$word_{count}$: 190

$delta_x$ * $delta_p$ >= $\frac{h}{4*pi}$. Equivalently: $delta_x$ * m * $delta_v$ >= $\frac{h}{4*pi}$. This is fundamental — not a measurement limitation but an intrinsic property of quantum mechanics. For an electron confined to atomic dimensions (~10^-10 m): $delta_v$ ~ 10^6 m/s (comparable to actual velocity). For a 1 g object confined to 1 mm: $delta_v$ ~ 10^-28 m/s (completely negligible). Consequences: (1) Electron "orbits" are meaningless — replaced by probability distributions (orbitals). (2) The concept of trajectory doesn't apply to atomic particles. (3) Position and momentum are complementary variables — knowing one precisely makes the other completely uncertain. $delta_E$ * $delta_t$ >= $\frac{h}{4*pi}$ is the energy-time uncertainty relation (for excited state lifetimes). The uncertainty principle explains why electrons don't spiral into the nucleus: confining the electron to a smaller space increases its kinetic energy (higher momentum uncertainty), creating a balance.