Equation 1 · Part 3 · Radioactive Clocks: How Nuclear Physics Gave Evolution Its Time

Symbol N_0

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

N_0

What this part means

the initial population.

Its job in the formula

$N_0$ is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol N_0Article 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

…makes decay first-order: the number 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,…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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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.