Final answer:
The wave mechanical model of an atom, or the quantum mechanical model, was developed by Erwin Schrödinger and is based on the wave-particle duality of electrons. It utilizes a wavefunction to describe the probability of an electron's position and adheres to the Heisenberg uncertainty principle to express electron behavior in probabilistic terms.
Step-by-step explanation:
The wave mechanical model of an atom, also known as the quantum mechanical model, is based on the wave-particle duality principle that describes the behavior of electrons within atoms. This model was extensively developed by Erwin Schrödinger in 1926, who formulated a complex mathematical equation, namely the Schrödinger equation, which solved the behavior of the electron in a hydrogen atom. This model suggests that electrons exhibit both wave-like and particle-like properties.
Unlike earlier models, which assumed quantized orbits for electrons without mathematical justification, this model requires quantization of electron energies as an innate outcome of the equation itself. In this model, electron’s position is described by a wavefunction, often represented by the Greek letter psi (ψ), which provides the probability amplitude of the electron's presence at a particular location near the nucleus. Max Born later interpreted the wavefunction as a probability density, where the square of its magnitude gives the likelihood of finding an electron in a certain region of space.
Moreover, the quantum mechanical model respects the Heisenberg uncertainty principle, which asserts that the more precisely the position of an electron is known, the less precisely its momentum can be known, and vice versa. This leads to describing electrons in terms of probabilistic 'clouds' rather than definitive orbits; such clouds depict the areas in which electrons are most likely to be found.