Many famous artifacts have been dated using ¹⁴C dating techniques. One of these were the Dead Sea Scrolls or manuscripts. A decay rate of 0.20 Bq per gram of carbon was measured. If the half-life of ¹⁴C is 5730 years and there are about 15 decays per minute per gram of carbon in a living organism, then calculate the approximate age of the famous manuscripts.

Question

Quizplus · Accepted Answer

We can use the formula for carbon dating: t = (ln(Nf/N0) / (-0.693)) * t1/2 where t1/2 is the half-life, N0 is the initial amount of ¹⁴C, Nf is the final amount of ¹⁴C measured, and t is the age of the artifact. We know that: - t1/2 = 5730 years - N0/Nf = 2^(number of half-lives) - number of half-lives = (decay rate) / (number of decays per gram per minute) * (1 minute / 60 seconds) * (1 gram of carbon) Plugging in the numbers, we get: number of half-lives = (0.20 Bq/g) / (15 decays/min/g) * (1/60 min/sec) * (1 g) number of half-lives = 0.0002222 N0/Nf = 2^(0.0002222) = 1.000057 t = (ln(1.000057) / (-0.693)) * 5730 years t ≈ 1900 years Therefore, the approximate age of the manuscripts is 1900 years. So the best choice is B.

Many Famous Artifacts Have Been Dated Using 14C Dating Techniques

Many Famous Artifacts Have Been Dated Using ¹⁴C Dating Techniques