Scientists have analyzed charcoal from Stonehenge by radiocarbon dating and found that the activity is about 9.5 dpm per gram of carbon.If carbon-14 has an activity of 15.3 dpm,what is the estimated age of the charcoal? (t1/2 = 5730 years)

Question

Quizplus · Accepted Answer

We can use the equation for exponential decay of carbon-14:

A = A0e^(-kt)

where A is the activity after time t, A0 is the initial activity, k is the decay constant (ln2/t1/2), and t is the time elapsed.

We can solve for t by rearranging the equation:

t = -ln(A/A0)/k

First, we need to find the decay constant:

k = ln2/t1/2 = ln2/5730 = 0.000120968

Next, we can plug in the given values for A and A0:

9.5 = 15.3e^(-0.000120968t)

Simplifying:

e^(-0.000120968t) = 0.6209150327

Taking the natural logarithm of both sides:

-0.000120968t = ln(0.6209150327)

Solving for t:

t = -ln(0.6209150327)/0.000120968 ≈ 3820 years

Therefore, the estimated age of the charcoal is approximately 3800 years. Choice B is the correct answer.

Scientists Have Analyzed Charcoal from Stonehenge by Radiocarbon Dating and Found