A) \[2309\,yr,\,\frac{1}{2309}/yr\,\]
B) \[3309\,yr,\,\frac{1}{3309}/yr\,\]
C) \[1309\,yr,\,\frac{1}{1309}/yr\,\]
D) none of the above
Correct Answer: A
Solution :
The sum of half-lives of all atoms divided by the number of all atoms is called the mean-life \[(\tau )\]of radioactive substance. \[\tau ={{T}_{1/2}}/0.693\] where \[{{T}_{1/2}}\]is the half-life of radium. \[\therefore \] \[\tau =\frac{1600}{0.693}\,yr\approx 2309\,yr\] Also mean-life of a radioactive substance is given by \[\tau =\frac{1}{\lambda }\] or \[\lambda =\frac{1}{\tau }=\frac{1}{2309}/yr\]
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