A) 75 h
B) 65 h
C) 55 h
D) 45 h
Correct Answer: D
Solution :
Let initial amount be\[{{N}_{0}}\]. Remaining amount\[N={{N}_{0}}-\frac{7{{N}_{0}}}{8}=\frac{{{N}_{0}}}{8}\] \[\therefore \] \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[\frac{{{N}_{0}}}{8}={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[{{\left( \frac{1}{2} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[n=3\] \[\therefore \] \[\frac{t}{{{T}_{1/2}}}=3\] \[\Rightarrow \] \[\frac{t}{15}=3\] or \[t=15\times 3\] \[t=45\,\,h\]
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