Final answer:
The modern description of the atom, based on Schrödinger's mathematical equation, is called the quantum mechanical model, which describes electrons using probabilistic wavefunctions.
Step-by-step explanation:
The Quantum Mechanical Atomic Model
The modern description of the atom is known as the quantum mechanical model. Developed by Austrian physicist Erwin Schrödinger in 1926, this model arose from solving a mathematical equation that described the behavior of electrons with both wave and particle characteristics. In distinct contrast to previous atomic models, the Schrödinger equation introduced electron locations as probabilistic, rather than specific fixed orbits.
According to this model, electrons are described as three-dimensional stationary waves or wavefunctions. These wavefunctions, represented by the Greek letter psi (Ψ), are not physical waves but complex probability amplitudes. The square of the wavefunction's magnitude (|Ψ|2) indicates the likelihood of finding an electron in a particular region around the nucleus, defining the electron's probable location rather than a certain path.
The quantum mechanical model is foundational in modern chemistry and physics as it accurately explains the behavior of atoms and particles at subatomic levels, diverging from the oversimplified Bohr model by providing a more complex and accurate depiction of electron distributions and chemical bond formation.