The practical limit for ¹⁴C dating occurs when its activity falls to 0.20% of its original value due to interference in detectors by natural background radiation.If the half-life is 5715 years,what is the maximum age of a sample that can be dated by ¹⁴C without interference? A)1.3 × 10⁴ years B)2.9 × 10⁴ years C)5.1 × 10⁴ years D)2.9 × 10⁶ years

Question

Quizplus · Accepted Answer

The activity of a sample is related to its remaining fraction by the equation:
A = Ao * (1/2)^(t/T)
where A is the current activity, Ao is the original activity, t is the time elapsed, and T is the half-life.
When the current activity falls to 0.20% of its original value, we have:
0.002 * Ao = A = Ao * (1/2)^(t/T)
Simplifying, we get:
(1/2)^(t/T) = 0.002
Taking the logarithm of both sides, we get:
t/T = log(0.002) / log(1/2) = 9.97
Therefore, the maximum age of the sample is:
t = T * 9.97 = 5715 * 9.97 = 5.7 * 10^4 years, which is closest to choice C: 5.1 × 10^4 years.

The Practical Limit for 14C Dating Occurs When Its Activity

The Practical Limit for ¹⁴C Dating Occurs When Its Activity