$$\frac{N_{206}}{N_{238}} = e^{\lambda_{238} t} - 1, \qquad \frac{N_{207}}{N_{235}} = e^{\lambda_{235} t} - 1$$

Equation 6 · Evolutionary Nuclear Physics

Radioactive Clocks: How Nuclear Physics Gave Evolution Its Time

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Uranium’s usefulness as a clock is doubled by an accident of nuclear structure: natural uranium consists of two isotopes, uranium-238 and uranium-235, which decay through separate chains to two different stable lead isotopes, lead-206 and lead-207 respectively, at two different, independently measured rates. Uranium-238’s half-life is about four point four seven billion years and uranium-235’s is about seven hundred four million years, values fixed by direct laboratory counting experiments [ 6 ] and formally adopted as the field’s working convention shortly after [ 7 ] . Because both chains run inside the same mineral grain simultaneously, from the same crystallization event, a single zircon…

Meanings in this article

• $N_{206}$: the radiogenic lead atoms accumulated from each chain and $N_{238}$.
• $N_{207}$: the radiogenic lead atoms accumulated from each chain and $N_{238}$.
• $N_{235}$: the surviving parent uranium atoms.

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