A) \[\frac{13}{16}\]
B) \[\frac{1}{16}\]
C) \[\frac{8}{17}\]
D) \[\frac{15}{16}\]
Correct Answer: D
Solution :
From Rutherford-Soddys law, the fraction of sample remains undecayed after n half-lives is \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] where \[{{N}_{0}}\] is original number of atoms. \[\therefore \] \[n=\frac{6400}{1600}=4\] \[\therefore \] \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}={{\left( \frac{1}{2} \right)}^{4}}=\frac{1}{16}\] The fraction of sample disintegrated is \[=1-\frac{1}{16}=\frac{15}{18}\]
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