4 February, 07:55

# If you analyzed the chemical composition of a rock and found that it contained 1 atom of radioactive uranium (238U) for every 3 atoms of stable lead (207Pb), how old is this rock? Recall that 238U decays into 207Pb with a half life of 700 million years. You can assume that there was no lead in the rock when it initially solidified.

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1. 4 February, 09:46
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The rock is 1400 million years old.

Explanation:

Hi there!

The half-life of uranium 238 is the time it takes for half the atoms of the sample to decay into lead. The chemical composition of the rock shows that 1 of every 4 atoms is an atom of uranium. Then, only 25% of the original amount of uranium is present in the rock.

After one half-life the amount of uranium in the rock is 50% of the original amount. After a second half-life, the amount of uranium will be half the amount that remained after the first half-life, that is, 25% of the original amount. Then, the rock is 2 half-lives old, 1400 million years old.

Have a nice day!