Carbon 14 Dating Problems - Nuclear Chemistry & Radioactive Decay
The Organic Chemistry Tutor・8 minutes read
The decay rate of carbon 14 in living trees versus old dried wood is explained by the absorption of carbon dioxide maintaining a constant ratio in living trees. Calculating the rate constant k using the half-life of carbon 14 enables estimating the age of old wood based on radiation counts per minute per gram.
Insights
- The decay rate difference between living and dried wood from the same tree type is caused by the living tree's continuous absorption of carbon dioxide, maintaining a stable carbon 14 to carbon 12 ratio and decay rate, while dried wood no longer absorbs carbon dioxide, leading to a decrease in carbon 14 count and decay rate over time.
- By calculating the rate constant k using the half-life of carbon 14 and applying the formula n final over n initial equals negative kt, the age of old wood can be estimated to be approximately 11,457 years. This method can also be used to determine the age of a tree by summing the years it was alive and the years it has been dead, providing a total age calculation.
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Recent questions
How does carbon 14 decay in living trees differ from old dried wood?
The decay rate of carbon 14 in living trees is 13.6 counts per minute per gram, while in old dried wood, it is 3.4 counts per minute per gram. Living trees maintain a constant decay rate by absorbing carbon dioxide, while dried wood no longer absorbs carbon dioxide, causing its decay rate to decrease over time.
What causes the difference in decay rates between living trees and old dried wood?
The difference in decay rates is due to living trees constantly absorbing carbon dioxide, which maintains a constant carbon 14 to carbon 12 ratio and decay rate. In contrast, old dried wood no longer absorbs carbon dioxide, leading to a decrease in its carbon 14 count and decay rate over time.
How is carbon 14 created in the atmosphere?
Carbon 14 in the atmosphere is created when nitrogen 14 interacts with neutrons to form carbon 14. This carbon 14 then undergoes beta decay to produce nitrogen 14 again, maintaining a constant level of carbon 14 in the atmosphere.
How can the age of old wood be estimated using carbon 14 decay?
To estimate the age of old wood, calculate the rate constant k using the half-life of carbon 14, then use the formula n final over n initial equals negative kt. By comparing the initial and final radiation counts per minute per gram, an approximate age of the wood can be determined.
How can the age of a tree be calculated using carbon 14 decay?
The age of a tree can be calculated by adding the years it was alive (initial radiation) to the years it has been dead (final radiation). This total time represents the age of the tree based on the decay rate of carbon 14 in the tree's wood.
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Summary
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Carbon 14 Decay Rates Determine Wood Age
- Living tree has a carbon 14 decay rate of 13.6 counts per minute per gram, while old dried wood from the same tree type has a decay rate of 3.4 counts per minute per gram.
- The difference in decay rates is due to the living tree constantly absorbing carbon dioxide, maintaining a constant carbon 14 to carbon 12 ratio and decay rate, while the dried wood no longer absorbs carbon dioxide, causing its carbon 14 count and decay rate to decrease over time.
- Carbon 14 in the atmosphere remains constant, with nitrogen 14 interacting with neutrons to create carbon 14, which then undergoes beta decay to produce nitrogen 14 again.
- To estimate the age of the old wood, calculate the rate constant k using the half-life of carbon 14 (ln 2 divided by 5730 years), then use the formula n final over n initial equals negative kt, with initial radiation at 13.6 counts per minute per gram and final radiation at 3.4 counts per minute per gram, resulting in an age of approximately 11,457 years.
- The age of a tree can be calculated by adding the years it was alive (initial radiation) to the years it has been dead (final radiation), with the total time representing the age of the tree.
- To determine the radiation count per minute per gram if the wood was 18,000 years old, use the formula n final equals n initial times e raised to the negative kt, resulting in a final radiation count of 1.54 counts per minute per gram, indicating the wood's age to be just under 1.7 counts per minute per gram.
