Final answer:
The modern quantum mechanical model, based on Schrödinger's equation, provides a probabilistic framework for electrons in an atom, described by four quantum numbers and wave-particle duality, unlike deterministic previous models like Bohr's.
Step-by-step explanation:
The difference between the previous models of the atom and the modern quantum mechanical model lies in the understanding of electron behavior and the mathematical foundation of such behavior. Previously, models such as Bohr's model assumed quantization of electron orbits around the nucleus without a robust mathematical basis. In contrast, the quantum mechanical model, which developed from the solution to Schrödinger's equation, incorporates wave-particle duality and provides a complex mathematical description that accurately predicts electron behavior in an atom. This model explains that electrons exist in probabilistic orbitals rather than fixed paths and are described by four quantum numbers which dictate their properties, such as energy levels and spin orientation.
In summary, the quantum mechanical model provides a probabilistic and mathematically sound framework for the behavior and placement of electrons in an atom, moving away from previous deterministic models.