Question

47. Carbon-14 The oldest known frozen human mummy, discovered in the Schnalstal glacier of the Italian Alps in 1991 and called Otzi, was found wearing straw shoes and a leather coat with goat fur, and holding a copper ax and stone dagger. It was estimated that Otzi died 5000 years before he was discovered in the melting glacier. How much of the original carbon-14 remained in Otzi at the time of his discovery?

Accepted Answer

Understand that the problem involves exponential decay, specifically the decay of carbon-14 over time. The amount of carbon-14 decreases according to the formula for radioactive decay. Recall the radioactive decay formula: $$N(t) = N_0$ 	imes e$$^{-\lambda t}$$, where N(t$$)$$ is the amount of carbon-14 remaining after time t$, N_0$ is the original amount, and $$\lambda$$ is the decay constant related to the half-life. Identify the half-life of carbon-14, which is approximately 5730 years. Use this to find the decay constant $$\lambda$$ using the formula $$\lambda = \frac{\ln(2)}{T_{1/2}}$$, where T$$_{1/2}$$ is the half-life. Substitute the given time t = 5000$ years and the decay constant $$\lambda$$ into the decay formula to express the fraction of carbon-14 remaining: $$\frac{N(t)}{$$N_0$$} = $$e^{-\lambda t}. $$Evaluate the expression $$e^{-\lambda t} to $$find the proportion of the original carbon-14 remaining in Otzi at the time of discovery.

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Concetti chiave

Radioactive Decay and Half-Life

Exponential Decay Formula

Application of Carbon-14 Dating