Question

Find the age of the pottery bow nearest year. A student in Greece discovers a pottery bowl that contains 28% of its original amount of C-14. Hola Enter the correct answer. N = Noekt No = inital amount of C-14 (at time t = 0) N = amount of C-14 at time t k = 0.0001 Pa t = time, in years

Answer 1

Using the half-life of carbon-14 (5730 years) and the given that 28% of C-14 remains, the decay constant is calculated and used in the decay formula to determine the age of the pottery bowl.

Step-by-step explanation:

To find the age of the pottery bowl nearest year, we can use carbon-14 dating, which is based on the decay of C-14 to N-14 and uses the known half-life of C-14, which is 5,730 years. The formula for radioactive decay is N = Noe-kt, where N is the remaining amount of C-14, No is the original amount, k is the decay constant, and t is time. Given that only 28% of the original C-14 remains in the pottery bowl, we can rearrange the formula to find the time t using the proportion N/No = 0.28. We can find k using the relation k = 0.693/t1/2, where t1/2 is the half-life of C-14.

Using these values:

Calculate k: k = 0.693/5730 years = 0.000121

Rearrange the decay formula to solve for t: ln(N/No) = -kt

Substitute N/No and k into the equation: ln(0.28) = -0.000121t

Solve for t: t ≈ 1/0.000121 * ln(1/0.28)

Calculate the age of the pottery.

By following these steps with accurate calculations, we can determine the age of the pottery bowl.