A) 120 min
B) 60 min
C) 30 min
D) 15 min
Correct Answer: C
Solution :
From Rutherford-Soddys laws the number of atoms left after n half-lives is \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] Given, \[N=\frac{{{N}_{0}}}{16}\] \[\therefore \] \[\frac{{{N}_{0}}}{16}={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[\frac{1}{16}={{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[n=4\] Let T be half-life, then \[n=\frac{t}{T}\] Given, t = 2 h \[=2\times 60=120\] min \[\therefore \] \[T=\frac{120}{4}=30\] min
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