Main features of the quantum mechanical model of atom

Pulling together everything the Schrödinger equation implies about the atom, five key features define the quantum mechanical model:

1. Electron energy is quantised. As with Bohr's model, the energy an electron can have inside an atom is restricted to certain discrete values - but here that restriction falls directly out of the mathematics of the wave equation rather than being assumed.

2. The quantisation is a direct consequence of the electron's wave nature. The existence of quantised energy levels isn't a separate extra rule; it is exactly what you get when you demand well-behaved solutions to a wave equation, which is why solving the Schrödinger equation gives you the allowed energies (orbits) automatically.

3. Position and momentum give way to the concept of an orbital. Because Heisenberg's principle rules out ever knowing an electron's exact position and momentum simultaneously, quantum mechanics replaces the classical idea of a fixed orbital path with the idea of an orbital: a three-dimensional region of space around the nucleus within which the probability of finding the electron is at its maximum.

4. The wavefunction $\psi$ represents an orbital. Each valid solution of the Schrödinger equation for an allowed energy gives a wavefunction $\psi$, and this $\psi$ is what we call an atomic orbital - it is the mathematical object that fully describes the electron's wave behaviour while it occupies that orbital. …