Proven Mnemonics & Acronyms — fast to learn, hard to forget.
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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.
Nuclear Binding Energy
Mass defect × c² = binding energy — the mass that became energy when nucleus formed
How nuclear binding energy and mass defect relate via E = mc²
The nucleus weighs LESS than its parts — the missing mass is the binding energy
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.
Mass defect
Δm = sum of parts − actual nucleus mass
Iron-56
Most stable — peak binding energy per nucleon
Fusion vs Fission
Both release energy by moving toward iron on the curve
Compton Scattering
Photon hits electron → photon loses energy → wavelength INCREASES (redshifts)
Compton scattering — proof that photons have momentum
Compton scattering proved light behaves as particles — photons carry momentum p = h/λ
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.
Δλ increases
Scattered photon always has longer wavelength — less energy
Max at 180°
Backscatter gives maximum wavelength shift
p = h/λ
Photon momentum — proved by Compton experiment
Quantum Numbers
PAMS — Principal n, Angular momentum l, Magnetic m_l, Spin m_s
The four quantum numbers that completely describe an electron in an atom
Four numbers uniquely identify every electron — Pauli exclusion: no two electrons can share all four
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.
n
Principal — energy level, shell (1, 2, 3...)
l
Angular momentum — subshell shape (s, p, d, f)
Pauli
No two electrons share all four quantum numbers
Special Relativity — Key Results
TLED — Time dilation, Length contraction, Energy-mass, Doppler (relativistic)
Four key results of Einstein's Special Theory of Relativity
Nothing with mass can reach c — and as you approach it, time slows and length shrinks
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.
Time dilation
Moving clocks run slow — γ ≥ 1 always
Length contraction
Moving objects shorter in direction of travel
E = mc²
Rest mass energy — enormous, basis of nuclear power
🎓 Common Exam Questions
Q: Explain the wave-particle duality of light and matter with key experimental evidence.
A: Wave behavior of light: Young's double-slit experiment (1801) showed light produces interference patterns — only waves interfere. Diffraction, polarization. Particle behavior of light: photoelectric effect (Einstein, 1905) — light ejects electrons only if frequency exceeds a threshold, regardless of intensity. Energy comes in packets: E = hf. Compton scattering: X-rays scatter off electrons and lose energy — proves photons have momentum p = h/λ. Matter waves (de Broglie, 1924): particles have wavelength λ = h/p. Confirmed by: electron diffraction experiments (Davisson-Germer, 1927), electron interference patterns. The Copenhagen interpretation: quantum objects don't have definite properties until measured — wave function collapses on observation.
Q: State Heisenberg's Uncertainty Principle and explain its physical origin.
A: Heisenberg's Uncertainty Principle: ΔxΔp ≥ ℏ/2 where ℏ = h/2π. You cannot simultaneously know position and momentum with arbitrary precision — not due to measurement disturbance but fundamental to quantum nature. Physical origin: particles behave as wave packets. A well-localized wave packet (small Δx) requires many frequencies (large Δk, large Δp). A wave with definite momentum (single frequency, small Δp) extends infinitely (large Δx). Energy-time version: ΔEΔt ≥ ℏ/2 — excited states with short lifetimes have broad energy widths (spectral line broadening). Consequences: ground state energy of hydrogen is non-zero (zero-point energy), quantum tunneling is possible, virtual particles can exist briefly.
Q: Explain radioactive decay — the three types and the decay law.
A: Alpha decay: nucleus emits an alpha particle (⁴He) — A decreases by 4, Z decreases by 2. Heavy nuclei use this to reduce size. Penetrating power: stopped by paper or skin. Beta decay: neutron → proton + electron + antineutrino (β⁻) OR proton → neutron + positron + neutrino (β⁺). A unchanged, Z changes by ±1. Penetrating: stopped by aluminum. Gamma decay: nucleus in excited state emits high-energy photon — no change in A or Z. Most penetrating: needs lead or thick concrete. Decay law: N(t) = N₀e^(−λt) where λ is the decay constant. Half-life: t₁/₂ = ln2/λ = 0.693/λ. After n half-lives: N = N₀/2ⁿ. Activity: A = λN (decays per second) — decreases exponentially with time.
Q: Explain Einstein's Special Theory of Relativity — postulates and key consequences.
A: Two postulates: (1) The laws of physics are the same in all inertial reference frames. (2) The speed of light c is the same in all inertial frames regardless of source or observer motion. Key consequences: Time dilation — moving clocks run slow: Δt = γΔt₀ where γ = 1/√(1−v²/c²) ≥ 1. Length contraction — moving objects are shorter: L = L₀/γ. Mass-energy equivalence: E = mc² (rest energy). Total energy: E² = (pc)² + (mc²)². Relativistic momentum: p = γmv → ∞ as v → c. Simultaneity is relative — events simultaneous in one frame may not be in another. These are not approximations — they are experimentally confirmed to high precision (GPS satellites require relativistic corrections).
Q: What is the photoelectric effect and what did it reveal about the nature of light?
A: The photoelectric effect: when light hits a metal surface, electrons are ejected. Classical wave theory prediction: any frequency of light should eventually eject electrons given enough intensity. Experimental observation: (1) Below a threshold frequency, NO electrons are ejected regardless of intensity. (2) Above threshold, electrons are ejected immediately. (3) Kinetic energy of ejected electrons depends on frequency, not intensity. (4) Intensity affects number of electrons, not their energy. Einstein's explanation (1905): light is quantized into photons with energy E = hf. Photon energy must exceed the work function φ (binding energy of electron): KE_max = hf − φ. This won Einstein the Nobel Prize. Confirmed that light is both a wave (interference) and a particle (photoelectric effect) — wave-particle duality.