A) 20 minutes
B) 40 minutes
C) 30 minutes
D) 25 minutes
Correct Answer: B
Solution :
Here \[{{T}_{1/2}}=20\]minutes; we know \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/{{T}_{1/2}}}}\] For 20% decay \[\frac{N}{{{N}_{0}}}=\frac{80}{100}={{\left( \frac{1}{2} \right)}^{{{t}_{1}}/20}}\] ..... (i) For 80% decay \[\frac{N}{{{N}_{0}}}=\frac{20}{100}={{\left( \frac{1}{2} \right)}^{{{t}_{2}}/20}}\] ..... (ii) Dividing (ii) by (i) \[\frac{1}{4}={{\left( \frac{1}{2} \right)}^{\frac{({{t}_{2}}-{{t}_{1}})}{20}}};\] on solving we get \[{{t}_{2}}-{{t}_{1}}=40\]min.
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