You have equal numbers of two radioactive nuclei to start with. The A nuclei have a half life of 4 days, while the half life of the B nuclei is unknown. After waiting for 12 days, you find that there are twice as many B nuclei remaining as there are A nuclei. What is the half life of the B nuclei?
The A nuclei have gone through three half-lives. If there are now twice as many B nuclei remaining, the B nuclei must only have gone through two half-lives. Because 12 days represents two half-lives for the B nuclei, the B nuclei have a half-life of 6 days.
Imagine there are 200 nuclei of A and B at start.
After 4 day no of A nuclei =100
After 8 day no of A nuclei = 50
After 12 day no of A nuclei =25
No of B nuclei is twice of that of A
No of B nuclei = 25*2 = 50
The number of B nuclei has reduced twice. So the half life of B =12/2 = 6 days
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