A) 2 hour
B) 3 hour
C) 6 hour
D) 12 hour
Correct Answer: C
Solution :
Time of decay \[t=1\]day \[=24\] hours Initial amount of the substance \[={{N}_{0}}\] No Final amount of the substance\[N=\frac{{{N}_{0}}}{16}\] The relation for the number of half lives is given by \[n=\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\left( \frac{1}{16} \right)={{\left( \frac{1}{2} \right)}^{n}}\] \[{{\left( \frac{1}{2} \right)}^{4}}={{\left( \frac{1}{2} \right)}^{n}}\] so \[n=4\] Therefore, half life is \[{{t}_{\frac{1}{2}}}=\frac{t}{n}=\frac{24}{4}=6\,\text{hours}\]
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