What is the shape of the p orbital?

The shape of the p orbital is indeed described as dumbbell-shaped. This shape arises from the way that the electron density is distributed in these orbitals.

In quantum mechanics, p orbitals are characterized by their angular momentum and are associated with the quantum number l = 1. Each p orbital has two lobes that extend in opposite directions from the nucleus, resembling a dumbbell. This configuration allows for the regions of high electron probability to be located along the axes, which is typical of the three types of p orbitals: px, py, and pz, each oriented along a different Cartesian axis.

The angular nature of the p orbitals enables them to participate in covalent bonding, where they may overlap with other atomic orbitals, thus contributing to the formation of molecules in specific geometries. Understanding the shape of p orbitals is crucial because it influences how atoms interact and bond with each other in various chemical reactions.