Unit 15 · Modern Physics

Quantum theory ● (core concept) — The framework needed to explain phenomena classical mechanics cannot — atomic spectra, blackbody radiation, the photoelectric effect — and to describe matter at atomic and subatomic scales, where particles exhibit both particle-like and wave-like behavior.

Photon ● (core concept) — A massless, electrically neutral particle of light with energy E = hf = hc/λ, proportional to its frequency. Photons travel in straight lines at c in free space (slower in media, with speed inversely proportional to the index of refraction) unless they interact with matter.

de Broglie wavelength ● (core concept) — λ = h/p: the wavelength associated with a particle's momentum. It grows as momentum shrinks, and quantum theory is required when it is comparable to the system's size (as in electron double-slit experiments).

Quantization (bound systems) ● (core concept) — For bound systems described by quantum theory, energy and momentum take only discrete (quantized) values.

Wave–particle duality ● (core concept) — The principle that light and matter exhibit both wave-like behavior (interference, diffraction) and particle-like behavior (photoelectric effect, Compton scattering) depending on the experiment.

Planck's constant ● (core concept) — h = 6.63×10⁻³⁴ J·s: the fundamental constant relating a photon's energy to its frequency (E = hf) and a particle's momentum to its de Broglie wavelength (λ = h/p).

Atom (structure) ● (core concept) — A small, positively charged nucleus (protons and neutrons) surrounded by negatively charged electrons. Each element is defined by its unique proton number; the total of protons plus neutrons identifies the isotope; an atom with nonzero net charge is an ion. Almost all the mass is in the nucleus.

Bohr model of the atom ● (core concept) — A historical model in which electrons circle the nucleus in orbits set by the Coulomb attraction balanced against centripetal motion (F_E = kq₁q₂/r², F_net = mv²/r). It introduced discrete electron energy states for hydrogen.

Standing-wave condition for electron orbits ● (core concept) — The reason only certain electron energies are allowed: an orbit's circumference must be an integer multiple of the electron's de Broglie wavelength, so only standing electron waves fit.

Isotope ● (core concept) — Atoms of the same element (same proton number) with different numbers of neutrons, hence different nucleon numbers. Isotopes of an element share its chemistry but differ in mass and nuclear stability.

Ion ● (core concept) — An atom with nonzero net charge, produced by gaining or losing electrons. Removing an electron from an atom is ionization.

Atomic absorption and emission ● (core concept) — An atom absorbs a photon only if the photon's energy exactly matches the gap to a higher energy state; an excited atom emits a photon of the matching energy when dropping to a lower state. Each transition involves a single frequency (single wavelength).

Emission and absorption spectra ● (core concept) — Each element has a unique set of allowed energy levels, hence a unique set of emission/absorption frequencies — a spectral fingerprint. Emission spectra identify elements in a light source; absorption spectra identify elements in a substance by the light it removes. Energy-level diagrams (single-electron atoms only) visualize the states.

Binding energy (atomic) ● (core concept) — The energy needed to remove an electron from an atom and ionize it. Removing an electron from the ground state (lowest level) costs the most energy.

Ground state vs. excited state ● (core concept) — The ground state is an atom's lowest allowed electron energy level; any higher level is an excited state. Removing an electron from the ground state (ionization) requires the most energy.

Blackbody ● (core concept) — An idealized body that absorbs all radiation falling on it; in thermal equilibrium it must re-emit energy. Its continuous emission spectrum depends only on its temperature.

Planck's law (qualitative) ● (core concept) — The classical prediction fails for blackbody spectra; the observed distribution is explained only by assuming light energy is quantized — the historical birth of quantum theory.

Wien's law ● (core concept) — λ_max = b/T: the peak wavelength of a blackbody's spectrum decreases as temperature increases — hotter objects peak at shorter (bluer) wavelengths.

Stefan–Boltzmann law ● (core concept) — P = AσT⁴: a blackbody's radiated power is proportional to its surface area and to the fourth power of its absolute temperature.

Photoelectric effect ● (core concept) — The emission of electrons when electromagnetic radiation strikes a photoactive material. It occurs only above a threshold frequency — intensity (photon count) cannot compensate — and the emitted electrons' energy is independent of intensity, proving light arrives as discrete photons.

Work function ● (core concept) — φ: the minimum energy needed to eject an electron from a material. Values are given on the exam; students do not memorize them.

