☢️ The decay law — count the survivors and N = N₀e^(−λt) draws itself
No one can say when a single nucleus will decay, yet a large population is perfectly predictable. Give every nucleus a random lifetime set by the half-life, run the clock, and COUNT how many survive. The measured curve lands exactly on N = N₀e^(−λt).
A population of 160 identical nuclei (teal). Each is given a random lifetime — you cannot predict which one goes next, only the odds set by the half-life T½.
Decay law N = N₀e−λt ·
λ = ln2 / T½ = —
N = — of 160 · t = — ·
T½ = — (every T½ the count halves)