Physics
Particle-in-a-Box Model
Quick fact
The particle-in-a-box model predicts that the energy of the particle is proportional to the square of an integer (n²), meaning the energy levels are spaced farther apart as you go higher — unlike the equally spaced steps of a ladder.
Why this is interesting
Imagine a marble trapped inside a perfectly sealed, frictionless box — it can only bounce back and forth. Now shrink that box to the size of an atom; suddenly, the marble doesn't just bounce — it becomes a wave, and only certain bounces are allowed. Why?