Final answer:
The quantum mechanical model uses the principal, azimuthal, magnetic, and spin quantum numbers to describe the probable location and energy of electrons within an atom, replacing the concept of exact orbits with probabilistic electron distributions.
Step-by-step explanation:
The quantum mechanical approach to atomic structure is a sophisticated model that determines the location and energy of electrons within an atom using quantum numbers. This model replaces the simplistic notion of well-defined orbits with a probability-based description of electron positions, which are calculated using solutions to the Schrödinger equation. The principal quantum number (n) indicates the energy level and the general region where an electron is likely to be found. It is important to note that the exact path of an electron cannot be pinpointed due to the Heisenberg uncertainty principle.
Subsequently, the azimuthal quantum number (l), ranging from 0 to n-1, describes the shape of the electron distribution, while the magnetic quantum number (m₁), ranging from −1 to +l, indicates the orientation of an electron's orbital in space. Finally, the spin quantum number (ᴇʟ₁) determines the direction of the electron's spin, which can be either up (+1/2) or down (−1/2). Collectively, these quantum numbers allow us to predict a region around the nucleus where an electron is most likely to be found.