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Equation 1 · Part 10 · Radioactive Clocks: How Nuclear Physics Gave Evolution Its Time

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N(t)=N0 e−λt,t1/2=ln⁡2λ,N(t) = N_0\, e^{-\lambda t}, \qquad t_{1/2} = \frac{\ln 2}{\lambda},
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

The property that makes radioactive decay useful as a clock is not that it happens on a convenient timescale — some isotopes decay in fractions of a second, others over timescales longer than the universe’s age — but that it happens with no memory. An atom of uranium-238 that has existed, undecayed, for four billion years is exactly as likely to decay in the next second as one formed a microsecond ago. There is no wear, no fatigue, no accumulated probability of failure the way there is in a mechanical clock’s escapement or a living organism’s senescence. This absence of memory is what makes decay first-order: the number of decays in a short interval is proportional only to the number of…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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