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A radioactive isotope A with half life 693 \times 10^{6} \mathrm{yrs} decay to \mathrm{B} which is stable. A sample of rock from the Mars was found to contain both the elements A and B in the mole ratio 1:8, what is the age of the rock?

Option: 1

1.1 \times 10^{9} yrs


Option: 2

4.5 \times 10^{8} yrs


Option: 3

2.2 \times 10^{9}\, yrs


Option: 4

10^{10}\, yrs


Answers (1)

best_answer

                          \mathrm{A\rightarrow B}
At \mathrm{t= t\, n_{0}-x}         \mathrm{x}              

\mathrm{\frac{n_{0}-x}{x}=\frac{1}{8} \Rightarrow n_{0}=\frac{9 x}{8}}
\mathrm{\lambda=\frac{0.693}{693 \times 10^{6}}=10^{-9} \text { yrs }^{-1}}

\mathrm{t= \frac{2.303}{10^{-9}} \log \left(\frac{n_{0}}{n_{0}-x}\right)=2.303 \times 10^{9} \log 9}
\mathrm{t=2.2 \times 10^{9} \text { yrs }}

Posted by

Ritika Jonwal

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