SATHEE: Nuclei - Result Question 63

Nuclei - Result Question 63

64. The half life of a radioactive isotope ’ $X$ ’ is 20 years. It decays to another element ’ $Y$ ’ which is stable. The two elements ’ $X$ ’ and ’ $Y$ ’ were found to be in the ratio of $1 : 7$ in a sample of a the given rock. The age of the rock is estimated to be

[2013]

(a) 60 years

(b) 80 years

(d) 40 years

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Answer:

Correct Answer: 64. (a)

Solution:

(a) The value of $x$ is $\frac{1}{8}$ $= \frac{x_{0}}{8} = \frac{x_{0}}{2^{3}} \Rightarrow t = 3 T = 3 \times 20 = 60$ years Hence the estimated age of the rock is 60 years

$\begin{aligned} X \to Y_{0} \\ at t = 0 N_{0} 0 \\ at t = t N N_{0} - N \end{aligned}$

$\begin{aligned} \frac{N}{N_{0} - N} = \frac{1}{7} = \frac{N}{N_{0}} = \frac{1}{8} \\ t = 3 T \\ = 3 \times 20 = 60 years \end{aligned}$

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Nuclei - Result Question 63

64. The half life of a radioactive isotope ’ X ’ is 20 years. It decays to another element ’ Y ’ which is stable. The two elements ’ X ’ and ’ Y ’ were found to be in the ratio of 1:7 in a sample of a the given rock. The age of the rock is estimated to be

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64. The half life of a radioactive isotope ’ $X$ ’ is 20 years. It decays to another element ’ $Y$ ’ which is stable. The two elements ’ $X$ ’ and ’ $Y$ ’ were found to be in the ratio of $1 : 7$ in a sample of a the given rock. The age of the rock is estimated to be