Answer :
Final answer:
The counting rate decreases by half every 2 minutes following the concept of half-life in radioactive decay. After 2, 6, 10, and 20 minutes the counting rates are 1500, 375, 93.75, and 2.93 counts/s respectively. The mean life of this nucleus is 2.88 minutes.
Explanation:
The question is about the concept of half-life in radioactive decay.
a) The counting rate after 2 minutes will be half of the initial count rate because one half-life has passed. Therefore, the counting rate is 1500 counts/s.
b) After 6 minutes, three half-lives have passed. Using the half-life formula, the counting rate will be 3000/(2^3) = 375 counts/s.
c) After 10 minutes, five half-lives have passed. The counting rate will be 3000/(2^5) = 93.75 counts/s.
d) After 20 minutes, ten half-lives have passed. The counting rate will be 3000/(2^10) = 2.93 counts/s.
e) The mean life, or the average lifespan, of a radioactive nucleus is given by the formula mean life = half-life/ln2. Therefore, the mean life of this nucleus is 2/0.693 = 2.88 minutes.
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