U-238 Decay Chain: Bateman Equations & Secular Equilibrium (2D)

The 3D original shows individual uranium nuclei emitting alpha particles at a fixed rate. This 2D companion instead models the whole natural U-238 series — the real 14-isotope chain from uranium-238 down through thorium, protactinium, radium, radon, polonium, lead and bismuth to stable lead-206 — as the coupled linear system it actually is, dN_i/dt = λ_i-1N_i-1 − λ_iN_i, solved exactly with the closed-form Bateman equation rather than approximated by animating single atoms. A time-window zoom (seconds through gigayears) lets you watch each daughter build up and settle into secular equilibrium at the timescale where that actually happens — microsecond-lived polonium-214 equilibrates almost instantly, while uranium-234 takes hundreds of thousands of years — and an isotope inspector reports each nuclide's live population, activity in becquerels, and whether it has reached equilibrium with its parent.