The ¹⁴C activity of some ancient Peruvian corn was found to be 10 disintegrations per minute per gram of carbon. If present-day plant life shows 15 dpm/g, how old is the Peruvian corn? (The half-life of ¹⁴C is 5730 yr.)

Question

Quizplus · Accepted Answer

The age of the Peruvian corn can be calculated using the formula for radioactive decay, which is $N = N_0 \times (1/2)^{t/T}$, where $N$ is the final activity, $N_0$ is the initial activity, $t$ is the time, and $T$ is the half-life. Given that the initial activity (present-day) is 15 dpm/g and the final activity (ancient Peruvian corn) is 10 dpm/g, and knowing the half-life of $^{14}C$ is 5730 years, we can solve for $t$. Rearranging the formula to solve for $t$, we get $t = T \times \log_2(N_0/N)$. Substituting the given values, $t = 5730 \times \log_2(15/10)$, which calculates to approximately 3350 years.

The 14C Activity of Some Ancient Peruvian Corn Was Found

The ¹⁴C Activity of Some Ancient Peruvian Corn Was Found