The Naive Question: If the electron is attracted to the proton, why doesn't it spiral in and collapse into the nucleus?

Classical Answer (Wrong): In classical physics, an orbiting charged particle continuously radiates energy and should spiral into the nucleus in ~10^{-8} seconds. Atoms should be unstable. But they're not.

Bohr's Answer (Partial): Electrons can only exist in specific orbits with quantized angular momentum. The ground state (n=1) is the lowest allowed orbit — it cannot go lower.

Quantum Mechanical Answer (Complete):

1. If the electron were confined to the nucleus ($\Delta x$ ≈ 10^{-15} m), by Heisenberg's principle: $\Delta p$ ≥ h/(4π×10^{-15}) = enormously large momentum.
2. Large $\Delta p$ means large KE = $p^{2}$/2m — the electron would have too much kinetic energy to stay near the nucleus.
3. The ground state (n=1) is the equilibrium where total energy (KE + PE) is minimized.
4. Going closer: KE increases faster than PE decreases → total energy increases → NOT favorable.
5. Therefore, the electron settles at the first Bohr radius (0.529 Å) as a natural equilibrium.

Bottom Line: Atoms are stable because quantum mechanics (Heisenberg uncertainty + wave nature) prevents the electron from collapsing. The ground state is not the lowest energy position — it is the lowest TOTAL energy state.