The age of fossils can sometimes be determined by radiometric dating, which is based on the constant rate of decay of radioactive isotopes. the time required for half of a radioactive isotope to decay is called the half-life of that isotope. for example, the isotope carbon-14 has a half-life of 5,730 years. suppose it is determined that a fossilized leaf contains 12.5% of the carbon-14 that was present when the fossil formed. how old is the fossil? express your answer numerically.

Question

Chemistry

Gia Byrd

24 January, 05:17

The age of fossils can sometimes be determined by radiometric dating, which is based on the constant rate of decay of radioactive isotopes. the time required for half of a radioactive isotope to decay is called the half-life of that isotope. for example, the isotope carbon-14 has a half-life of 5,730 years. suppose it is determined that a fossilized leaf contains 12.5% of the carbon-14 that was present when the fossil formed. how old is the fossil? express your answer numerically.

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Isaac · Answer 1

The age of the fossil given the present amount of Carbon-14 is given in the equation,

A (t) = A (o) (0.5) ^t/h

where A (t) is the current amount, A (o) is the initial amount, t is time and h is the half-life. Substituting the known values to the equation,

A (t) / A (o) = 0.125 = (0.5) ^ (t/5730)

The value of t from the equation is 17190.

Thus, the age of the fossil is mostly likely to be 17190 years old.