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 :
1 : 16
4 : 1
1 : 4
5 : 4
As we learnt in
Number of nuclei in terms of half life -
- wherein
Very useful to determine number of nuclei in terms of half life
A (T1/2 = 20 minutes)
B (T1/2 = 40 minutes)
at t = 80 min.
at t = 80 min.
Decayed number of
Decayed number of
Ratio
Correct option is 4
Option 1)
1 : 16
This is an incorrect option.
Option 2)
4 : 1
This is an incorrect option.
Option 3)
1 : 4
This is an incorrect option.
Option 4)
5 : 4
This is the correct option.
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After 80 minutes 1/16th part of initial nuclei of element A is left and 1/4th part of initial nuclei of element B is left
So the decayed number of nuclei of element A will be 15/16th of initial nuclei and that of element B will be 3/4th of initial nuclei
Hence the ratio of decayed number of A and B nuclei after 80 minutes will be 5/4.
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