A) 4 days
B) 12 days
C) 18 days
D) 24 days
Correct Answer: C
Solution :
Half-life \[{{T}_{3/2}}=3.6\]day Amount left after time t \[N=\frac{1}{32}\times {{N}_{0}}\] Number of half-lives in time (n) is given bv \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\frac{\frac{N}{32}}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] \[=\frac{1}{32}=\frac{1}{{{2}^{n}}}\] \[n=5\]or \[\frac{1}{{{t}_{1/2}}}=5\] Hence time of decay \[t=5\times \frac{{{t}_{1}}}{2}=5\times 3.5\] \[=18\,\,day\]
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