Question

A wooden object from a prehistoric site has a carbon-14 activity of 10 counts per minute (cpm) compared to 40 cpm for new wood. If carbon-14 has a half-life of 5730 years, what is the age of the wood?

Please explain your steps and conversions.

Answer 1

Answer: 11,500

Step-by-step explanation:

I took the same test and this was the correct answer

Answer 2

• 11,560 years

Step-by-step explanation:

While trees are alive, they exchange carbon with the atmosphere and the content of carbon-14 remains constant. Once, the plants die the exchange of carbon with the atmospher ends, and carbon-14 content will decrease only by the radioactivity.

Thus, it is assumed that when the prehistorical object was manufactured the carbon-14 activity was 40 cpm (that of new wood), and the ratio of the current carbon-14 activity 10 cpm is related with the number of half-lives elapsed since the object was manufactured in this way:

• actual radioactivity / original radioactivity = (1/2) ⁿ

Where n is the number of half-lives elapsed.

Hence, you can do the calculations:

• (10 cpm / 40 cpm) = (1/2)ⁿ

• (1 / 4) = (1/2)ⁿ

• (1 / 2²) = (1/2)ⁿ

• 1 / 2² = 1 / 2ⁿ

• n = 2

As stated that carbon-14 has a half-life of 5730 year, and we obtained that two half-lives have elapses, 2 × 5730 years = 11,560 years is the age ot the wood.