A) \[\frac{{{N}_{0}}}{128}\]
B) \[\frac{{{N}_{0}}}{64}\]
C) \[\frac{{{N}_{0}}}{32}\]
D) None
Correct Answer: B
Solution :
[b] \[{{N}_{0}}\xrightarrow{3t}\frac{{{N}_{0}}}{16}\] \[t=0\] \[t=t\] \[t=4t\] \[A={{A}_{0}}{{e}^{-\lambda t}}\] \[\frac{{{N}_{0}}}{16}={{N}_{0}}{{e}^{-\lambda (3t)}}\] \[{{e}^{3\lambda t}}=16\] \[{{N}_{0}}~\xrightarrow{9t/2}N=?\] \[t=t\] \[t=\frac{11}{2}t\] \[A={{A}_{0}}{{e}^{-\lambda t}}\] \[N={{N}_{0}}{{e}^{-\frac{9t}{2}\lambda }}\] \[N={{N}_{0}}{{\left( {{e}^{-3\lambda t}} \right)}^{3/2}}\] \[N={{N}_{0}}{{\left( \frac{1}{16} \right)}^{3/2}}\] \[N=\frac{{{N}_{0}}}{64}\]
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