Summary of Fundamentals of Materials Science and Solid-State Physics

## Introduction Atomic physics studies the structure, properties, and behavior of atoms — the basic units of ordinary matter. This material covers atomic structure, quantum numbers, fundamental principles that govern electron configurations, basic particles, and polarization mechanisms relevant to atomic-scale response to electric fields. The presentation emphasizes clear definitions, practical examples, and connections to real-world applications. ## 1. Basic constituents of the atom - An atom consists of a nucleus (containing **protons** and **neutrons**) surrounded by **electrons** in quantized states. > Definition: An atom is a neutral or charged entity made of a dense nucleus of protons and neutrons and electrons that occupy discrete quantum states around the nucleus. Practical example: A hydrogen atom has one proton in its nucleus and one electron; a helium atom has two protons, typically two neutrons, and two electrons. Fun fact: Electrons occupy discrete energy levels, and the spectral lines of elements are direct fingerprints of these allowed transitions. ## 2. Elementary particles relevant to atomic physics - Fermions (matter particles): - Quarks (make up protons and neutrons) - Leptons (electrons, muons, taus, and their neutrinos) - Bosons (force carriers relevant for interactions): - Photon (electromagnetic force) - Gluon (strong force, binds quarks) - W and Z bosons (weak force) - Higgs boson (gives mass via Higgs field) > Definition: Fermions are particles with half-integer spin that obey the Pauli exclusion principle; bosons have integer spin and can occupy the same quantum state. ## 3. Quantum numbers and their orbital meaning Electrons in atoms are described by four quantum numbers. Each quantum number encodes a specific property of the electron's orbital or spin. 1. Principal quantum number $n$ — shell - Determines the primary energy level and size of the orbital. - $n = 1,2,3,\dots$; larger $n$ means larger average distance from the nucleus. 2. Azimuthal (orbital) quantum number $l$ — subshell - Determines orbital angular momentum and subshell shape. - $l = 0,1,\dots,n-1$ often labeled as $s,p,d,f,\dots$ for $l = 0,1,2,3,\dots$ respectively. 3. Magnetic quantum number $m_l$ — orbital orientation - Determines the orientation of the orbital in space and the degeneracy within a subshell. - $m_l = -l, -l+1, \dots, 0, \dots, +l$. 4. Spin projection quantum number $m_s$ — electron spin - Describes the intrinsic spin projection of the electron along a chosen axis. - $m_s = +\tfrac{1}{2}$ or $-\tfrac{1}{2}$. > Definition: A quantum number is a discrete value that characterizes an electron's allowed state in an atom. Table: Quantum numbers and meaning | Quantum number | Symbol | Allowed values | Physical meaning | |---|---:|---|---| | Principal | $n$ | $1,2,3,\dots$ | Shell, energy level and size | | Azimuthal | $l$ | $0,1,\dots,n-1$ | Subshell, orbital shape (s,p,d,f) | | Magnetic | $m_l$ | $-l,\dots,+l$ | Orbital orientation | | Spin projection | $m_s$ | $+\tfrac{1}{2},-\tfrac{1}{2}$ | Electron spin projection | Practical example: For $n=3,\; l=1,\; m_l=0,\; m_s=+\tfrac{1}{2}$ the electron is in a 3p orbital with a specific orientation and spin-up. ## 4. Fundamental principles for electron configuration ### Pauli exclusion principle - No two identical fermions (electrons) may occupy the same quantum state. This means two electrons in the same orbital must have opposite spins ($m_s = +\tfrac{1}{2}$ and $m_s = -\tfrac{1}{2}$). > Definition: Pauli exclusion principle — two identical fermions cannot share the same set of quantum numbers. ### Aufbau (building-up) principle - Electrons fill orbitals starting from the lowest available energy states before occupying higher-energy orbitals. - Ordering often approximated by increasing $n + l$, with ties broken by lower $n$. ### Hund's rule of maximum multiplicity - Within a subshell, electrons first occupy different orbit