A) \[\frac{1}{2}\]
B) \[\frac{3}{8}\]
C) \[\frac{1}{4}\]
D) \[\frac{3}{4}\]
Correct Answer: D
Solution :
Number of half-lives \[n=\frac{8}{4}=2\] As, \[N=\frac{{{N}_{0}}}{{{2}^{n}}}=\frac{{{N}_{0}}}{{{2}^{2}}}=\frac{{{N}_{0}}}{4}\] Thus, remaining atom \[N=\frac{{{N}_{0}}}{4}\] Decayed atoms \[={{N}_{0}}-N={{N}_{0}}-\frac{{{N}_{0}}}{4}=\frac{3}{4}{{N}_{0}}\] \[\therefore \]Probability of decay \[=\frac{{{N}_{0}}-N}{{{N}_{0}}}=\frac{\frac{3}{4}{{N}_{0}}}{{{N}_{0}}}=\frac{3}{4}\]
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