OUTLINE
JURSE TOOLS
Absolute Age of Rocks and Fossils Quick Check
3 of 4 pa
Use this paragraph: The half-life of carbon-14 is 5,700 years. A certain sample of wood has 20 grams of carbon-14 when it is alive.
Item 1
Item 2
How many grams of carbon will it have after 5,700 years?
ltem3
(1 point)
自
Item 4
• 2 grams
O 10 grams
• 40 grams
• 5 grams
I. Introduction
- Explain the concept of half-life
- Example of carbon-14 and its half-life of 5,700 years
II. Main Body
Item 1: Half-life Calculation
- Explain that to calculate the amount of carbon after a certain period of time, the half-life needs to be taken into account
- Breakdown the process of calculating the amount of carbon remaining after 5,700 years
Item 2: Initial Amount of Carbon
- State that the sample of wood initially had 20 grams of carbon-14 when it was alive
Item 3: Calculation Results
- Present the options for the amount of carbon remaining after 5,700 years
- Explain that one option is correct and the others are incorrect
Item 4: Correct Answer
- Provide the correct answer and explain why it is correct
- Emphasize the importance of understanding and using half-life calculations in determining the age of rocks and fossils
III. Conclusion
- Recap the concept of half-life and its application in absolute dating
- Highlight the significance of accurate age determination in geological and paleontological studies.
To find out how many grams of carbon-14 the sample of wood will have after 5,700 years, we need to understand the concept of half-life and how it relates to the decay of carbon-14.
Each radioactive element has a half-life, which is the amount of time it takes for half of the atoms in a sample to decay. For carbon-14, the half-life is 5,700 years. This means that after 5,700 years, half of the carbon-14 atoms in the sample will have decayed.
Using this information, we can determine how many grams of carbon-14 will be left in the sample after 5,700 years. Since we start with 20 grams of carbon-14, we can calculate it as follows:
After 5,700 years, half of the carbon-14 will have decayed, leaving us with 10 grams (half of 20 grams).
After another 5,700 years, half of the remaining carbon-14 will decay, leaving us with 5 grams (half of 10 grams).
After another 5,700 years, half of the remaining carbon-14 will decay, leaving us with 2.5 grams (half of 5 grams).
Since we are dealing with half-lives, we can approximate the amount of carbon-14 remaining after multiple half-lives by dividing the initial amount by 2 for each half-life.
Therefore, after 5,700 years, the wood sample will have approximately 2 grams of carbon-14.
So the correct answer to item 3 is:
• 2 grams.
To answer this question, we can use the concept of half-life to determine how many grams of carbon-14 the wood sample will have after 5,700 years. Here's a step-by-step breakdown:
1. Start with the given information:
- The half-life of carbon-14 is 5,700 years.
- The wood sample initially has 20 grams of carbon-14.
2. Determine the number of half-lives that occur in 5,700 years:
- Since the half-life is 5,700 years, divide the total time (5,700 years) by the half-life:
5700 years ÷ 5700 years = 1 half-life
3. Calculate the amount of carbon-14 remaining after 1 half-life:
- After 1 half-life, half of the carbon-14 will have decayed.
- Multiply the initial amount of carbon-14 by 0.5:
20 grams × 0.5 = 10 grams
4. Therefore, after 5,700 years, the wood sample will have 10 grams of carbon-14 remaining.
Hence, the correct answer to Item 4 is:
- 10 grams.