A) 3 hrs
B) 2 hrs
C) \[1.5\] hrs
D) \[2.5\] hrs
Correct Answer: B
Solution :
\[\frac{{{N}_{A}}}{{{N}_{B}}}=\frac{1}{7}\] \[\frac{{{N}_{A}}+{{N}_{B}}}{{{N}_{B}}}=\frac{{{N}_{0}}}{{{N}_{B}}}=\frac{8}{7}\] where \[{{N}_{0}}\] is number of atoms of \[A\]at \[t=0\] \[\frac{{{N}_{B}}}{{{N}_{0}}}=\frac{7}{8}\] and \[\frac{{{N}_{B}}}{{{N}_{0}}}=\frac{1}{8}\] \[{{N}_{B}}=\frac{{{N}_{0}}}{8}={{\left( \frac{1}{2} \right)}^{3}}{{N}_{0}}\] After 3 half-lives, ratio of atoms of A and B is given. So, half life of A = 2 hrs.
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