⚛️ Modern Physics
Relativity, quantum ideas, atomic structure and nuclear physics — physics beyond everyday intuition.
What you will learn
- Explain the photoelectric effect and photons
- Describe time dilation and mass-energy equivalence
- Compare atomic models
- Use half-life in decay problems
Study guide
High School concepts
Atomic Models — From Dalton to Quantum Mechanics
Models of the atom from Dalton to quantum mechanics: Thomson's plum pudding, Rutherford's nucleus, Bohr's orbits (E_n = −13.6 eV/n²), and electron clouds.
E = mc² — Mass-Energy Equivalence Explained
E = mc² explained: what mass-energy equivalence really means, why c² makes tiny mass enormous energy, and nuclear examples with numbers.
Nuclear Binding Energy — Mass Defect, E = mc² and the Curve of Stability
Why a nucleus weighs less than its parts: mass defect, binding energy in MeV, the binding-energy-per-nucleon curve, and how it explains fusion and fission.
Nuclear Decay and Half-Life — Alpha, Beta, Gamma
Radioactive decay and half-life: alpha, beta, gamma decay, the exponential law N = N₀e^(−λt), half-life calculations, and carbon dating.
The Particle Zoo — A Friendly Tour of the Standard Model
Quarks, leptons and bosons: the fundamental particles of the Standard Model, what each family does, and why everyday matter needs only three of them.
Beginner concepts
Introductory College concepts
Photoelectric Effect — Einstein's Photons Explained
The photoelectric effect: Einstein's photon explanation, E = hf = φ + KE_max, threshold frequency, and why it proved light is quantized.
Quantum Numbers — n, l, m_l and m_s Explained
The four quantum numbers (n, l, m_l, m_s) that describe every electron: allowed values, the Pauli exclusion principle, and how they build the periodic table.
The Schrödinger Equation — A Plain-Language Introduction
Wavefunctions, probability and quantization: what Schrödinger's equation says, how the particle in a box gets discrete energies, and why it underlies modern…
Special Relativity Basics — Einstein's Two Postulates
Einstein's special relativity: the two postulates, why the speed of light is constant, time dilation, length contraction, and E = mc² — clearly explained.
Time Dilation — Why Moving Clocks Run Slow
Time dilation explained: why moving clocks run slow, the Lorentz factor γ = 1/√(1−v²/c²), the light clock, muons, and the twin paradox resolved.
Heisenberg Uncertainty Principle — Explained Simply
Heisenberg's uncertainty principle: Δx·Δp ≥ ℏ/2 explained — why it is not about clumsy instruments, and what it really limits.
Wave-Particle Duality — De Broglie Wavelength Explained
Wave-particle duality: de Broglie's λ = h/p, the double-slit with electrons, and what duality really means — explained without mysticism.
Formulas
N = N₀(½)^(t/t½) — Radioactive Half-Life Law
Remaining nuclei equal the initial number times one-half raised to the number of elapsed half-lives.
Mass-Energy Equivalence — E = mc²
Energy equals mass times the speed of light squared.
KE_max = hf − Φ — Photoelectric Equation
Maximum electron kinetic energy equals photon energy minus the metal's work function.
Calculators
Practice
Atomic Structure Practice
10 problems · 10 practice problems on atomic structure — Bohr model, energy levels, spectra and electron shells.…
Modern Physics Practice — Photoelectric Effect, Relativity and Radioactivity
10 problems · 10 practice problems on modern physics — the photoelectric effect, E = mc², half-life and relativity…
Nuclear Physics Practice
10 problems · 10 practice problems on nuclear physics — radioactivity, half-life, fission, fusion and binding ener…
Photoelectric Effect Practice 2
10 problems · 10 practice problems on the photoelectric effect — work function, threshold frequency and photon ene…
Quantum Basics Practice
10 problems · 10 practice problems on quantum basics — photons, wave-particle duality, and the uncertainty princip…
Special Relativity Practice
10 problems · 10 practice problems on special relativity — time dilation, length contraction, and mass-energy equi…