Humboldt State University ® Department of Chemistry

	Fundamentals of Chemistry
	© Humboldt State University
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Atomic Orbitals

 

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 descibed 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.

• 1s The 1s orbital has a single node at infinity, as can be seen in the Y² 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 Y² 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! (Caution, if you're off campus note the size of this movie - it will take a while to download!)

• 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-orbitlas have identical plots except that they are rotated to lie along the y and z axis respectively.

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.

• 3p Note that the 3p orbitals have a spherical node in addition to the planar node through the nucleus and the spherical node at infinity.

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 3d_z² has two nodal cones, giving two lobes and a "donut").

Sample orbitals for n = 1-6

Sample orbitals for n = 1-6 have also been prepared to demonstate size relationships and the increasing complexity of orbitals as n increases. Orbitals in the rest of the Periodic Table are also related to the hydrogenic orbitals.

f-orbitals

A set of f-orbitals have also been prepared for your enjoyment and aesthetic pleasure. Click here and enjoy!

© R A Paselk

Last modified 4 June 2001