Equation 1 · Part 5 · Radioactive Clocks: How Nuclear Physics Gave Evolution Its Time

Symbol t_1/2

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

t_{1/2}

What this part means

the half-life derived from it.

Its job in the formula

$t_1$ /2 is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol t_1/2Article 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 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 geneticist’s model of a large population with a fixed…

Read this part in the article →

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.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

[20] Ernest Rutherford ↗

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