Shapes of Atomic Orbitals

Shapes (aka Boundary Diagrams) of Atomic Orbitals

• There is one s orbital in a subshell, which is a sphere
• There are three p orbitals in a subshell, each orientated along an axis (px, py and pz)

• There are five d orbitals in a subshell. The shapes of the d orbitals are more complicated than their s and p counterparts.
• Three orbitals look like 3D cloverleaves, each lying in a plane with the lobes pointed between the axes (dxy, dxz and dyz).
• A fourth orbital is also a cloverleaf, but its lobes point along the axes ($d_{x^2-y^2}$).
• The fifth orbital looks quite different with its major lobes pointing along the z- axis, but there is also a “doughnut” of electron density in the xy plane ($d_{z^2}$)

Things to Keep in Mind:

• As the energy level increases, so does the size of the orbitals Example: A 2s orbital is higher in energy and larger than a 1s orbital
• As the energy level increases, so does the number of orbitals Example: when n=1 (lower energy level), we see 1 orbital, whereas when n=2 (higher energy level), there are 4 possible orbitals
• As the number of orbitals increases, so does their complexity Example: d orbitals are more complex than p orbitals

Drawing Atomic Orbitals

Shown below are the s, p and d orbitals:

• The angular momentum quantum number, l, gives us information about the shape of the orbital.
• Note: There are 5 d-orbitals and 5 allowed value for ml. Similarly for s and p the number of orbitals is determined by the # of allowed values of ml.
• Note: Each ml is not associated with a particular orbital (ex. dxy vs dxz). Which means given a set of quantum numbers (n,l,ml) one cannot determine which direction the orbital will be pointing