Equation 1 · Part 6 · Radioactive Clocks: How Nuclear Physics Gave Evolution Its Time

Symbol λ

N(t) = N_0\, e^{-\lambda t}, \qquad t_{1/2} = \frac{\ln 2}{\lambda},

\lambda

What this part means

the decay constant characteristic of the isotope.

Its job in the formula

λ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Full expressionSymbol λArticle meaning

Where the article explains it

where $N_0$ is the initial population, $\lambda$ is the decay constant characteristic of the isotope, and $t_{1/2}$ is the half-life derived from it.

The passage around this formula

…of decays in a short interval is proportional only to the number of atoms present, not to their age, giving the population as a whole an exponential decline, $N(t) = N_0\, e^{-\lambda t}, \qquad t_{1/2} = \frac{\ln 2}{\lambda}$ . where $N_0$ is the initial population, $\lambda$ is the decay constant characteristic of the isotope, and $t_{1/2}$ is the half-life derived from it. This is the one place in the article where the evolutionary-population analogy is exact rather than suggestive: a sample of $N_0$ identical atoms behaves, statistically, exactly as a population…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

[20] Ernest Rutherford ↗

These citations provide research context; check each source for the exact claim it supports.