What is the 14C activity in decay events per minute of 1.0 g of a 3000-year-old wooden object? All living organisms contain an equilibrium concentration of radioactive 14C that gives rise to an average of 15.3 nuclear decay events per minute per gram of carbon. (14C, t1/2 = 5715 years)

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1. Step 1: Understand the problem. We need to find the current activity of 14C in a 1.0 g sample of a 3000-year-old wooden object. We know the initial activity in living organisms is 15.3 decay events per minute per gram.
2. Step 2: Use the half-life formula to determine the decay constant (k). The half-life (t_{1/2}) of 14C is 5715 years. The decay constant k can be calculated using the formula: k = \frac{0.693}{t_{1/2}}.
3. Step 3: Calculate the number of half-lives that have passed in 3000 years. This can be done by dividing the age of the object by the half-life of 14C: \text{Number of half-lives} = \frac{3000}{5715}.
4. Step 4: Determine the remaining fraction of 14C using the formula: \text{Remaining fraction} = (0.5)^{\text{Number of half-lives}}.
5. Step 5: Calculate the current activity of 14C in the sample. Multiply the initial activity (15.3 decay events per minute per gram) by the remaining fraction to find the current activity in decay events per minute for the 1.0 g sample.