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Equation 6 · Part 7 · Radioactive Clocks: How Nuclear Physics Gave Evolution Its Time

=

N206N238=eλ238t−1,N207N235=eλ235t−1,\frac{N_{206}}{N_{238}} = e^{\lambda_{238} t} - 1, \qquad \frac{N_{207}}{N_{235}} = e^{\lambda_{235} t} - 1,
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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