Final answer:
The s, p, d, and f orbitals differ in shape and orientation: s is spherical, p has a dum/bbell shape with three orientations, d orbitals have a four-lobed rosette or a dum/bbell with a torus, and f orbitals are complex with intricate shapes. Hybrid sp3 and sp3d2 orbitals also have unique characteristics, arranged tetrahedrally or octahedrally respectively.
Step-by-step explanation:
The differentiating characteristics for each of the spdf orbitals are based on their unique shapes and orientations in space. The s orbital, with a spherical electron density distribution, is the simplest of the orbitals. Each s subshell has just one orbital, which is spherically symmetrical around the nucleus.
The p orbitals have a dum/bbell shape with electron density concentrated in two lobes on opposite sides of the nucleus. There are three p orbitals in each p subshell, usually aligned along the x, y, and z axes. In contrast, the d orbitals are more complex with a four-lobed rosette shape and contain two nodal surfaces, except for the dz2 orbital, which has a dum/bbell with a torus shape around it. The d subshell has five such orbitals. Finally, f orbitals are even more complex with intricate shapes and three nodal surfaces, and there are seven f orbitals in each f subshell.
Hybrid orbitals like sp3 and sp3d2 also have distinct characteristics. When an s and three p orbitals mix, they form sp3 orbitals, which are arranged in a tetrahedral geometry and have two lobes along a straight line. Conversely, an ns orbital, all three np orbitals, and two nd orbitals can combine to create sp3d2 orbitals, which orient towards the vertices of an octahedron.