The half-life of carbon-14 is 5730 years.If a sample initially contains 2.67 mg carbon-14,what mass of carbon-14 remains in the sample after 2.40 × 10⁴ years?

Question

Quizplus · Accepted Answer

The half-life of carbon-14 is 5730 years. This means that after 5730 years, half of the carbon-14 in a sample will have decayed. After another 5730 years, half of the remaining carbon-14 will have decayed, and so on.After 2.40 × 10^4 years, there will have been 2.40 × 10^4 / 5730 = 4.21 half-lives. This means that 2^4.21 = 16.0 times as much carbon-14 will have decayed as remained. Therefore, the mass of carbon-14 remaining in the sample will be 2.67 mg / 16.0 = 0.17 mg.

The Half-Life of Carbon-14 Is 5730 Years