An unknown radiaactive element decays into non radioactive substance. In 200 day

Question

An unknown radiaactive element decays into non radioactive substance. In 200 days the radioactivity of a sample decreases by 49 %

A: What is the half life of the element

B: How long would it take for a sample of 100 mg to decay to 90 mg

Explanation / Answer

Dear Student Thank you for using Chegg !! Let initial amount of radioactive substance be A0 Given that after 200 days quantity reduces by 49% Equation for radioactive decay is given by A = A0 e^(-kt) A = Radioactivity at time t (in this case after 200 ddays = 51%) A0= Initial radioactivity (A / A0 ) = 51% t = time (200) k : Rate of decay a) A/ A0 = e^(-kt) 0.51 = e^(-200k) taking natural log both sides -0.673 = -200k k = 0.003365 Nw for half life A = A0/2 => A0/2 = A0 e^(-0.003365)t 0.5 = e^(-0.003365)t -0.693147181 = -0.003365t t = 205.9872751 206 days approx b) 100 mg sample to decay 90% 90 = 100 e^ (- 0.003365t) 0.9 = e^ (-0.003365t) Taking natural log both sides -0.10536 = -0.003365t t = 31.3 Time = 31.3 days Solution

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