Quantised Energy Levels of Hydrogen
Lesson notes
Overview
Bound energies fall as −13.6/n² eV, crowding toward zero. This topic is rated advanced and is number 212 of 227 in Physics. Deeper models, formal results and harder reasoning.
What you are seeing
The panel above shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
In the hydrogen atom, the allowed energies of the bound electron are Eₙ = −13.6 eV/n², for n = 1, 2, 3, …. The ground state is at −13.6 eV, the energy needed to ionise it. Levels crowd closer together as n increases and approach zero, the point at which the electron is free. Transitions between levels give the lines of the hydrogen spectrum, and the simple formula was one of the early triumphs of quantum theory.
Reading the relationship
The expression "Eₙ = −13.6 eV/n²" is a compact summary of the idea. It uses the symbols Eₙ, e, V, n; name what each one stands for before you start. Notice that it contains a squared term, so doubling that quantity changes the result by a factor of four, and a ratio, so increasing the denominator makes the result smaller. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Set every slider to its middle value and note the shape of the curve. 2. Move one slider at a time and describe whether the curve shifts, stretches or turns. 3. Find the value where the behaviour changes sharply, then connect it to the formula.
Try this
Try to explain why the pattern holds, not just what it is. Look for limiting cases and what happens at the edges.
Common pitfalls
Check units and directions first. Many mistakes come from mixing up a scalar with a vector, or from using a formula outside the conditions where it holds.
How it connects
It builds on “Compton Scattering”, the topic before it in Physics. Once you are comfortable, continue with “Quantum Tunnelling Probability”.
Why it matters
Physics explains how the world moves, heats, shines and interacts, and the same principles power technology around you.
Where you might use it
- Revising “Quantised Energy Levels of Hydrogen” before a class, exam or certification
- Designing vehicles, bridges and devices where motion, forces or waves must be predicted
- Understanding how sensors, lasers and communication links actually work
- Explaining everyday phenomena such as sound, light, heat and orbits
Frequently asked questions
What is Quantised Energy Levels of Hydrogen?
Bound energies fall as −13.6/n² eV, crowding toward zero. It is an advanced topic in Physics.
How do I use the Quantised Energy Levels of Hydrogen simulation?
The panel at the top shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression Eₙ = −13.6 eV/n² packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Deeper models, formal results and harder reasoning. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “Compton Scattering”, the previous topic in Physics. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.