A) 2
B) 4
C) between 4 and 6
D) 6
Correct Answer: C
Solution :
[c] Let \[{{N}_{0}}\] be the number of atoms of X at time \[t=0.\] Then at \[t=4\]hrs (two half-lives) \[{{N}_{x}}=\frac{{{N}_{0}}}{4}\] and \[{{N}_{y}}=\frac{3{{N}_{0}}}{4}\] \[\therefore \,\,\,\,\,\,\,\,\,\,{{N}_{x}}/{{N}_{y}}=1/3\] and at \[t=6\]hrs (three half-lives) \[{{N}_{x}}=\frac{{{N}_{0}}}{8}\] and \[{{N}_{y}}=\frac{7{{N}_{0}}}{8}\]or \[\frac{{{N}_{x}}}{{{N}_{y}}}=\frac{1}{7}\] The given ratio \[\frac{1}{4}\] lies between \[\frac{1}{3}\] and \[\frac{1}{7}\]. Therefore, t lies between 4 hrs and 6 hrs.
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