Photoelectric equation ● (core concept) — K_max = hf − φ: the maximum kinetic energy of an ejected electron equals the photon energy minus the work function.

Stopping potential ● (core concept) — In the standard photoelectric setup, the reverse potential difference between the plates is adjusted until the photocurrent just reaches zero; that stopping voltage measures the most energetic electrons' kinetic energy (K_max = e·V_stop) and hence the material's work function.

Threshold frequency ● (core concept) — The minimum light frequency that can eject electrons from a photoactive material (hf = φ at threshold). Below it no electrons are emitted, no matter how intense the light.

Compton scattering ● (core concept) — A photon colliding with a free electron emerges with lower energy and longer wavelength; the shift grows with the scattering angle: Δλ = (h/mc)(1 − cosθ). Treating the photon as a particle and applying conservation of energy and momentum explains it — further evidence that light is quantized.

Strong force ● (core concept) — The force acting at nuclear scales that dominates interactions between nucleons (protons and neutrons), binding the nucleus despite proton–proton repulsion.

Mass–energy equivalence ● (core concept) — E = mc²: mass and energy are interchangeable, so nuclear reactions can convert mass into energy. Released energy appears as kinetic energy of the products or as photons.

Nuclear fission ● (core concept) — A heavy nucleus splits into two or more smaller nuclei plus subatomic particles. It can occur spontaneously or require an energy input, depending on the nucleus's binding energy.

Nuclear fusion ● (core concept) — Two or more small nuclei combine into a larger nucleus plus subatomic particles, releasing energy from mass difference.

Radioactive decay (statistical nature) ● (core concept) — The spontaneous transformation of a nucleus into different nuclei or a lower energy state. When an individual nucleus decays is indeterminable, but the decay rate of a large sample follows probability — described by the half-life and decay constant.

Half-life and decay constant ● (core concept) — The half-life t₁/₂ is the time for half of a sample's nuclei to decay; the decay constant λ = ln2/t₁/₂. The survivors after time t are N = N₀e^(−λt), which also lets the age of a sample be estimated from the remaining fraction.

Nucleon ● (core concept) — A proton or neutron — a particle of the atomic nucleus. The nucleon number (protons + neutrons) is conserved in nuclear reactions.

Nuclear binding energy ● (core concept) — The energy that would be needed to disassemble a nucleus into separate protons and neutrons — equivalently, the energy released when the nucleus formed. Whether fission or fusion releases energy depends on the binding energies of the nuclei involved.

Conservation laws in nuclear reactions ● (core concept) — In all nuclear decays, three quantities are conserved: nucleon number (neutrons + protons), lepton number (electrons and neutrinos), and charge.

Alpha decay ● (core concept) — A nucleus ejects an alpha particle — a helium-4 nucleus of two protons and two neutrons. Nucleon number drops by 4 and charge by 2.

Beta-minus decay ● (core concept) — A neutron in the nucleus changes into a proton, emitting an electron and an antineutrino. Nucleon number is unchanged; the atomic number rises by 1.

Beta-plus decay ● (core concept) — A proton in the nucleus changes into a neutron, emitting a positron (antielectron, same mass as an electron but opposite charge) and a neutrino. The atomic number falls by 1.

Gamma decay ● (core concept) — An excited nucleus (typically after alpha or beta decay) drops to a lower energy state by emitting a photon. The nucleus's composition is unchanged — only its energy changes.

Decay modes not in scope ● (core concept) — Neutron emission and electron capture are excluded from the AP Physics 2 framework, as are the types of neutrinos, what distinguishes neutrinos from antineutrinos, and any explanation or application of the weak force. The decay type a nucleus exhibits is determined by its isotope, but specific isotopes' decay modes and half-lives are not memorized.

Lepton number ● (core concept) — A quantity conserved in nuclear reactions, carried by leptons such as electrons, positrons, neutrinos, and antineutrinos. Beta decay conserves it by emitting a neutrino or antineutrino alongside the electron or positron.

Neutrino ● (core concept) — A nearly massless neutral particle emitted in beta decay (a neutrino in beta-plus decay, an antineutrino in beta-minus decay). The CED names neutrinos as decay products but excludes neutrino types, how neutrinos differ from antineutrinos, and the weak force.

Positron ● (core concept) — The antielectron: same mass as an electron but positive charge. It is emitted in beta-plus decay when a nuclear proton converts to a neutron.