A) \[4\,\,mg\]
B) \[8\,\,mg\]
C) \[1\,\,mg\]
D) \[2\,\,mg\]
Correct Answer: D
Solution :
Half-life\[({{t}_{1/2}})=12.3\,\,yr\]. Initial amount\[({{N}_{0}})=32\,\,mg\] Amount left\[(N)=?\] Total time\[(T)=49.2\,\,yr\] \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] where \[n=\]total number of half-life \[n=\frac{Total\,\,time}{Half-time}\] \[\frac{49.2}{12.3}=3\] So, \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{4}}\] \[\frac{N}{32}={{\left( \frac{1}{2} \right)}^{4}}\] \[\frac{N}{32}=\frac{1}{16}\] \[N=\frac{32}{16}=2\,\,mg\]
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