A) 0.125
B) 0.875
C) 1.125
D) 1.875
Correct Answer: A
Solution :
Let number of atoms per gram\[={{N}_{0}}\] Here, \[t=9\]min, \[r=3\] min Numbers of atoms remain undecayed after 9 min \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/T}}={{\left( \frac{1}{2} \right)}^{9/3}}\] \[={{\left( \frac{1}{2} \right)}^{3}}=\frac{1}{8}\] Or \[N=\frac{{{N}_{0}}}{8}\] Now fraction of radioactive decayed \[=\frac{{{N}_{0}}-N}{{{N}_{0}}}\] \[=\frac{{{N}_{0}}-N/8}{{{N}_{0}}}\] \[=1-\frac{1}{8}=\frac{7}{8}=0.875\] \[\therefore \]Fraction of radioactive remain undecayed \[=1-0.875=0.125\]
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