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Quantum Engineering Year 1: Quantum Mechanics Core Month 18Day 495

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Year 1·Month 18·Week 3

Day 495: Multi-Electron Atoms

Day 495 of 2,016~19 min read

Learning Objectives

•**Explain** the central field approximation and its validity
•**Apply** the aufbau principle to determine electron configurations
•**Use** Hund's rules to predict ground state term symbols
•**Understand** the structure of the periodic table from quantum mechanics
•**Calculate** approximate ionization energies using screening constants
•**Connect** atomic structure to chemical and physical properties

Today's Schedule (7 hours)

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Overview Schedule Learning Objectives 1 The Many-Electron Problem The Full Hamiltonian Why Exact Solution is Impossible Approximation Strategy 2 Central Field Approximation The Key Insight Physical Picture Effective Nuclear Charge Separability Restored Quantum Numbers Preserved 3 Single-Particle Orbitals Notation Energy Ordering The n l Rule Madelung Rule Exceptions 4 The Aufbau Principle Statement Building Electron Configurations Capacity of Each Subshell The Periodic Table Emerges 5 Hunds Rules The Three Rules Physical Basis of Hunds Rules Example Carbon 2p2 Term Symbol Notation 6 Slaters Rules for Screening Empirical Screening Constants Example Oxygen Z 8 1s2 2s2 2p4 Ionization Energy Estimate 7 Periodic Trends Atomic Radius Ionization Energy Electronegativity Magnetic Properties 8 Worked Examples Example 1 Electron Configuration of Iron Example 2 Ionization Energy Comparison Example 3 Magnetic Moment 9 Practice Problems Level 1 Direct Application Level 2 Intermediate Level 3 Challenging 10 Computational Lab Multi-Electron Atoms 11 Summary Key Concepts Key Formulas 12 Daily Checklist Conceptual Understanding Mathematical Skills Computational Skills Quantum Computing Connection 13 Preview Day 496 References

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