Quantum models help us understand why electrons in atoms are stable. They use ideas that are quite different from the rules of classical physics. Let’s break it down into simpler parts:

1. Wave-Particle Duality: Electrons aren’t just tiny balls; they can also behave like waves. This means they have something called wave functions. These functions tell us how likely we are to find an electron in different spots around the atom’s center, known as the nucleus.

2. Quantized Energy Levels: Unlike regular particles that can have any amount of energy, electrons can only have certain amounts of energy in an atom. These specific energy levels come from a special math equation called the Schrödinger equation. For example, in a hydrogen atom (which has one electron), the energy levels can be described by this formula:

   $E_n = -\frac{13.6 \, \text{eV}}{n^2}$

   Here, $n$ is a whole number (like 1, 2, 3, and so on).

3. Heisenberg Uncertainty Principle: This idea tells us that we can’t know exactly where an electron is and how fast it’s moving at the same time. Because of this uncertainty, electrons can’t just fall into the nucleus; they stay in their places.

These quantum ideas help us build a better picture of how atoms work. They explain why electrons can stay in their orbits without crashing into the nucleus.