A) 16 h
B) 12 h
C) 8h
D) 4h
Correct Answer: B
Solution :
Key Idea: First calculate the amount left after n half-lives and then time taken. \[\frac{{{N}_{t}}}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] where, \[{{N}_{t}}=1\] amount left after expiry n half lives = 1 \[{{N}_{0}}=\] initial amount = 64 \[\therefore \] \[\frac{1}{64}={{\left( \frac{1}{2} \right)}^{n}}\] or \[{{\left( \frac{1}{2} \right)}^{6}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\therefore \] \[n=6\] Given, \[{{t}_{1/2}}=2h\] \[\therefore \] Time taken \[(T)={{t}_{1/2}}\times n\] \[=2\times 6\] = 12 h
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