A) 2.5
B) 5
C) 10
D) 20
Correct Answer: C
Solution :
From Rutherford-Soddy law, the number of atoms after n half-lives is given by \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[\frac{1}{16}={{\left( \frac{1}{2} \right)}^{n}}\] \[{{\left( \frac{1}{2} \right)}^{4}}={{\left( \frac{1}{2} \right)}^{n}}\] \[n=4\] Also \[n=\frac{t}{T}\] \[\Rightarrow \] \[T=\frac{t}{n}=\frac{40}{4}=10\,days.\]
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