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III. Quantum Model of the Atom (p. 129-134) Ch. 5 - Electrons in Atoms C. Johannesson A. Electrons as Waves • Louis de Broglie (1924) – Applied wave-particle theory to e– e- exhibit wave properties QUANTIZED WAVELENGTHS C. Johannesson A. Electrons as Waves QUANTIZED WAVELENGTHS C. Johannesson A. Electrons as Waves EVIDENCE: DIFFRACTION PATTERNS ELECTRONS VISIBLE LIGHT C. Johannesson B. Quantum Mechanics • Heisenberg Uncertainty Principle – Impossible to know both the velocity and position of an electron at the same time C. Johannesson B. Quantum Mechanics • Schrödinger Wave Equation (1926) – finite # of solutions quantized energy levels – defines probability of finding an e- Ψ 1s 1 Z 3/2 σ π a0 C. Johannesson e B. Quantum Mechanics • Orbital (“electron cloud”) – Region in space where there is 90% probability of finding an e- Orbital Radial Distribution Curve C. Johannesson C. Quantum Numbers • Four Quantum Numbers: – Specify the “address” of each electron in an atom UPPER LEVEL C. Johannesson C. Quantum Numbers 1. Principal Quantum Number ( n ) – Energy level – Size of the orbital – n2 = # of orbitals in the energy level C. Johannesson C. Quantum Numbers 2. Angular Momentum Quantum # ( l ) – Energy sublevel – Shape of the orbital s p d C. Johannesson f C. Quantum Numbers • n = # of sublevels per level • n2 = # of orbitals per level • Sublevel sets: 1 s, 3 p, 5 d, 7 f C. Johannesson C. Quantum Numbers 3. Magnetic Quantum Number ( ml ) – Orientation of orbital – Specifies the exact orbital within each sublevel C. Johannesson C. Quantum Numbers px py C. Johannesson pz C. Quantum Numbers • Orbitals combine to form a spherical shape. 2s 2px 2py 2pz C. Johannesson C. Johannesson http://www.chem.tamu.edu/rgroup/hughbanks/courses/673/handouts/4f_orbitals.jpg C. Quantum Numbers 4. Spin Quantum Number ( ms ) – Electron spin +½ or -½ • Draw them as “up” or “down” – An orbital can hold 2 electrons that spin in opposite directions. C. Johannesson C. Quantum Numbers • Pauli Exclusion Principle – No two electrons in an atom can have the same 4 quantum numbers. – Each e- has a unique “address”: 1. Principal # 2. Ang. Mom. # 3. Magnetic # 4. Spin # energy level sublevel (s,p,d,f) orbital Electron (up or down) C. Johannesson Energy level Sublevels Number of Atomic Orbitals Total Number of orbitals 1 s 1 1 2 s p 1 3 4 3 s p d 1 3 5 9 4 s p d f 1 3 5 7 16 C. Johannesson Feeling overwhelmed? Read Chapter 5! C. Johannesson