A) \[7/{{8}^{th}}\]part of the substance will disintegrate in 3 months
B) \[1/{{8}^{th}}\]part of the substance will remain undecayed at the end of 4 months
C) The substance will disintegrate completely in 4 months
D) \[1/{{16}^{th}}\] part of the substance will remain undecayed at the end of 3 months
E) The substance will disintegrate completely in 2 months
Correct Answer: A
Solution :
\[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\]or \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/{{t}_{1/2}}}}\]or \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/1}}\] For\[t=3\]months \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{3}}=\frac{1}{8}\] Therefore, disintegrated part of substance in 3 months \[=1-\frac{1}{8}=\frac{7}{8}.\]
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