A sample of radioactive material decays simultaneously by two processes A and B with half-lives 1 2 and 1 4 hours respectively. For first half-hour, it decays with process A , next one hour with proce

Question

A sample of radioactive material decays simultaneously by two processes A and B with half-lives 1 2 and 1 4 hours respectively. For first half-hour, it decays with process A , next one hour with process B and for a further half an hour with both A and B . If originally there were N 0 nuclei, find the number of nuclei after 2 hours of such decay-

TestHub · Accepted Answer

After first half hour with the process A , N = N 0 2 for next one hour with the process B , i.e. t = 1 2 hr to t = 1 1 2 hr N = N 0 2 1 2 4 = N 0 1 2 5 Half life for both A and B , 1 t 1 / 2 = 1 1 / 2 = 1 1 / 4 1 t 1 / 2 = 2 + 4 t 1 / 2 = 1 6 h r for further half an hour with both A and B , i.e. t = 1 1 2 hr to t = 2 hr N = N 0 1 2 5 1 2 3 = N 0 1 2 8

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