CHEMystery: Atomic Structure and Bonding: Shapes of Atomic Orbitals

Shapes of Atomic Orbitals

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The energies of atomic orbitals also describes their shapes. The shapes are uncertain, but predictions have been made by experimentation. Another difficult task is describing where an electron is. We can think of it as a wave, and describing its exact location is impossible for us to comprehend. Instead, we can think of it as the statistical probability of the electron being found at a particular place. An electron cloud is used for showing the probability of where an electron is using a dot-density diagram. The denser the dots are in the diagram, the more probability that an electron could be found there.
For example, these are dot-density diagrams for the s and p orbitals (cross sections):

s orbital

p orbital

Electron density relates to how much of an electron's charge is packed into a given volume. In dense places on the dot-diagram, there is a high concentration of electrical charge.
An s orbital's shape is spherical, but the p orbital's shape is quite different. They have two lobes extending out into three dimensional space. Since there are 3 p orbitals per energy level, the lobes extend out along the x-axis (p_x orbital), the y-axis (p_y orbital), and the z-axis (p_z orbital).

p_x orbital

p_y orbital

p_z orbital

The d orbital's shapes are even more complex because there are 5 orbitals in a d subshell. Four of the five d orbitals (d_xy, d_xz, d_yz, and d_x²-y²) have four lobes extending out perpendicular to each other. The last one, d_z², has two lobes extending out along the z-axis with a torus (doughnut-shaped ring) around the center on the x-y plane.