Einstein's most famous equation — mass and energy are the same thing
c = 3×10⁸ m/s, so c² is enormous. A small amount of mass converts to huge energy. Nuclear reactions release energy by converting tiny amounts of mass. Basis of nuclear power and nuclear weapons.
Quantum Duality
Wave-particle duality: light and electrons are both — which shows depends on measurement
Quantum Duality
Everything at quantum scale behaves as wave and particle simultaneously
Light: shows interference (wave) and photoelectric effect (particle). Electrons: show diffraction (wave) and definite positions when measured (particle). Measurement collapses the wave function.
Uncertainty Principle
Heisenberg: Δx × Δp ≥ ℏ/2 — can't know both position and momentum exactly
Uncertainty Principle
A fundamental limit — not a measurement problem, a property of nature
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.
Radioactive Decay
Half-life: time for half a radioactive sample to decay
Radioactive Decay
After one half-life: 50% remains. After two: 25%. After three: 12.5%.
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.
Photoelectric Effect
Photoelectric effect: light hits metal → ejects electrons. Proved light is quantized.
Photoelectric Effect
Einstein's Nobel Prize — light comes in packets called photons
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.
Special Relativity Effects
Special relativity: time dilation — moving clocks run slow. Length contraction — moving objects shrink.
Special Relativity Effects
Two strange consequences of moving near the speed of light
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 vs Fusion
Nuclear fission: heavy nucleus splits → lighter nuclei + energy. Fusion: light nuclei combine → heavier + MORE energy.
Fission vs Fusion
Two types of nuclear reactions — both release energy via E=mc²
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).
Bohr Model of the Atom
Bohr model: electrons orbit in fixed energy levels. Jump to higher level = absorb photon. Fall to lower = emit photon.
Bohr Model of the Atom
Electrons in fixed orbits — the origin of atomic spectra
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.
de Broglie Wavelength
de Broglie wavelength: λ = h/mv. All matter has wave properties — more obvious for small, fast particles.
de Broglie Wavelength
Every moving particle has an associated wavelength
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.
Types of Radioactive Decay
Radioactive decay types: Alpha (α) = helium nucleus. Beta (β) = electron or positron. Gamma (γ) = high-energy photon.
Types of Radioactive Decay
Three types of radiation — what each is and how penetrating
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.
Alpha
Helium nucleus — stopped by paper
Beta
Electron/positron — stopped by aluminum
Gamma
High-energy photon — requires lead shielding
Quantum Tunneling
Quantum tunneling: particle passes through a barrier it classically shouldn't have enough energy to cross
Quantum Tunneling
The quantum mechanical effect that makes nuclear fusion possible
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.
The Standard Model
Standard Model: matter = quarks + leptons. Forces carried by bosons. Higgs gives particles mass.
The Standard Model
The most complete theory of fundamental particles and forces
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.