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Question

Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be

A
1:16
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B
4:1
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C
1:4
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D
5:4
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Solution

The correct option is D 5:4
n=noeαt
αA=ln2/20
αB=ln2/40
After 80 min, remaining number of nuclei for A, nA=no/16
After 80 min, remaining number of nuclei for B, nB=no/4
Decayed number of nuclei for A, ΔnA=1516no
Decayed number of nuclei for B, ΔnB=34no
Ratio of decayed number of nuclei is
ΔnAΔnB=15/163/4=5:4

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