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# A radioactive sample S1 having an activity of 5μCi has twice the number of nuclei as another sample S2 which has an activity of 10μCi. The half lives of S1 and S2 can be20 years and 5 years, respectively20 year and 10 years, respectively10 years each5 years each

A
20 years and 5 years, respectively
B
5 years each
C
20 year and 10 years, respectively
D
10 years each
Solution
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#### Given: R1=5μci,R2=10μci,N1=2N2By, λN=R 0.693TN=R T=0.693NR For sample S1: T1=0.693N15 T1=0.693×2N25 ......................eq1,For sample S2: T2=0.693N210 ....................eq2,By dividing eq1 by eq2, we get: T1T2=41 It is clear that the ratio of half lives of the two samples is 4:1, therefore half lives can be 20 (4k) years and 5 (1k) years respectively.

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