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Quantum & Atomic Physics

Balmer Series

The spectral series of hydrogen atom emission lines resulting from electron transitions dropping from higher levels (n_i ≥ 3) to the n=2…

1 / λ = R_H (1 / 2² - 1 / n_i²), n_i = 3, 4, 5... Visible Light Wavelengths (nm) Condensed Matter & Materials Physics

Band Gap

The energy range in a solid where no electronic quantum states can exist, separating the top of the valence band from the bottom of the…

E_g = E_c - E_v = h ν_threshold eV (Electron-Volts) Nuclear & Particle Physics

Baryons

Subatomic composite hadrons made of three valence quarks held together by gluons, possessing half-integer spin (fermions).

Quark Content: q q q, Spin = ½, ³/₂..., Baryon Number B = 1 Composite Fermion Class Foundations of Physics

Base Units

The set of seven mutually independent fundamental units of measurement defined by the International System of Units.

The 7 SI Base Units Condensed Matter & Materials Physics

BCS Theory

The microscopic quantum theory of superconductivity developed by Bardeen, Cooper, and Schrieffer in 1957.

2 Δ(0) ≈ 3.52 k_B T_c, E_gap = 2 Δ K (Critical Temperature T_c) Waves, Oscillations & Acoustics

Beats

The periodic volume fluctuation or throbbing sound produced by the interference of two sound waves with slightly different frequencies.

f_beat = |f1 - f2| Hz Quantum & Atomic Physics

Bell's Theorem

A mathematical theorem proving that no physical theory incorporating local hidden variables can reproduce all predictions of quantum…

|E(a, b) - E(a, b')| + |E(a', b) + E(a', b')| ≤ 2 Dimensionless Inequality Classical Mechanics

Bernoulli's Principle

The principle in fluid dynamics stating that an increase in fluid speed occurs simultaneously with a decrease in static pressure or…

P + ½ ρ v² + ρ g h = constant Pa Mathematical & Computational Physics

Bessel Functions

A family of canonical special functions J_α(x) and Y_α(x) serving as solutions to Bessel's differential equation.

x² y'' + x y' + (x² - α²) y = 0 ⇒ y(x) = A J_α(x) + B Y_α(x) Cylindrical Special Functions Nuclear & Particle Physics

Beta Decay

A radioactive decay process mediated by the weak nuclear force in which a nucleus emits a beta particle (electron or positron) and a…

β⁻: n → p + e⁻ + ν̄_e; β⁺: p → n + e⁺ + ν_e MeV (Continuous Spectrum) Astrophysics, Cosmology & Relativity

Big Bang

The prevailing cosmological model describing the universe as originating from an extremely hot, dense state ~13.8 billion years ago and…

T_universe ≈ 13.787 ± 0.020 billion years Cosmological Epoch (Years) Mathematical & Computational Physics

Big O Notation

A mathematical notation classifying algorithms according to how their execution time or memory requirements grow as input size N increases.

f(N) = O(g(N)) if |f(N)| ≤ C |g(N)| for N ≥ N₀ Algorithmic Asymptotic Complexity Astrophysics, Cosmology & Relativity

Binary Star System

A stellar system consisting of two gravitationally bound stars orbiting around their common center of mass.

P² = (4 π² / (G (M₁ + M₂))) a³ (Kepler's 3rd Law) AU (Semi-major axis) & Years (Period) Nuclear & Particle Physics

Binding Energy per Nucleon

The average energy required to remove a single proton or neutron from an atomic nucleus, representing relative nuclear stability.

BE / A = Total Binding Energy / Mass Number MeV/nucleon Biophysics & Medical Physics

Bio-optics

The study of light interaction with biological tissues and the development of optical diagnostic and therapeutic instruments.

Radiative Transport Equation (RTE) in Turbid Tissues Scattering Coefficient μ_s (cm⁻¹) & Absorption μ_a (cm⁻¹) Biophysics & Medical Physics

Bioenergetics

The branch of biophysics and biochemistry studying energy transformation, transfer, and coupling mechanisms in living organisms.

ΔG = ΔH - T ΔS, ΔG'° = -R T ln K_eq kJ/mol (Gibbs Free Energy) Biophysics & Medical Physics

Bioimpedance

The measure of a biological tissue's opposition to the flow of electric alternating current.

Z = R + i X_c = √(R² + X_c²) Ω (Ohms) Biophysics & Medical Physics

Biological Transducers

Specialized sensory receptor cells that convert external physical or chemical stimuli into graded bioelectrical signals.

Transduction: Physical Stimulus Energy → Receptor Potential (mV) mV / pA (Receptor Signal Output) Biophysics & Medical Physics

Bioluminescence

The enzymatic production and emission of light by living organisms through chemical reactions converting ATP into photon energy.

Luciferin + O₂ + ATP → Oxyluciferin + AMP + PPi + h ν (Light) Photons/s (Bioluminescent Flux) Biophysics & Medical Physics

Biomechanics of Gait

The quantitative analysis of human locomotion mechanics, muscle force coordination, and ground reaction forces during walking or running.

Center of Mass Inverted Pendulum Energy Exchange (T ↔ V) m/s (Walking Speed) & Ground Reaction Force (N) Electromagnetism & Electronics

Biot-Savart Law

An equation describing the magnetic field vector generated at a point in space by a steady differential electric current element.

dB = (μ₀ / 4π) (I dl × r̂) / r² T (Tesla) Electromagnetism & Electronics

Bipolar Junction Transistor (BJT)

A three-terminal active semiconductor device (NPN or PNP) in which a small base current controls a much larger collector-emitter current.

I_E = I_B + I_C, I_C = β I_B A (Current) Astrophysics, Cosmology & Relativity

Black Hole

A region of spacetime where gravitational acceleration is so intense that nothing, including light, can escape beyond its event horizon.

R_s = 2 G M / c² Solar Masses (M_☉) or Kilograms Condensed Matter & Materials Physics

Bloch's Theorem

A fundamental theorem of solid-state physics stating that wave functions for electrons in a periodic crystal potential equal plane waves…

ψ_k(r) = e^(i k · r) u_k(r), u_k(r + R) = u_k(r) Quantum Wave Function State