Radioactive Dating?
A sample of igneous rock is found to contain the radioactive parent and daughter isotopes uranium, ^235U, and lead, ^207Pb, in the ration of 12.5%:87.5%. Assuming that no ^207Pb was present when the rock first formed, estimate the age of this sample.
Answer: 2.14 billion years old
How did they get that? I know the half life formula, which we did in math, but I guess the ratio part is confusing me. Thanks!
Don’t worry about the ratio. All that means in this context is that 87.5% of the Uranium has decayed into lead. This is also equal to 7/8. Every half-life, approximately one-half of the material will decay. Since there is only one eighth left, that means that three half lives have passed. (The first decays 1/2, the second decays 1/4, and the third decays 1/8, leaving 1/8.) The half-life of U-235 is 7.038×108 y, or 703.8 million years. Multiplying that by three gives 2.14 billion years.
Radiometric Dating age of the earth