Bohr Model · n = 1–5
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Where Physics Becomes Interactive Thought.
Explore quantum wavefunctions, tunnelling, orbitals, and uncertainty states.
An interactive journey from classical crisis to quantum reality. Each lesson builds on the last, guiding you from intuition to formalism.
Research Archive
Interactive quantum physical models built from numerical first principles.
3D interactive simulation of Niels Bohr's atomic model. Visualise electron shells, orbital energies, and quantum transitions in real time.
Explore 3D probability density clouds of hydrogen orbitals computed from Laguerre polynomials and spherical harmonics.
Solves 1D finite difference Hamiltonian matrices for particle-in-a-box energy eigenstates and wavefunction amplitudes.
Static bound state penetration & dynamic Gaussian wavepacket reflection and transmission through potential walls.
Visualise trade-offs between position and velocity precision with spectral expansion and live stats overlay.
The Project
This is an evolving experimental project — a personal lab notebook rendered interactive. Each simulation is built from mathematical first principles, not borrowed libraries or pre-baked demos.
The goal is simple: to let curious minds encounter physics as something you can touch, rotate, break, and rebuild — not just read about.
Every concept in quantum mechanics connects to others. Click any node to jump to that lesson.
In 1913, a young Danish physicist proposed something radical: electrons can only exist at specific, quantized distances from the nucleus — and nothing in between.
Overview
The Bohr Model was a pivotal step in the development of quantum mechanics. It introduced the idea that electrons occupy discrete energy levels and that transitions between these levels produce or absorb specific wavelengths of light.
Historical Context
By 1900, classical physics had hit a wall. The prevailing model of the atom — Thomson's "plum pudding" — and later Rutherford's nuclear model could not explain why atoms emit light in discrete spectral lines instead of a continuous rainbow.
J.J. Thomson discovers the electron, shattering the idea of the indivisible atom.
Ernest Rutherford proves the atom has a dense positive nucleus. But why don't electrons spiral inward?
Niels Bohr proposes that electrons occupy fixed, quantized orbits and emit photons when jumping between them.
Core Idea
Bohr's radical postulate was that electrons don't just orbit anywhere — they can only exist in specific, allowed orbits. Each orbit corresponds to a discrete energy level, labelled by the principal quantum number n.
The key insight: Between orbits, there is no in-between. An electron does not smoothly drift from one level to another — it makes an instantaneous quantum leap.
When an electron falls from a higher orbit (n=2) to a lower one (n=1), the energy difference is released as a photon with a precise wavelength. This is why hydrogen emits specific spectral lines, not a smeared spectrum.
Interactive Demonstration
Adjust the principal quantum number n and atomic number Z to see how the orbital radius and energy change — live, with the electron orbit and energy ladder updating as you drag.
Mathematics
The negative sign indicates a bound state — energy must be added to remove the electron. As \(n\) increases, the electron is farther from the nucleus and less tightly bound.
Common Misconceptions
Misconception: Electrons physically travel between orbits during a quantum leap.
Reality: There is no trajectory. The electron simply “is” in one state, then “is” in another. There is no in-between path to describe.
Misconception: The Bohr Model is correct quantum mechanics.
Reality: It is a historical approximation. It fails for multi-electron atoms and cannot predict spectral fine structure. The Schrödinger equation supersedes it.
Real-World Applications
Spectroscopy: Every element emits a unique spectral fingerprint. Astronomers use the Bohr Model’s predictions to identify elements in distant stars.
Lasers: The population inversion mechanism exploits electron transitions between discrete energy levels — a direct consequence of quantized orbits.
Interactive Lab
Now that you understand the theory, explore the Bohr atom in a fully interactive 3D simulation. Adjust electron shells, atomic number, and rotation speed.
A comprehensive overview of the Quantum Codex component library.
Used for general scientific facts or contextual information.
A mathematical description of the quantum state of an isolated quantum system.
Focuses the user's attention on the fundamental principle of the lesson.
Highlights a profound realization or mathematical consequence.
The user should remember this specific point before proceeding.
Electrons do not orbit the nucleus like planets around a star.
Niels Bohr proposes that electrons travel in quantized orbits.
Erwin Schrödinger formulates wave mechanics.
Interactive Demonstration Container
Solve 1D potentials numerically.
Interactive 3D simulation of Niels Bohr's atomic model. Electrons orbit the nucleus in quantised shells — each shell at radius r₀ · n². Hover over orbits for quantum data. Scroll to zoom. Drag to rotate.
Theoretical derivations, formulas, and educational explanations will be added in a future update.
3D probability density clouds of hydrogen-like atomic orbitals computed from Laguerre polynomials and spherical harmonics using Monte Carlo sampling.
Theoretical derivations, formulas, and educational explanations will be added in a future update.
1D Finite Difference Eigensolver & Wavefunction Visualizer. Computes exact discrete Hamiltonian matrix eigenvalues and eigenstate amplitudes for particle in a box.
Theoretical derivations, formulas, and educational explanations will be added in a future update.
Static bound state penetration & dynamic wavepacket reflection/transmission through potential barriers.
Theoretical derivations, formulas, and educational explanations will be added in a future update.
Visualise trade-offs between position and velocity precision with spectral expansion and live stats overlay.
Theoretical derivations, formulas, and educational explanations will be added in a future update.