Quantum & Atomic Physics — 60 Terms Defined

Atomic Orbital Quantum & Atomic Physics Dimensionless Spatial Function A mathematical function describing the three-dimensional spatial wave function and probability distribution of an electron in an atom. ψ_n,l,m_l(r, θ, φ) = R_n,l(r) Y_l,m_l(θ, φ)

Aufbau Principle Quantum & Atomic Physics Dimensionless Rule A rule governing electron configuration stating that electrons fill atomic orbitals of lower energy levels before occupying higher energy levels. Order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s...

Auger Effect Quantum & Atomic Physics eV (Electron-Volts) A non-radiative atomic process in which the filling of an inner-shell electron vacancy causes the ejection of a second outer-shell (Auger) electron. E_Auger = E_K - E_L1 - E_L2,3

Balmer Series Quantum & Atomic Physics Visible Light Wavelengths (nm) The spectral series of hydrogen atom emission lines resulting from electron transitions dropping from higher levels (n_i ≥ 3) to the n=2 level. 1 / λ = R_H (1 / 2² - 1 / n_i²), n_i = 3, 4, 5...

Bell's Theorem Quantum & Atomic Physics Dimensionless Inequality A mathematical theorem proving that no physical theory incorporating local hidden variables can reproduce all predictions of quantum mechanics. |E(a, b) - E(a, b')| + |E(a', b) + E(a', b')| ≤ 2

Bohr Model Quantum & Atomic Physics eV (Energy), m (Orbit Radius) An early semi-classical atomic model proposing that electrons orbit the atomic nucleus only in discrete stationary orbits with quantized angular momentum. L = m v r = n ℏ, E_n = -13.6 eV / n²

Bose-Einstein Condensate (BEC) Quantum & Atomic Physics nK (Nanokelvin Temperatures) A state of matter formed by bosons cooled close to absolute zero, where a macroscopic fraction of particles collapse into the lowest quantum state. T_c = (2 π ℏ² / (m k_B)) (n / ζ(3/2))^(2/3)

Bosons Quantum & Atomic Physics Dimensionless Particle Class Subatomic particles possessing integer intrinsic spin that obey Bose-Einstein statistics and do not obey the Pauli Exclusion Principle. Spin = 0, 1, 2...

Bragg's Law Quantum & Atomic Physics m or nm (Wavelength and Spacing) The mathematical condition for constructive interference of waves scattered from parallel atomic lattice planes in a crystal. n λ = 2 d sin θ

Casimir Effect Quantum & Atomic Physics N/m² (Pressure) An attractive physical force acting between two uncharged parallel conductive plates in vacuum, arising from quantum vacuum fluctuations. F / A = - (π² ℏ c) / (240 d⁴)

Commutator Quantum & Atomic Physics Product Unit of Â and B̂ A mathematical operator evaluating whether two quantum mechanical operators commute with one another. [Â, B̂] = Â B̂ - B̂ Â

Compton Effect Quantum & Atomic Physics m or pm (Wavelength Increase) The decrease in energy (increase in wavelength) of an X-ray or gamma-ray photon when scattered by a stationary electron. Δλ = λ' - λ = (h / (m_e c)) (1 - cos θ)

Davisson-Germer Experiment Quantum & Atomic Physics nm (Wavelength) A 1927 physics experiment that experimentally confirmed De Broglie's matter wave hypothesis by demonstrating electron diffraction from a nickel crystal. n λ = 2 d sin θ = h / p

De Broglie Wavelength Quantum & Atomic Physics m or nm (Wavelength) The wavelength associated with a massive particle, expressing its intrinsic wave-like character. λ = h / p = h / (m v)

Electron Spin Quantum & Atomic Physics J·s (Spin Angular Momentum) An intrinsic form of angular momentum carried by elementary particles, independent of orbital spatial motion. S = √(s (s + 1)) ℏ, s = ½, S_z = ± ½ ℏ

Expectation Value Quantum & Atomic Physics Same as measured quantity The probabilistic average or expected value of many physical measurements performed on an ensemble of identically prepared quantum states. ⟨A⟩ = ∫ ψ* Â ψ dx / ∫ ψ* ψ dx

Fermi Energy Quantum & Atomic Physics eV or Joules The highest occupied kinetic energy state of non-interacting fermions in a quantum system at absolute zero temperature (0 K). E_F = (ℏ² / (2 m)) (3 π² n)^(2/3)

Fermions Quantum & Atomic Physics Dimensionless Particle Class Subatomic particles possessing half-integer intrinsic spin that obey Fermi-Dirac statistics and the Pauli Exclusion Principle. Spin = ½, ³/₂, ⁵/₂...

Fine Structure Quantum & Atomic Physics eV (Energy Splitting) The small splitting of atomic spectral lines resulting from relativistic mass corrections and spin-orbit coupling. E_fine ~ α² E_n, α ≈ 1 / 137

Finite Potential Well Quantum & Atomic Physics eV or Joules A quantum potential well model with barriers of finite energy height V₀. V(x) = V₀ for |x| > a, V(x) = 0 for |x| ≤ a

Fluorescence Quantum & Atomic Physics Nanoseconds (Lifetime) The rapid absorption of light at a shorter wavelength followed by immediate emission of light at a longer wavelength. h ν_emitted < h ν_absorbed (Stokes Shift)

Franck-Hertz Experiment Quantum & Atomic Physics eV (Electron-Volts) An influential 1914 physics experiment that directly demonstrated the existence of quantized discrete energy states in mercury atoms. E_loss = h ν = 4.9 eV (for Mercury vapor)

Heisenberg Uncertainty Principle Quantum & Atomic Physics J·s (Action Units) A fundamental quantum limit stating that canonical conjugate physical variables (such as position and momentum, or energy and time) cannot be simultaneously measured with arbitrary precision. Δx Δp ≥ ℏ / 2, ΔE Δt ≥ ℏ / 2

Hund's Rule of Maximum Multiplicity Quantum & Atomic Physics Dimensionless Rule A rule stating that when filling degenerate atomic orbitals, electrons occupy separate orbitals singly with parallel spins before pairing up. S_total = ∑ s_i (Maximized spin in degenerate orbitals)