Quantum & Nuclear: every key term you need (+ practice quiz)

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• Fluids
• Thermodynamics
• Electric Forces & Potential
• Circuits
• Magnetism

Quantum Mechanics

Physics of atomic/subatomic scale. Classical mechanics fails; quantization, probability, wave-particle duality.

Photons

Particles of light. E = hf where h = Planck's constant. p = E/c. Energy proportional to frequency.

Photoelectric Effect

Light ejects electrons from metal. E = hf = KE_max + Φ where Φ = work function. Threshold frequency f₀ = Φ/h.

Wave-Particle Duality

Light and matter exhibit both wave and particle properties. Depends on observation method.

de Broglie Wavelength

λ = h/p where h = Planck's constant, p = momentum. All particles have associated wavelength.

Uncertainty Principle

Δx·Δp ≥ h/(4π). Can't know position and momentum precisely simultaneously. Fundamental quantum limit.

Atomic Structure

Nucleus: protons (charge +), neutrons (neutral). Electrons orbit in shells. Nuclear force >> electromagnetic force.

Bohr Model

Electrons in discrete orbits; quantized energy levels. Transitions between levels emit/absorb photons.

Radioactivity

Unstable nuclei decay: alpha (He nucleus), beta (electron), gamma (photon). Half-life: time for half to decay.

Nuclear Reactions

Fission: heavy nucleus splits. Fusion: light nuclei combine. Both release energy (E=mc²).

Unit 7 Summary

Quantum: quantized energy, probabilistic. Photons E=hf. Wave-particle duality. Nuclear: decay, fission, fusion.

Photoelectric Graph Analysis

K_max vs frequency is a straight line: slope = h (same for every metal), x-intercept = threshold frequency f₀, y-intercept = −φ (work function). Intensity changes the current, never the slope or intercept.

Stopping Potential

eV_stop = K_max = hf − φ. Doubling light intensity leaves V_stop unchanged; raising frequency raises it linearly. Instantaneous emission even at low intensity contradicts the wave model.

Photon Momentum

p = h/λ = E/c. Photons carry momentum despite zero mass; light pressure and Compton scattering (wavelength lengthens after scattering off an electron) confirm it.

Compton Scattering

An X-ray photon striking an electron loses energy and emerges at longer wavelength; the shift grows with scattering angle. Cannot be explained by waves — energy and momentum are conserved photon-by-photon.

de Broglie Applications

λ = h/p = h/√(2mK). A 100 eV electron has λ ≈ 0.12 nm — comparable to atomic spacing, so electrons diffract from crystals (Davisson–Germer). Baseballs have λ ~ 10^-34 m, unobservable.

Energy Level Transitions

Photon emitted or absorbed with E = |E_i − E_f| = hc/λ. Only exact energy matches are absorbed; a photon with more energy than the ionization energy can eject the electron with leftover kinetic energy.

Hydrogen Energy Levels

E_n = −13.6 eV/n². Ionization from ground state needs 13.6 eV (91 nm). Balmer series (to n = 2) gives visible lines; Lyman (to n = 1) is ultraviolet; Paschen (to n = 3) is infrared.

Number of Spectral Lines

An electron in level n can produce n(n − 1)/2 distinct downward transitions when many atoms are excited to n; from n = 4 that gives 6 lines.

Standing Waves in Bohr Orbits

Allowed orbits fit an integer number of de Broglie wavelengths: 2πr = nλ, equivalent to angular momentum quantization L = nh/2π. Explains why energy levels are discrete.

Mass–Energy Equivalence

E = mc²; 1 u ≈ 931.5 MeV/c². Binding energy = (mass of separate nucleons − nuclear mass) × c². Iron-56 region has the highest binding energy per nucleon, so fission of heavy and fusion of light nuclei both release energy.

Conservation Laws in Nuclear Reactions

Mass number A and charge Z are conserved (nucleon and charge conservation), as are total energy and momentum. Mass alone is not conserved — the mass defect appears as kinetic energy or photons.

Decay Modes

Alpha: A − 4, Z − 2. Beta-minus: n → p + e⁻ + antineutrino, Z + 1. Beta-plus: p → n + e⁺ + neutrino, Z − 1. Gamma: nucleus de-excites, A and Z unchanged.

Half-Life Reasoning

N = N₀(½)^(t/T). After 3 half-lives 1/8 remains; the activity (decays per second) also drops to 1/8. Half-life is unaffected by temperature, pressure, or chemical state.

Wave Function and Probability

|ψ|² gives the probability per unit length of finding a particle; regions where the wave function is large are where the particle is likely detected. Nodes are positions of zero probability.

Heisenberg Uncertainty Consequences

Δx·Δp ≥ h/4π. Confining an electron to an atom (Δx ~ 10^-10 m) forces a momentum spread that keeps it from sitting on the nucleus — the reason atoms have size.