A) 6 min
B) 12 min
C) 48 min
D) 30 min
E) 24 min
Correct Answer: D
Solution :
Let the initial amount of \[Y=1\] So, the initial amount of \[X=8\] X decomposes as \[8\xrightarrow[{}]{1}4\xrightarrow[{}]{2}2\xrightarrow[{}]{3}1\xrightarrow[{}]{{}}\frac{1}{2}\xrightarrow[{}]{5}\frac{1}{4}\] Number of half-lives of \[X=5\] Y decomposes as \[1\xrightarrow[{}]{1}\frac{1}{2}\xrightarrow[{}]{2}\frac{1}{4}\] Number of half-lives of \[Y=2\] So, total time \[T=n\times {{t}_{1/2}}\] \[=5\times 6=30\text{ }min\] or \[T=n\times {{t}_{1/2}}=2\times 15=30\text{ }min\]
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