Carbon-14 has a half-life of 5730 years. A sample of wood has been recovered by an archaeologist. The sample is sent to a laboratory, where it is determined that the activity of the sample is 0.144 Bq/g. By comparing this activity with the activity of living organic matter, 0.230 Bq/g, the scientist determines how old the wood sample is, or more precisely, when the tree that the sample came from died. How old is the sample of wood? O 2630 years O 2940 years O 4250 years O 4590 years O 3870 years o o o
Radioactive decay
The emission of energy to produce ionizing radiation is known as radioactive decay. Alpha, beta particles, and gamma rays are examples of ionizing radiation that could be released. Radioactive decay happens in radionuclides, which are imbalanced atoms. This periodic table's elements come in a variety of shapes and sizes. Several of these kinds are stable like nitrogen-14, hydrogen-2, and potassium-40, whereas others are not like uranium-238. In nature, one of the most stable phases of an element is usually the most prevalent. Every element, meanwhile, has an unstable state. Unstable variants are radioactive and release ionizing radiation. Certain elements, including uranium, have no stable forms and are constantly radioactive. Radionuclides are elements that release ionizing radiation.
Artificial Radioactivity
The radioactivity can be simply referred to as particle emission from nuclei due to the nuclear instability. There are different types of radiation such as alpha, beta and gamma radiation. Along with these there are different types of decay as well.
![### Determining the Age of a Wooden Artifact Using Carbon-14 Dating
**Carbon-14 has a half-life of 5730 years. A sample of wood has been recovered by an archaeologist. The sample is sent to a laboratory, where it is determined that the activity of the sample is 0.144 Bq/g. By comparing this activity with the activity of living organic matter, 0.230 Bq/g, the scientist determines how old the wood sample is, or more precisely, when the tree that the sample came from died. How old is the sample of wood?**
#### Possible Answers:
- 2630 years
- 2940 years
- 4250 years
- 4590 years
- 3870 years
### Explanation:
To find the age of the wood sample, we use the formula for carbon dating, which is based on the exponential decay of Carbon-14. The formula is:
\[ N(t) = N_0 \cdot ( \frac{1}{2} )^{t/T} \]
Where:
- \( N(t) \) is the current activity (0.144 Bq/g).
- \( N_0 \) is the initial activity (0.230 Bq/g).
- \( t \) is the time elapsed.
- \( T \) is the half-life of Carbon-14 (5730 years).
Rearranging to solve for \( t \), we get:
\[ t = T \cdot \left( \frac{\log (N(t)/N_0)}{\log (1/2)} \right) \]
Applying the values:
\[ t = 5730 \cdot \left( \frac{\log (0.144/0.230)}{\log (1/2)} \right) \]
Calculating the logarithms:
\[ t = 5730 \cdot \left( \frac{\log (0.626)}{\log (0.5)} \right) \]
\[ t = 5730 \cdot \left( \frac{-0.204}{-0.301} \right) \]
\[ t = 5730 \cdot 0.678 \]
So:
\[ t \approx 3885.54 \]
The closest answer:
- **3870 years**
Remember to always cross-check your calculations and verify against provided options to ensure accuracy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F212d4b15-52d8-4abc-bca6-3221f0b23928%2Fb992785f-4c29-4605-bad9-ce4d6a9ca681%2F29w94df_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
