Day 312 · Nov 7

The Birthday of Marie Curie (1867) – Mathematics of Radioactivity

Marie Curie discovered radium and polonium. The mathematics of radioactive decay: dN/dt = –λN, so N(t) = N₀e^(–λt). Half‑life T₁/₂ = ln2/λ. She used differential equations to model decay chains (e.g., uranium to radium to radon). She also used integral calculus to measure the heat released by radium. Her notebooks are still radioactive and must be handled with protective gear. Her work led to cancer treatments (radiotherapy) and the understanding of atomic structure. Mathematics and physics together revealed the invisible.

If a sample has half‑life 1,600 years (radium‑226), how much remains after 4,800 years? (Three half‑lives: 1/8 of original.)

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