Orbitals and quantum-derived structure — probability distributions, not paths

An orbital is a mathematical function whose square gives the probability of finding an electron in a region — not a path, not a container, not a shell of a specified radius. The conceptual difficulty is that the student is asked to abandon a picture (the Bohr circle) for a probability distribution, and to accept ordering rules (aufbau, Hund, Pauli) that look arbitrary because their justification is quantum-mechanical and out of scope. Hybridisation compounds this: sp³ orbitals are a mathematical recombination chosen because it reproduces observed geometry, not a physical process that happens to an atom.