A) 40 minutes
B) 20 minutes
C) 25 minutes
D) 30 minutes
Correct Answer: A
Solution :
From the relation \[{N={{N}_{0}}{{\left( \frac{1}{23} \right)}^{t}}}/{{{T}_{1/2}}}\;\] We have \[\frac{{{N}_{1}}}{{{N}_{0}}}=100-20=80%\] \[\frac{{{N}_{1}}}{{{N}_{2}}}=100-20=80%\] Therefore \[\frac{\frac{80}{100}}{\frac{20}{100}}=\frac{{{\left( \frac{1}{2} \right)}^{{{t}_{1}}/20}}}{{{\left( \frac{1}{2} \right)}^{{{t}_{2}}/20}}}\] So \[{{\left( \frac{1}{2} \right)}^{2}}={{\left( \frac{1}{2} \right)}^{\frac{({{t}_{2}}-{{t}_{1}})}{20}}}\] \[i.e.,\] \[\Delta t=2\times 20=40\] minutes
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