A) \[15\min \]
B) \[30\min \]
C) \[45\min \]
D) \[60\min \]
Correct Answer: B
Solution :
If\[N\]be the number of radioactive 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, \[\frac{N}{{{N}_{0}}}=16\] \[\therefore \] \[\frac{1}{16}={{\left( \frac{1}{2} \right)}^{n}}\] \[\frac{1}{16}=\frac{1}{{{2}^{4}}}\] \[\Rightarrow \] \[n=4\] Also \[n=\frac{t}{{{T}^{1/2}}}\] \[{{T}_{1/2}}=\frac{t}{n}=\frac{2}{4}\times 60\min =30min\]
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