As more half-lives pass, the number of parent atoms remaining approaches zero. This work is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.Based on this principle, geologists can count the number of parent atoms relative to daughter products in a sample to determine how many half-lives have passed since a mineral grain first formed. An example of how the initial number of radioactive parent atoms (blue diamonds) in two mineral grains (gray hexagons) changes over time (measured in half-lives) relative to the number of daughter products (red squares). The left-most box in the figure above represents an initial state, with parent atoms distributed throughout molten rock (magma).Carbon's (C) atomic number is 6 because it has six protons in its nucleus; gold's (Au) atomic number is 79 because it has 79 atoms in its nucleus.
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In 1650, Archbishop James Ussher famously used the genealogy of the Old Testament of the Bible (e.g., Genesis, Chapter 5)--and the human lifespans recorded in it--to estimate the age of the Earth; he concluded that the Earth was young in age, having formed in 4004 B. In the 1800's, practitioners of the young science of geology applied the uniformitarian views of Hutton and Lyell (see the introduction to this chapter) to try to determine the age of the Earth.
For example, some geologists observed how long it took for a given amount of sediment (say, a centimeter of sand) to accumulate in a modern habitat, then applied this rate to the total known thickness of sedimentary rocks.
When they did this, they estimated that the Earth is many millions of years old.
We now know that this estimate is far, far too young*.
After one half-life has passed, half (50%, or four) of the parent atoms in each mineral grain have been transformed into their daughter products (red squares).
After two half-lives have passed, 75% (six) of the original parent atoms in each grain have been transformed into daughter products.You might be wondering how it is possible to know the number of parent atoms that were originally in a sample.This number is attained by simply adding the number of parent and daughter atoms currently in the sample (because each daughter atom was once a parent atom).How many parent atoms would remain if three half-lives passed?By counting the numbers of parent atoms remaining in a sample relative to the number originally present, it is possible to determine the number of half-lives that have passed since the initial formation of a mineral grain (that is, when it became a "closed system" that prevented parent and daughter atoms from escaping).As the magma cools, grains of different minerals begin to crystalize.