1. (a) (i) A radioactive sample produces 5120 decays at one point in an experime

Question

1.      (a) (i) A radioactive sample produces 5120 decays at one point in an experiment and 40.96 minutes later produces 320 decays per minute. What is the half life? (ii) What is the decay constant? (iii) What is the mean lifetime of the material?

(b) What fraction of a sample of germanium-68 is left after 4.5 yr. (the half-life of germanium-68 is about 9 months)

(c) What period of time is required for a sample of radioactive sulfur-35 to lose 85% of its activity? (The half-life of this sample is 87.38 days)?   

Explanation / Answer

a)

(i)Since 5120 is halved 4 times to get 320, 40.96 = 4 half-lives => 1 half-life = 40.96/4 = 10.24.

(ii)T = half-life/0.693 = 10.24/0.693 = 14.776

(iii) lambda = 1/T = 1/14.776 = 0.6767

b) 4.5 years = 53 months = 53/9 half lives,

so N =N0 /(2)^(53/9) = 0.016876 N0 is left where N0 is initial amount.

c) T = 87.38/0.693 = 126.01,

log(N0/N) = t/T => t = 126.01* ln(100/15) = 239.056

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