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.

• Z tells us what the element is, where it resides on Periodic table, and thus what its chemistry is like. Remember, Chemistry is due largely to the outer electrons of an atom!

• Atomic weight, AW, gives the mass of the individual particle, and has a subtle influence on chemistry. It has a greater influence on small mass atoms (a difference in neutron number has a greater % effect on mass), since chemical differences are due essentially to differences in vibrational modes of an atom in a covalent bond.

• Much of chemistry can be crudely understood by looking at size of atom and its nuclear charge "visible" to the outside world.

• Electrons around atoms are arranged in shells : regions of electron occupancy having the same average radial distance from the nucleus. As additional electrons are added additional shells are added making the atom larger. (Note that each additional shell shows up as a new period in the Periodic table.)

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.

Note to the User: the animations below are generally set to go through one cycle of rotation. After an initial viewing you may want to click on the scrollbar and arrow-keys to "step-through" the animations.

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 s orbital in the figure.

1s The 1s orbital has a single node at infinity, as can be seen in the psi-squared plot. You may also note that the cross-section shows a continuous decrease in the density of points as the radius increases.

2s Note the spherical node in addition to the spherical node at infinity. This is readily seen in the psi-squared plot, as well as in the shell with no dots in the cross section.

3s Note the two spherical nodes in addition to the spherical node at infinity. This is readily seen in the Y² plot, as well as in the shells with no dots in the cross section.

p orbitals

p orbitals are bi-lobe shaped, with three in a shell along mutually perpendicular axis. The first image/movie represents the 2 p_x orbital. The second movie shows the three 2p orbitals and how they add up to a completely spherical distribution!

2p_x The images below represent the 2 p_x orbital. Thus we readily see the planar node in the x-y plane as a region of zero probability for electron density (there are no dots, and the Y² plot goes to zero at x = 0). Note that the other two p-orbitals have identical plots except that they are rotated to lie along the y and z axis respectively.

2p orbital set

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

3p_x Note that the 3p orbitals have a spherical node in addition to the planar node through the nucleus and the spherical node at infinity (look carefully as the relative opacities of the red and white clouds can hide this).

3p orbital set

Notice that as the orbitals are added in this set that the p_x + p_y make "donuts" of electron density (the inner donut is so small it appears to be spherical in this animation), while the p_x + p_y + p_z makes a fully symmetrical spherical shell of electron density (look carefully as the relative opacities of the red and white clouds can hide this).

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 3d_z² 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.

The representative orbitals shown in the images below show how the nodes increase with increasing n, giving increasingly complex substructure to the orbitals. Note that though the orbital images and movies are all about the same size, the actual orbitals grow significantly with increasing values of n, as shown for the s-orbitals below. Note that the radii of the sets of the other orbitals will be similar.

s orbitals for hydrogen

The figure above shows scale drawings of the 90% probability spheres for the n = 1-6 s-orbitals for hydrogen.

Note that as n increases the number of possible orbital sets (geometries) increases, corresponding to the value of n, though we are only showing images for n= 1-4 geometries (s-f). For the d and f orbitals a single orbital shape was chosen to represent each set. Note that the geometries of the orbital set added above n = 4 will have even more complex shapes, since more than just three orthogonal and other axis are involved in determining symmetry.

For the orbital scatterplots below I am only including animations for n = 4 since the other orbital animations have already been seen above

Finally, I have included side-by-side animated comparisons of the p, d, and f orbitals for n = 5 and n = 6 to demonstrate the increasing complexity of these orbitals as n increases.

Electronic Configurations of Atoms with Z > 1

Under normal earth conditions atoms are in their ground state configurations, that is the electrons all occupy the lowest energy orbitals available. Of course only two electrons of paired spin may occupy an orbital. And electrons "spread out" to occupy as many orbitals in each subshell (orbital type) as possible.

For atoms with multiple electrons we assume the orbitals will be similar to those of hydrogen, thus the term "hydrogenic orbitals" for these atoms. We use hydrogenic orbitals for atoms with Z > 1 because we cannot calculate exact solutions for the orbitals of atoms with more than one electron - mathematically exact solutions are possible for the "two-body problem" but not for the "three-body problem" or above. However, approximate solutions are consistent with the hydrogenic orbitals.

Thus for atoms above hydrogen:

• We assume the orbitals for the outer electrons fill orbitals with shapes like those shown above for hydrogen. (There is some evidence, though controversial, for orbital shapes in metals in metals following the hydrogenic model. I invite you to search the internet for the current status of these images.)

• The radii of the orbitals will of course be much smaller than hydrogen's orbitals because of the greater nuclear charge attracting the electrons.

f-orbitals

A set of 4f-orbitals are provided below 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.