Question

Why do orbitals have different shapes?

Answer 1

orbitals have different shapes because....

Explanation:

1. s orbitals are wavefunctions with ℓ = 0. They have an angular distribution that is uniform at every angle. That means they are spheres.
2. p orbitals are wavefunctions with ℓ = 1. They have an angular distribution that is not uniform at every angle. They have a shape that is best described as a "dumbbell"
3. There are three different p orbitals that are nearly identical for the three different mℓ values (-1,0,+1). These different orbitals essentially have different orientations.
4. d orbitals are wavefunctions with ℓ = 2. They have an even more complex angular distribution than the p orbitals. For most of them it is a "clover leaf" distribution (something like 2 dumbbells in a plane).
5. There are five different d orbitals that are nearly identical (n=2, ℓ =1) for the five different mℓ values (-2,-1,0,+1,+2). These different orbitals essentially have different orientations. There is one that is a little
6. As n increases there are ever larger available ℓ numbers. These give even more complex angular distributions with more angular nodes. After the d orbitals ℓ=2, come the f ℓ=3, then g ℓ=4, then hℓ=5, .... different than the others (this is the mℓ=0)