The quantum mechanical model of the atom is the most advanced and accurate theory describing the behavior and location of electrons in atoms. Developed primarily by Erwin Schrödinger in 1926, this model treats electrons as wave- like entities rather than particles traveling in fixed paths. Instead of defined orbits as in the Bohr model, electrons are described by wave functions that define a probabilistic electron cloud—giving the likelihood of finding an electron in a particular region around the nucleus. Key features of the quantum mechanical model include:

• Use of Schrödinger's equation to calculate wave functions (ψ), which provide the probability distributions of electrons rather than exact locations.
• The concept of atomic orbitals, three-dimensional regions where there is a high probability (about 90%) of finding an electron.
• Incorporation of quantum numbers (principal n, azimuthal l, magnetic m_l, and spin m_s) to uniquely define electron states.
• Recognition of the Heisenberg uncertainty principle, which states it is impossible to simultaneously know both the exact position and momentum of an electron.

This model revolutionizes understanding by replacing fixed electron paths with probabilistic orbitals and explains chemical behavior, periodic trends, and atomic spectra more accurately than earlier atomic models like Bohr's.