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We have 238U which decays with a half-life of 4.51 X 105 years, the decay series eventually ending as 206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of 206Pb to 238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]
- a)195.2 X 103 years
- b)1952.4 years
- c)1952.4 X 103 years
- d)19.5 X 103 years
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
We have238U which decays with a half-life of 4.51 X 105years, the deca...
Initially, we had the number of U as N0 and Pb to be 0.
After a time t we have the number of U as Nut and Pb to be Npbt.
We are given that the ratio of the number of atoms of 206Pb to 238U is 0.003 at the time of stability.
Hence, we get:
Also as the number of other particles produced in the chain is negligible we have:
Simplifying it we get:
which implies,
We know that
is the decay constant.
Hence, by putting this in the above equation we get:
From here we solve for t and we get:
t = 1952.4 years.
After a time t we have the number of U as Nut and Pb to be Npbt.
We are given that the ratio of the number of atoms of 206Pb to 238U is 0.003 at the time of stability.
Hence, we get:
Also as the number of other particles produced in the chain is negligible we have:Simplifying it we get:
which implies,We know that
is the decay constant.Hence, by putting this in the above equation we get:
From here we solve for t and we get:
t = 1952.4 years.
Most Upvoted Answer
We have238U which decays with a half-life of 4.51 X 105years, the deca...
Understanding the Decay Process
The decay of 238U to 206Pb follows a radioactive decay process where 238U transforms over time into stable 206Pb. Given the half-life of 238U, we can calculate the age of the rock sample using the ratio of 206Pb to 238U.
Given Data
- Half-life of 238U: 4.51 x 10^5 years
- Ratio of 206Pb to 238U: 0.003
- Natural logarithm: ln(1.003) = 0.003
Calculation Steps
1. Understanding the Ratio:
The ratio of 206Pb to 238U implies that for every 1,000 atoms of 238U, there are 3 atoms of 206Pb.
2. Using the Decay Formula:
The relationship between the number of radioactive atoms remaining (N) and the number of stable decay products (D) can be expressed as:
D = N0 - N, where N0 is the initial quantity of 238U.
3. Relating D to N:
From the ratio, we know:
D/N = 0.003
Thus, N = (1/0.003) * D = 333D.
4. Exponential Decay Formula:
Using the formula for radioactive decay:
N = N0 * e^(-λt), where λ = ln(2) / half-life.
5. Solving for Age (t):
Rearranging gives:
t = - (half-life / ln(2)) * ln(N/N0).
Plugging in the values, we can calculate the age of the rock sample.
Final Calculation
After performing the calculations, we find that the age of the rock sample is approximately 1952.4 years, matching option 'B'.
Conclusion
The age of the rock sample is confirmed to be:
- Answer: 1952.4 years (Option B).
The decay of 238U to 206Pb follows a radioactive decay process where 238U transforms over time into stable 206Pb. Given the half-life of 238U, we can calculate the age of the rock sample using the ratio of 206Pb to 238U.
Given Data
- Half-life of 238U: 4.51 x 10^5 years
- Ratio of 206Pb to 238U: 0.003
- Natural logarithm: ln(1.003) = 0.003
Calculation Steps
1. Understanding the Ratio:
The ratio of 206Pb to 238U implies that for every 1,000 atoms of 238U, there are 3 atoms of 206Pb.
2. Using the Decay Formula:
The relationship between the number of radioactive atoms remaining (N) and the number of stable decay products (D) can be expressed as:
D = N0 - N, where N0 is the initial quantity of 238U.
3. Relating D to N:
From the ratio, we know:
D/N = 0.003
Thus, N = (1/0.003) * D = 333D.
4. Exponential Decay Formula:
Using the formula for radioactive decay:
N = N0 * e^(-λt), where λ = ln(2) / half-life.
5. Solving for Age (t):
Rearranging gives:
t = - (half-life / ln(2)) * ln(N/N0).
Plugging in the values, we can calculate the age of the rock sample.
Final Calculation
After performing the calculations, we find that the age of the rock sample is approximately 1952.4 years, matching option 'B'.
Conclusion
The age of the rock sample is confirmed to be:
- Answer: 1952.4 years (Option B).
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We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer? for UGC NET 2025 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UGC NET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer?.
We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer? for UGC NET 2025 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UGC NET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer?.
Solutions for We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for UGC NET.
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We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice We have238U which decays with a half-life of 4.51 X 105years, the decay series eventually ending as206Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of206Pb to238U is 0.003. Assuming that all the Pb has been produced by the decay of U and that all other half-lives in the chain are negligible. The age of the rock sample is? Given that [ln (1.003) = 0.003]a)195.2 X 103yearsb)1952.4 yearsc)1952.4 X 103yearsd)19.5 X 103yearsCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice UGC NET tests.
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