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Equation 6 · Part 8 · Radioactive Clocks: How Nuclear Physics Gave Evolution Its Time

fraction

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,
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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