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

Question

Quizplus · Accepted Answer

Using the formula for radioactive decay, we can set up an equation to solve for the age of the wood:

activity = initial activity x (1/2)^(age/half-life)

where initial activity is the activity of the wood when it was new (40 cpm) and activity is the activity of the wood now (10 cpm).

10 = 40 x (1/2)^(age/5730)

Taking the natural logarithm of both sides and solving for age:

ln(10/40) = -age/5730 ln(1/2)

age = -5730 ln(10/40) / ln(1/2)

age = 11,502 years

Therefore, the age of the wood is approximately 11,500 years. The best choice is C.

A Wooden Object from a Prehistoric Site Has a Carbon-14