A) \[\frac{1}{9}\]
B) \[\frac{1}{27}\]
C) \[\frac{1}{6}\]
D) \[\frac{1}{8}\]
Correct Answer: D
Solution :
\[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/{{T}_{1/2}}}}\] Given: \[{{T}_{1/2}}=3\,h,\,\,t=9h\] \[\therefore \] \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{9/3}}={{\left( \frac{1}{2} \right)}^{3}}\] \[\Rightarrow \] \[\frac{N}{{{N}_{0}}}=\frac{1}{8}\] Activity \[=\left| \frac{-dN}{dt} \right|=N\lambda \] \[\therefore \] \[\frac{A}{{{A}_{0}}}=\frac{N\lambda }{{{N}_{0}}\lambda }=\frac{N}{{{N}_{0}}}=\frac{1}{8}\]
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