Water at various depths in the ocean is recirculated to the surface at different rates. The length of time elapsed since water has been brought up to the surface of the ocean can be estimated by measuring the radioactivity of the ¹⁴C in the CO₂dissolved in the water. If a sample of water brought up from a depth of 1000 meters displays 88.5% of the radioactivity of water at the surface, how "old" is the water? The rate constant for the decay of ¹⁴C is 1.21 x 10^-4 yr^-1.

Question

Quizplus · Accepted Answer

The decay of radioactivity can be described by the first-order decay equation, which is ln(N/N0) = -kt, where N is the remaining radioactivity, N0 is the initial radioactivity, k is the rate constant, and t is the time. Given that N/N0 = 0.885 and k = 1.21 x 10^-4 yr^-1, solving for t gives a value within the range of 900 to 1100 years.

Water at Various Depths in the Ocean Is Recirculated to the Surface