in a rigorous fashion we must first look at the simplest atom, hydrogen. It turns out the only hydrogens electronic structure can be determined exactly because our mathematics does not allow the exact calculation of problems involving more than two bodies (the nucleus and one electron).

Within an atom electrons reside in regions of space described as Atomic Orbitals. The discussion below looks at hydrogenic atomic orbitals as models for the structure of the remaining atoms of the Periodic Table.

Orbital Symmetry Node geometry Spherical nodes/shell* Orbitals/set
s spherical spherical n 1
p cylindrical around x, y, or z axis 1 planar - perpendicular to axis of orbital; remainder spherical  n - 1 3
d complex 2 planar surfaces diagonal to Cartesian axis; remainder spherical  n - 2 5
f complex complex  n - 3 7
* n = the shell, with n = 1 the ground state or lowest possible energy shell. Thus n may have integral values from 1 - infinity.

Atomic Orbital Images

If you click on the images below you can also look at a movie of the orbital rotating in space. These images and movies are provided for your entertainment and greater insight. You might think of these images as the result of a strobe effect - they are what the orbitals and atoms would look like if we could take "strobe" photos of the electrons moving in their undeterminant paths! The orbital and atomic images included are rigorously calculated using the Schrödinger equation (they are all based on hydrogen, so only two particles are involved, the proton and one electron - we assume other atoms are similar). Each dot represents the result of solving this equation. (There are 10,000 dots in each orbital image. Because of the statistical nature of Quantum mechanics, on average two calculations were required for each dot, one kept, and one discarded. )

s orbitals

s orbitals are spherical, thus shield nuclei essentially completely (remember from physics, for a spherically distributed field, like gravity or charge, can consider all to reside at a point in the middle of the field. Thus a spherically distributed set of , say, 4+ charges and 2- charges will look like 2+ charges to the outside world! You can see the spherical nature of the 2s orbital in the figure.

p orbitals

p orbitals are bi-lobe shaped, with three in a shell along mutually perpendicular axis. The first image/movie represents the 2 px orbital. The second movie shows the three 2p orbitals and how they add up to a completely spherical distribution! (Caution, if you're off campus note the size of this movie - it will take a while to download!)



Notice that as the orbitals are added in this set that the px + py makes a "donut" of electron density, while the px + py + pz makes a fully symmetrical spherical shell of electron density.



d orbitals

d orbitals. There are five d-orbitals in each d orbital set. Each d-orbital has two planar nodes (regions of zero probability) dividing most of the orbitals into four lobes (the 3dz2 has two nodal cones, giving two lobes and a "donut").



Sample orbitals for n = 1-6

Sample orbitals for n = 1-6 are provided to demonstrate size relationships and the increasing complexity of orbitals as n increases. Orbitals in the rest of the Periodic Table are related to these hydrogenic orbitals.



A set of f-orbitals are provided for your enjoyment and aesthetic pleasure.

*The animations and visualizations on these pages are copyrighted. They were created by Mervin P. Hanson, Richard L. Harper, Richard A. Paselk and John B. Russell from calculations performed by Mervin P. Hanson. This work was supported by the National Science Foundation, Apple Computer, and Humboldt State University.

© R A Paselk

Last modified 23 November 2004