Topic Cluster

Modern Physics

Modern physics: relativity and quantum mechanics, and the strange truths that surfaced once we looked closely enough at very fast and very small things.

What Is Modern Physics?

Modern Physics is what happens when the classical picture breaks down — at speeds close to light, and at scales close to a single atom. Relativity and quantum mechanics rebuild the fundamentals on stranger but deeper foundations.

Core equations in modern physics
Relationship	Equation	What it tells you
Mass-energy equivalence	E = m·c²	Rest energy of a mass
Photon energy	E = h·f	Energy of a single quantum of light
De Broglie wavelength	λ = h / p	Wavelength of a moving particle
Lorentz factor	γ = 1 / sqrt(1 − v²/c²)	Time dilation and length contraction
Uncertainty principle	Δx · Δp ≥ h-bar / 2	Position and momentum cannot both be sharp
Hydrogen energy levels	E = −13.6 / n² eV	Bohr model of the atom

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Modern Physics

Wave-Particle Duality: One Electron, Two Slits

Wave-particle duality is the principle that light and matter each travel as a wave and arrive as a particle, tied together by the relation wavelength equals the Planck constant divided by momentum. This page works through the evidence on both sides, the double slit run one electron at a time, what a which-slit measurement does to the fringes, and why everyday objects never show them. Seven worked problems, two original diagrams and an interactive lab.

20 min read

Modern Physics

Atomic Structure: Protons, Neutrons and Electrons

Atomic structure is the arrangement of protons, neutrons and electrons in an atom. How the three counts fix the element, the isotope and the charge, why a tiny nucleus holds almost all the mass, isotopes and ions with NIST data, worked problems and a build-an-atom lab.

18 min read

Modern Physics

What Is a Neutrino? The Ghost Particle of Physics

A neutrino is a chargeless, near-massless particle that barely interacts with matter. Here is what it is, why beta decay demanded it, and how oscillation proved it has mass.

14 min read

Modern Physics

The Schrodinger Equation Explained

The Schrodinger equation predicts every energy an atom is allowed to have. This guide explains both forms, what the wave function really means, and works through six problems step by step.

15 min read

Modern Physics

What Is the Heisenberg Uncertainty Principle?

The Heisenberg uncertainty principle says a particle cannot have both a sharp position and a sharp momentum — the product of the two spreads can never fall below h/4π. This guide covers the formula, what it really forbids, five real effects and eight worked problems.

15 min read

Modern Physics

Quantum Mechanics: A Beginner Guide

A beginner's guide to quantum mechanics: energy quanta, wave-particle duality, uncertainty, worked examples and the myths that trip students up.

15 min read

Modern Physics

Antimatter Explained: What It Is and How It Works

Antimatter is matter made of antiparticles that destroy ordinary matter on contact, turning mass entirely into energy. This guide covers the physics, the E = mc2 maths, seven worked problems, and where antimatter turns up in real life.

14 min read

Modern Physics

Atomic Structure and the Bohr Model

The Bohr model places electrons in fixed, quantised energy levels given by E = -13.6/n² eV, and explains why hydrogen emits sharp coloured lines instead of a rainbow. Covers the three postulates, the spectral series, seven worked problems, and exactly where the model breaks down.

14 min read

Modern Physics

What Are Quarks?

Quarks are the fundamental particles inside every proton and neutron, carrying fractional charges of +2/3 or -1/3. Learn all six flavours, why a quark can never be isolated, and why they account for just 1% of your mass.

16 min read

Modern Physics

De Broglie Wavelength: Formula, Examples and Worked Problems

Every moving particle has a wavelength given by the de Broglie equation. This guide covers the formula, the electron voltage shortcut, six real examples and eight fully worked problems.

14 min read

Modern Physics

Time Dilation: Formula, Twin Paradox and Real Experiments

Time dilation is the difference in elapsed time between two clocks caused by relative motion or gravity. This guide covers the formula, the twin paradox, worked examples and the real experiments that measured it.

15 min read

Modern Physics

Photon Energy Formula (E = hf): Explained

The photon energy formula E = hf links a photon's energy to the frequency of its light. See both forms of the equation, real examples from radio to gamma rays, and eight fully worked problems.

13 min read

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