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Quantum Numbers Electron Configuration MI standards C4.8e, C4.8h, C4.8i, C4.9x The Bohr Model of the Atom I pictured electrons orbiting the nucleus much like planets orbiting the sun. Neils Bohr But I was wrong! They’re more like bees around a hive. WRONG!!! The Wave-like Electron The electron propagates through space as an energy wave. To understand the atom, one must understand the behavior of electromagnetic waves. Louis deBroglie Wave Mechanical Model Quantum Numbers Each electron in an atom has a unique set of 4 quantum numbers which describe it. Principal quantum number (n) Main energy levels, or shells Angular momentum quantum number (l) Subshell, sublevel Describes the shape of the orbital s, p, d, or f Magnetic quantum number (ml) Orbital (Position) Spin quantum number Principal Quantum Number Generally symbolized by n, it denotes the shell (energy level) in which the electron is located. Number of electrons that can fit in a shell: 2n 2 Angular Momentum Quantum Number The angular momentum quantum number, generally symbolized by l, denotes the subshell in which the electron is located. Magnetic Quantum Number The magnetic quantum number, generally symbolized by ml, denotes the orientation of the electron’s orbital with respect to the three axes in space. Spin Quantum Number Spin quantum number denotes the behavior (direction of spin) of an electron within a magnetic field. Possibilities for electron spin: +½ or –½ Main energy level (n) Subshells in Number of main energy orbitals per level subshell (n subshells) 1 s 1 2 s p 1 3 3 s p d 1 3 5 s p d f 1 3 5 7 4 Number of Number orbitals per of e- per main subshell energy level (n2) Total number of e- per main energy level (2 n2) 1 2 2 4 2 6 8 9 2 6 10 18 16 2 6 10 14 32 Pauli Exclusion Principle No two electrons in an atom can have the same four quantum numbers. Wolfgang Pauli Aufbau Principle Electrons fill the lowest energy level first Hund’s Rule Orbitals of equal energy are all occupied by one electron before any orbital is occupied by a second electron and all singly occupied orbitals have the same spin Fill in one at a time “Bus rule” Heisenberg Uncertainty Principle “One cannot simultaneously determine both the position and momentum of an electron.” You can find out where the electron is, but not where it is going. Werner Heisenberg OR… You can find out where the electron is going, but not where it is! Schrodinger Wave Equation d h V 8 m dx 2 2 2 2 E Equation for probability of a single electron being found along a single axis (x-axis) Erwin Schrodinger Orbital filling table Electron configuration of the elements of the first three series Irregular configurations of Cr and Cu Chromium steals a 4s electron to half fill its 3d sublevel Copper steals a 4s electron to FILL its 3d sublevel Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3. To remember the shapes, think of “double dumbbells” …and a “dumbbell with a donut”! d orbital shapes Shape of f orbitals