# Chap 40: All About Atoms

## Sections

| Sec | Topic |
|-----|------|
| 40-1 | [Properties of Atoms](40-1-properties-of-atoms.ipynb) |
| 40-2 | [The Stern-Gerlach Experiment](40-2-the-stern-gerlach-experiment.ipynb) |
| 40-3 | [Magnetic Resonance](40-3-magnetic-resonance.ipynb) |
| 40-4 | [Exclusion Principle and Multiple Electrons in a Trap](40-4-exclusion-principle-and-multiple-electrons-in-a-trap.ipynb) |
| 40-5 | [Building the Periodic Table](40-5-building-the-periodic-table.ipynb) |
| 40-6 | [X Rays and the Ordering of the Elements](40-6-x-rays-and-the-ordering-of-the-elements.ipynb) |
| 40-7 | [Lasers](40-7-lasers.ipynb) |

## Review & Summary

:::{glossary}
Properties of Atoms
  Atoms have quantized energy levels. The electron has **spin** $s = 1/2$ and **orbital angular momentum** $\ell = 0, 1, 2, \ldots$ (with $m_\ell = -\ell, \ldots, +\ell$). The combination determines the magnetic properties and the structure of the periodic table.

The Stern-Gerlach Experiment
  A beam of silver atoms passing through an *inhomogeneous* magnetic field splits into discrete beams. This reveals that the magnetic moment (and thus angular momentum) is quantized. The two beams correspond to the two possible values of the $z$-component of electron spin: $S_z = \pm \hbar/2$.

Magnetic Resonance
  **Nuclear magnetic resonance (NMR)** and **magnetic resonance imaging (MRI)** exploit the precession of magnetic moments in an external magnetic field $\vec{B}$. The **Larmor frequency** is $\omega_L = \gamma B$, where $\gamma$ is the gyromagnetic ratio. Resonance occurs when an applied RF field matches this frequency, causing transitions between spin states.

Exclusion Principle and Multiple Electrons
  The **Pauli exclusion principle:** no two electrons in an atom can have the same set of quantum numbers $(n, \ell, m_\ell, m_s)$. This determines the maximum occupancy of each subshell (e.g., 2 electrons per orbital) and the structure of multi-electron atoms.

Building the Periodic Table
  The periodic table is built by filling orbitals in order of increasing energy: $1s$, $2s$, $2p$, $3s$, $3p$, $4s$, $3d$, $\ldots$ **Hund's rule:** when filling degenerate orbitals (e.g., the three $p$ orbitals), maximize the total spin—place electrons in separate orbitals with parallel spins before pairing.

X Rays and the Ordering of the Elements
  **Characteristic x-rays** are emitted when a high-energy electron knocks out an inner-shell electron and an outer electron falls into the vacancy. The frequency of the $K_\alpha$ line obeys **Moseley's law:** $\sqrt{f} \propto Z - 1$, where $Z$ is the atomic number. This established the ordering of elements in the periodic table.

Lasers
  A **laser** (Light Amplification by Stimulated Emission of Radiation) produces coherent, monochromatic, highly directional light. **Stimulated emission** occurs when an incident photon induces an excited atom to emit a photon in phase with the incident one. **Population inversion** (more atoms in the upper state than the lower) is required for net amplification. Applications include spectroscopy, communications, medicine, and manufacturing.
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