The Math of Time
How random chaos becomes predictable order.
The Roll of the Dice
Radioactive decay is fundamentally random. You cannot look at a specific atom and predict when it will decay. It might happen in the next second, or in a billion years.
However, each isotope has a specific intrinsic probability of decaying per unit time. We call this the Decay Constant (λ).
The Dice Analogy
Imagine a billion dice. You can't predict what
one die will roll. But you know with certainty
that roughly 1/6th of them will roll a '6' if
you throw them all at once.
A High λ is like
rolling a 20-sided die where 19 sides are
"Decay".
A Low λ is like rolling
a coin where "Heads" is decay? No, it's more like
rolling a 1,000,000-sided die.
The likelihood that a single nucleus will decay in the
next second.
Units: s⁻¹
Measurement of Time
Because λ is often a tiny, abstract number (like 1.4 × 10⁻¹¹ s⁻¹), we prefer to talk about the Half-Life (t1/2).
This is simply the time it takes for 50% of your sample to decay. It is inversely proportional to the decay constant.
- ↑ λHigh Probability Unstable. Decays fast. Short Half-Life.
- ↓ λLow Probability Stable-ish. Decays slowly. Long Half-Life.
Order from Chaos
While individual atoms are unpredictable, large populations follow a strict mathematical law. The number of atoms remaining (N) at any time (t) follows an exponential decay curve starting from the initial amount (N0).