A) 36 days
B) 12 days
C) 4 days
D) 24 days
Correct Answer: A
Solution :
Given half life, T= 12 days Fraction decayed\[=\frac{7}{8}\] \[\therefore \]Fraction undecayed\[=1-\frac{7}{8}=\frac{1}{8}\] \[\therefore \] \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[\frac{1}{8}={{\left( \frac{1}{2} \right)}^{n}}\] or \[{{\left( \frac{1}{2} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\therefore \] Time, taken for \[\frac{7}{8}th\]sample to decayed\[t=3T=3\times 12=36\] days
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