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The halt life of a radioactive isotope $\mathrm{X}$ is 60 years. It decays in to another stable element $\mathrm{Y}$ .The two elements $\mathrm{X}$ and $\mathrm{Y}$ were found to be in the ratio $\mathrm{1: 7}$ in a sample of a given ruck. Then age of sample is
Option: 1
$120 \, \mathrm{yrs}$

Option: 2
$180\, \mathrm{yrs}$

Option: 3
$210\, \mathrm{yrs}$

Option: 4
$240 \, \mathrm{yrs}$

Answers (1)

best_answer

                             $\mathrm{X}$         $\longrightarrow$          $Y$

$\mathrm{Initially \: (t=0)}$      $\mathrm{N_{0}}$                       0
       $\mathrm{At \: t=t \quad \quad \mathrm{~N}}$                        $\mathrm{N_{0}-N}$ .

$\mathrm{given \: \frac{N}{N_0-N}=\frac{1}{7} \: \: \Rightarrow\: \: 8 N=N_0}$
$\mathrm{\Rightarrow \quad N=\frac{N_0}{8}=\frac{N_0}{2^3} . }$
$\mathrm{ \Rightarrow \frac{t}{t_1 / 2}=3\: \: \Rightarrow \: \: t=3\, t_{1} / 2=180 \, \mathrm{yrs.} }$

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Rakesh

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