A) \[\frac{1}{27}\]
B) \[\frac{1}{8}\]
C) \[\frac{1}{18}\]
D) \[\frac{1}{64}\]
Correct Answer: B
Solution :
\[A={{A}_{0}}{{e}^{-\frac{b}{2m}t}}\] \[\Rightarrow \frac{{{A}_{0}}}{2}=\,\,{{A}_{0}}{{e}^{-\frac{b}{2m}t}}\] \[\Rightarrow \,\,\,\frac{1}{2}={{e}^{-\frac{b}{m}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......(i)\] In 6 minutes \[\Rightarrow \,\,\,A\,\,=\,{{A}_{0}}e{{\,}^{-\frac{b}{2m}\times 6}}\] \[\Rightarrow \,\,\,A\,\,=\,{{A}_{0}}{{\left[ {{e}^{-b/m}} \right]}^{3}}\,\,=\,\,{{A}_{0}}\,{{\left( \frac{1}{2} \right)}^{3}}\] \[\Rightarrow \,\,\,\,A=\frac{{{A}_{0}}}{8}\]
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