The relationship between the activity R and the number of nuclei in the sample, N, can be written as follows:
R=Nλ,here, λ is decay constant.
Since, both samples have the same size (and, therefore, have the same initial number of nuclei), we can write:
RG=NoλG,RH=NoλH.Dividing RG by RH, we get:
RHRG=λHλG,RH2RH=λHλG,λG=2λH.The relationship between the half-life of a sample, T1/2, and its decay constant λ can be written as follows:
T1/2=λln2.Then, we can write the half-life of each samples as follows:
T1/2,G=λGln2,T1/2,H=λHln2.Dividing T1/2,G by T1/2,H and substituting λG we get:
T1/2,HT1/2,G=λGλH=2λHλH=21,T1/2,H=2T1/2,G.As we can see from calculations, the half-life of sample H is two times larger than that of G. Therefore, the correct answer is (A).
Answer:
(A) it is two times larger than that of G.
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