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?

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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?

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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 N_ut and Pb to be N_pbt.
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.

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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?

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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?.

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