Historical Context & Motivation
By the late 1800s, classical physics — the physics of Newton and Maxwell — seemed nearly complete. Scientists could predict the motion of planets, describe electromagnetic waves, and explain heat engines. Yet several stubborn experiments refused to fit the classical framework. The spectrum of light emitted by hot objects, the way light ejects electrons from metals, and the discrete colors produced by glowing gases all pointed toward something fundamentally new. These puzzles ignited a revolution that became quantum physics, a theory describing nature at the smallest scales.
The central question driving all of these breakthroughs was deceptively simple: How do energy and matter actually behave at very small scales? The answer — that particles can act like waves and waves can act like particles — shattered centuries of intuition and gave rise to the quantum world we explore in IB Physics E.2.
Core Principles of Quantum Physics
Quantum physics rests on a handful of ideas that differ dramatically from everyday experience. In the classical world, a ball is always a particle and an ocean ripple is always a wave. In the quantum world, that neat separation breaks down. Below are the foundational concepts you need to master for IB Physics E.2.
Quantization of Energy
The Photoelectric Effect
Wave–Particle Duality
Atomic Energy Levels
The Heisenberg Uncertainty Principle
Visualizing the Photoelectric Effect
The photoelectric effect is one of the most important experiments in quantum physics. When light shines on a metal surface, electrons can be ejected — but only if the frequency of light is high enough. The diagram below shows the key features of this phenomenon and the graph that convinced physicists that light is quantized.
Notice that the graph is a straight line with a positive slope starting at the threshold frequency f₀. Below this frequency, no electrons are emitted regardless of how bright the light is. This was the key observation that disproved the classical wave theory of light: if light were purely a wave, even dim light of any frequency should eventually provide enough energy to free electrons. Instead, quantum theory tells us each photon must individually carry enough energy (hf ≥ φ) to liberate a single electron.
Mathematical Framework
Quantum physics at the IB level relies on a small set of powerful equations. Each one connects a measurable quantity to Planck's constant h = 6.63 × 10⁻³⁴ J·s, the fundamental constant of quantum mechanics. Let's walk through the key relationships.
Atomic Energy Levels & Emission Spectra
One of the most striking pieces of evidence for quantum physics is the line emission spectrum of hydrogen. When hydrogen gas is excited by an electric current, it glows with a characteristic pinkish-purple color. Passing this light through a prism or diffraction grating reveals not a continuous rainbow but a set of distinct colored lines. Each line corresponds to electrons dropping from one quantized energy level to another, releasing a photon of a very specific wavelength.
Notice how the energy levels get closer together as n increases. This means the energy differences between high levels are small, producing low-energy (long-wavelength, infrared) photons. Transitions down to the ground state (n = 1) involve the largest energy jumps and produce high-energy ultraviolet photons. The visible Balmer series — the only transitions you can see with your eyes — all end at n = 2.
Worked Example: Photoelectric Effect Calculation
Let's solve a typical IB-style problem involving the photoelectric effect. This example brings together several of the equations and concepts from earlier sections.
Classical Physics vs. Quantum Physics
To truly appreciate quantum physics, it helps to compare its predictions side by side with those of classical physics. The table below highlights the key differences that the IB syllabus expects you to understand.
| Feature | Classical Prediction | Quantum Reality |
|---|---|---|
| Photoelectric threshold | Any frequency of light should eject electrons if the intensity is high enough. | Only photons with f ≥ f₀ can eject electrons; intensity only changes the number, not the energy. |
| Time delay for emission | Dim light should require time for energy to accumulate at the surface. | Emission is instantaneous when hf ≥ φ, because a single photon delivers all its energy at once. |
| Effect of intensity | Higher intensity should increase electron kinetic energy. | Higher intensity increases the number of emitted electrons (current) but not their maximum kinetic energy. |
| Nature of light | Light is a continuous electromagnetic wave. | Light has both wave and particle properties (wave–particle duality). |
| Atomic spectra | Atoms should emit a continuous range of wavelengths. | Atoms emit only specific wavelengths corresponding to energy-level differences. |
Connections to Advanced Quantum Theory
The concepts in E.2 form the foundation for much deeper physics. While you don't need to master these advanced topics for the IB exam, understanding where they fit helps you see the bigger picture and prepares you if you continue studying physics at university.
| IB E.2 Concept | Advanced Extension |
|---|---|
| E = hf (photon energy) | Quantum electrodynamics (QED) — photons as mediators of the electromagnetic force, Feynman diagrams. |
| λ = h/p (de Broglie wavelength) | Schrödinger wave equation — probability amplitudes, wave functions, electron orbitals as standing waves. |
| Discrete energy levels | Quantum numbers (n, l, m_l, m_s) — electron configurations, periodic table structure, spectroscopy. |
| Heisenberg uncertainty principle | Quantum tunnelling — particles crossing barriers they classically shouldn't, tunnel diodes, nuclear fusion in stars. |
| Wave–particle duality | Quantum superposition and entanglement — the basis of quantum computing and quantum cryptography. |
The de Broglie wavelength, for example, leads directly into the Schrödinger equation — the central equation of quantum mechanics. Instead of thinking of an electron as a tiny ball orbiting the nucleus, the wave function describes a cloud of probability. The electron is most likely to be found where the cloud is densest. This picture not only explains chemistry's electron orbitals but also underpins technologies like electron microscopes, which exploit the tiny de Broglie wavelengths of fast electrons to image structures smaller than visible light can resolve.
Practice Problems
Quantum Physics — Key Concepts Review
Quantum physics reveals that energy is quantized — it comes in discrete packets called photons, each carrying energy E = hf. The photoelectric effect shows that photons must exceed a metal's work function φ to eject electrons, with the maximum kinetic energy given by E_k(max) = hf − φ. Atoms have discrete energy levels, and transitions between them produce line spectra with photon energies equal to hf = E₂ − E₁.
Wave–particle duality extends to matter: all particles have a de Broglie wavelength λ = h / p, though this wavelength is only measurable for very small, low-momentum particles. The Heisenberg uncertainty principle sets a fundamental limit on how precisely we can simultaneously know a particle's position and momentum. Together, these ideas replace the deterministic world of classical physics with a probabilistic description of nature at the atomic scale — and they form the foundation for modern technologies from lasers to semiconductors.