SATHEE: Atoms And Nuclei Question 383

Atoms And Nuclei Question 383

Question: In a sample of rock, the ratio of $^{206} P b$ to $^{238} U$ nuclei is found to be 0.5. The age in year of the rock is (given half-life of $, U^{238}$ is $4.5 \times 10^{9}$ years)

Options:

A) $2.25 \times 10^{9}$

B) $4.5 \times 10^{9} l n 3$

C) $4.5 \times 10^{9} \frac{l n (\frac{3}{2})}{l n 2}$

D) $2.25 \times 10^{9} l n (\frac{3}{2})$

Show Answer

Answer:

Correct Answer: C

Solution:

Suppose an initial radionuclide I decays to a final product F with a half- life $T_{1 / 2} .$

At any time, $N_{1} = N_{0} e^{- λ t}$ Number of product nuclei $= N_{F} = N_{0} - N_{I}$ $\frac{N_{F}}{N_{I}} = \frac{N_{0} - N_{I}}{N_{I}} = (\frac{N_{0}}{N_{I}} - I)$

$\frac{N_{0}}{N_{I}} = (1 + \frac{N_{F}}{N_{I}}) = 1 + 0.5 = 1.5$
$∴, \frac{T_{1 / 2} I n (1.5)}{I n 2} = 4.5 \times 10^{9} \frac{ℓ n (\frac{3}{2})}{ℓ n 2} y e a r$

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Atoms And Nuclei Question 383

Question: In a sample of rock, the ratio of 206Pb to 238U nuclei is found to be 0.5. The age in year of the rock is (given half-life of ,U238 is 4.5×109 years)

Options:

Answer:

Solution:

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Question: In a sample of rock, the ratio of $^{206} P b$ to $^{238} U$ nuclei is found to be 0.5. The age in year of the rock is (given half-life of $, U^{238}$ is $4.5 \times 10^{9}$ years)