A) 100s
B) 200s
C) 300s
D) 400s
Correct Answer: C
Solution :
Key Idea: Use the following formulae find correct answer. (i) \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] (ii) \[{{t}_{1/2}}=\frac{0.693}{k}\] (iii) \[T=n\times {{t}_{1/2}}\] Given, \[{{N}_{0}}=\]initial concentration = 1 N = concentration after time\[t=\frac{1}{8}\] \[k=6.9\times {{10}^{-3}}{{s}^{-1}}\] \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] Or \[\frac{1}{8}=1{{\left( \frac{1}{2} \right)}^{n}}\] Or\[\therefore \] \[n=3\] \[{{t}_{1/2}}=\frac{0.693}{k}=\frac{0.693}{6.9\times {{10}^{-3}}}=100s\] \[T=n\times {{t}_{1/2}}\] \[=3\times 100\] \[=300\text{ }s\] \[\therefore \] After 300 s it will be reduced to\[\frac{1}{8}\]of original concentration.
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