A) 2 hours
B) 3 hours
C) 90 minutes
D) 1 hours
Correct Answer: D
Solution :
Given, \[{{N}_{0}}=100,\text{ }N=100-87.5=12.5,\] \[t=3\,hours,\,{{t}_{1/2}}=?\] We know that \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{\frac{t}{{{t}_{1/2}}}}}\] \[\frac{12.5}{100}={{\left( \frac{1}{2} \right)}^{3/{{t}_{1/2}}}}\] or \[{{\left( \frac{1}{2} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{3/{{t}_{1/2}}}}\] Hence, \[\frac{3}{{{t}_{1/2}}}=3\] or \[{{t}_{1/2}}=\frac{3}{3}=1\text{ }hour\]
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