The half-life of carbon-14 is 5730 years. How many grams of carbon-14 remain after 28,650 years if the original amount was 28.0 g?
A.5.60 g
B.2.80 g
C.0.875 g
D.14.0 g
The Correct Answer and Explanation is:
To find out how much carbon-14 remains after 28,650 years, we can use the concept of half-life. The half-life of carbon-14 is 5,730 years, meaning that every 5,730 years, half of the existing carbon-14 will decay.
Step-by-Step Calculation:
- Determine the number of half-lives that have passed:
To find out how many half-lives fit into 28,650 years, we divide the total time by the half-life:
[
\text{Number of half-lives} = \frac{28,650 \text{ years}}{5,730 \text{ years/half-life}} \approx 5
] - Calculate the remaining amount of carbon-14:
The amount of carbon-14 remaining after each half-life can be calculated using the formula:
[
\text{Remaining amount} = \text{Original amount} \times \left(\frac{1}{2}\right)^{\text{number of half-lives}}
]
Substituting the values:
[
\text{Remaining amount} = 28.0 \, \text{g} \times \left(\frac{1}{2}\right)^{5}
]
[
= 28.0 \, \text{g} \times \frac{1}{32} \approx 0.875 \, \text{g}
]
Conclusion:
After 28,650 years, the remaining amount of carbon-14 is approximately 0.875 grams.
Answer:
C. 0.875 g
Explanation:
Carbon-14 dating is widely used in archaeology and geology to determine the age of organic materials. This radioactive isotope of carbon is present in the atmosphere and is absorbed by living organisms. Once an organism dies, it stops taking in carbon-14, and the existing carbon-14 begins to decay at a known rate, defined by its half-life.
The half-life is crucial for dating because it allows us to estimate how long it has been since the death of the organism. In this case, knowing that the half-life is 5,730 years, we determined that over 28,650 years, the initial amount of carbon-14 would undergo five half-lives, resulting in a final mass of 0.875 grams. This demonstrates the exponential decay characteristic of radioactive isotopes, illustrating how, over time, the quantity diminishes significantly, making carbon-14 a powerful tool in dating ancient organic remains.