☢️ Radioactive Decay & Half-life
📖 The Physics
Radioactive nuclei decay randomly — you can never predict which one goes next, only the probability that any given one will. It seems completely unpredictable.
Yet with a huge number of nuclei, the total follows a smooth exponential curve. The half-life T½ is the time for half of them to decay; after each half-life the number left halves again.
N = N₀ · (1/2)^(t / T½) = N₀ · e^(−λt), λ = ln 2 / T½
Watch the green count halve every T½ (red lines). The jagged green line is this random run; the blue line is the ideal law it hugs. This is the basis of carbon dating.
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