Memory tricks for quantum and relativity

Light: shows interference (wave) and photoelectric effect (particle). Electrons: show diffraction (wave) and definite positions when measured (particle). Measurement collapses the wave function.

The more precisely you pin down an electron's position, the more uncertain its momentum becomes. This is not a limitation of instruments — it's built into quantum mechanics.

Start with 100g, half-life = 1 hour: after 1 hr → 50g, after 2 → 25g, after 3 → 12.5g. Used in carbon dating, nuclear medicine, and reactor design.

Light below a threshold frequency ejects NO electrons regardless of intensity. Above threshold, electrons ARE ejected even at low intensity. Conclusion: light energy comes in discrete quanta (photons), not continuous waves.

Time dilation: a moving clock ticks slower than a stationary one. T = T₀/√(1-v²/c²). At 87% of c, time runs at half speed. Length contraction: moving objects are shorter in the direction of motion. L = L₀√(1-v²/c²). Both effects are reciprocal and only significant near the speed of light.

Fission: U-235 or Pu-239 splits when struck by neutron → chain reaction → nuclear reactor or bomb. Fusion: hydrogen isotopes combine to form helium → powers the sun and stars. Fusion releases more energy per unit mass and produces less radioactive waste but requires extreme temperatures (100 million K).

Electrons occupy discrete energy levels (shells). To jump to a higher level: must absorb a photon of exactly the right energy (E = hf). When falling to lower level: emits a photon of that energy. Each element has a unique set of energy levels → unique spectral fingerprint. Explains hydrogen spectrum perfectly.

Louis de Broglie (1924): matter has wave-like properties. Wavelength λ = h/mv (h = Planck's constant, m = mass, v = velocity). For a baseball: wavelength is absurdly tiny — wave effects unmeasurable. For an electron: wavelength is comparable to atom size — diffraction and interference are real.

Alpha: helium-4 nucleus (2p + 2n). Least penetrating — stopped by paper or skin. Dangerous if inhaled/ingested. Beta: electron (β⁻) or positron (β⁺) from nucleus. Stopped by aluminum foil. Gamma: high-energy electromagnetic radiation. Most penetrating — requires lead or thick concrete. No mass change.

Classical physics: a particle can't cross an energy barrier higher than its kinetic energy. Quantum mechanics: the particle's wave function extends through the barrier — there's a probability of finding it on the other side. Applications: tunnel diodes, scanning tunneling microscopes, nuclear fusion in stars.

Quarks: combine to make protons and neutrons (hadrons). 6 types: up, down, charm, strange, top, bottom. Leptons: electrons, muons, taus and their neutrinos. Force carriers (bosons): photon (EM), W/Z bosons (weak), gluons (strong). Higgs boson: gives particles mass via Higgs field. Gravity not yet included.

Mass defect Δm: actual nuclear mass is less than sum of proton + neutron masses. Δm × c² = binding energy (how much energy holds the nucleus together). Binding energy per nucleon peaks at iron-56 — most stable nucleus. Elements lighter than Fe: fusion releases energy (energy per nucleon increases). Elements heavier than Fe: fission releases energy (energy per nucleon increases toward Fe). Nuclear fission of U-235: releases ~200 MeV per fission. 1 atomic mass unit (amu) = 931.5 MeV/c².

When X-rays scatter off electrons, the scattered photon has a LONGER wavelength (less energy) than the incident photon. The electron recoils with the lost energy. Compton shift: Δλ = (h/m_e c)(1 − cos θ) where θ is the scattering angle. Compton wavelength: h/m_e c = 2.43 × 10⁻¹² m. Maximum shift at θ = 180° (backscatter): Δλ = 2h/m_e c. This proved photons have momentum p = h/λ = E/c — wave-particle duality for light confirmed.

Principal quantum number n: energy level (1, 2, 3...). Angular momentum l: subshell shape (0=s, 1=p, 2=d, 3=f), values 0 to n−1. Magnetic m_l: orbital orientation, values −l to +l. Spin m_s: +½ or −½ only. Pauli Exclusion Principle: no two electrons in an atom can have identical sets of all four quantum numbers. Aufbau principle: fill lowest energy orbitals first. Hund's rule: maximize unpaired electrons in same subshell before pairing.

Time dilation: Δt = γΔt₀ — moving clocks run slow (γ = 1/√(1−v²/c²) ≥ 1). Length contraction: L = L₀/γ — moving objects are shorter in direction of motion. Mass-energy equivalence: E = mc² (rest energy). Total energy: E² = (pc)² + (mc²)². Relativistic momentum: p = γmv. Simultaneity is relative — events simultaneous in one frame may not be in another. Lorentz factor γ → ∞ as v → c — infinite energy required to reach light speed.