A) 15 min
B) 30 min
C) 45 min
D) 60 min
Correct Answer: B
Solution :
If N be the number of atoms of ratioactive substance, left at some instant of time and \[{{N}_{0}}\] be the number of atoms initially present in the substance, then number of atoms left after n half lives is given by \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] Given, \[\frac{N}{{{N}_{0}}}=\frac{1}{16}\] \[\therefore \] \[\frac{1}{16}={{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[\frac{1}{16}=\frac{1}{{{2}^{n}}}\] \[\Rightarrow \] \[n=4\] Also \[n=\frac{t}{{{T}^{1/2}}}\] \[\therefore \] \[{{T}_{1/2}}=\frac{t}{n}=\frac{2}{4}\times 60\,\min =30\,\min \]
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