(II) An ancient wooden club is found that contains 85 g of...

(II) An ancient wooden club is found that contains 85 g of
carbon and has an activity of 7.0 decays per second. Deter-
mine its age assuming that in living trees the ratio of
14 $\mathrm{C} /^{12} \mathrm{C}$ atoms is about $1.3 \times 10^{-12}$ .

Key Concepts

Radiocarbon Dating

Radiocarbon dating is a method used to determine the age of organic materials by measuring the remaining concentration of Carbon-14. Assuming a known ratio of Carbon-14 to Carbon-12 in living organisms, the decrease in Carbon-14 over time through radioactive decay can be used to estimate the time elapsed since the death of the organism.

Isotopic Ratio

An isotopic ratio is the proportion of a radioactive isotope relative to a stable isotope within a sample. This ratio serves as a reference for determining the original concentration of the radioactive isotope in living organisms and is fundamental to radiocarbon dating methods.

Activity

Activity refers to the number of radioactive decays per unit time, typically measured in decays per second (Becquerels). It provides a measure of the current rate of decay in a sample and is used in radiometric dating to infer the quantity of the radioactive isotope present.

Decay Constant

The decay constant is a parameter that quantifies the probability per unit time that a radioactive atom will decay. It is related to the half-life through the equation ? = ln(2)/t½ and is used to compute decay rates and understand the exponential nature of radioactive decay.

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This process follows a probabilistic and exponential law, meaning that the number of radioactive atoms decreases over time at a rate proportional to the current amount present.

Half-Life

Half-life is the time required for half of the radioactive nuclei in a sample to decay. It is a key parameter in understanding radioactive decay processes and is used to determine the age of objects by comparing the present amount of a radioactive isotope to its initial amount.

Transcript

Please give Ace some feedback