Quantized Orbits
Niels Bohr proposed that electrons orbit the nucleus like planets, but with a restriction: their Angular Momentum (\(L\)) must be an integer multiple of \(\hbar\):
\[L = n\hbar\]
This simple assumption perfectly predicted the energy levels of the hydrogen atom and explained why the Balmer series exists.
Worked Examples
Example 1: The Ground State
For \(n=1\), the electron is in the "Ground State"—the lowest possible energy. It cannot fall into the nucleus because there is no "zero" state for angular momentum. This is why atoms are stable!
The Bridge to Quantum Mechanics
Bohr's model was a "hybrid"—partly classical and partly quantum. We now know that electrons don't move in circles; they are 3D probability clouds. However, Bohr's core idea that Angular Momentum is Quantized remains perfectly true in the full Schrödinger Equation. The number \(n\) is our first Principal Quantum Number, and it is the master key to understanding the structure of the Periodic Table.