Becquerel Discovers Radioactivity (1896) — Exponential Decay

On February 25, 1896, Henri Becquerel was preparing to demonstrate that uranium salts fluoresced after sun exposure and then emitted X-rays. But the Paris sky was overcast; he stored the wrapped photographic plates in a drawer with the uranium on top. When he developed the plates days later, they were darkly exposed — without any sunlight. The uranium had emitted radiation spontaneously. Radioactivity is described by exponential decay: N(t) = N₀ e^(−λt), where λ is the decay constant and the half-life T₁/₂ = ln(2)/λ. The mathematics is identical to compound interest in reverse — and both are governed by the same differential equation: rate of change is proportional to current quantity.