A) 32 min
B) 48 min
C) 12 min
D) 24 min
Correct Answer: B
Solution :
Given, \[t=192\] minutes \[\frac{N}{{{N}_{0}}}=\frac{1}{16}\] \[{{t}_{1/2}}=?\] We know that, \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/{{t}_{1/2}}}}\] \[\therefore \] \[\frac{1}{16}={{\left( \frac{1}{2} \right)}^{\frac{192}{{{t}_{1/2}}}}}\] or \[{{\left( \frac{1}{4} \right)}^{4}}={{\left( \frac{1}{2} \right)}^{\frac{192}{{{t}_{1/2}}}}}\] or, \[4=\frac{192}{{{t}_{1/2}}}\] \[\therefore \] \[{{t}_{1/2}}=\frac{192}{4}=48\] minutes
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