A) \[\frac{{{N}_{0}}}{8}\]
B) \[\frac{{{N}_{0}}}{16}\]
C) \[\frac{{{N}_{0}}}{2}\]
D) \[\frac{{{N}_{0}}}{4}\]
Correct Answer: A
Solution :
\[{{N}_{0}}\] is the initial amount of substance and N is the amount left after decay. Thus, \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[n=\] number of half-lives \[=\frac{t}{{{t}_{1/2}}}=\frac{15}{3}=3\] Therefore, \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{3}}=\frac{{{N}_{0}}}{8}\]
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