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Real-World Applicationshard
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A radioactive decay chain follows N1toN2toN3N_1 \\to N_2 \\to N_3N1​toN2​toN3​ (stable), with decay constants lambda1=0.2\\lambda_1 = 0.2lambda1​=0.2 hr−1^{-1}−1 and lambda2=0.1\\lambda_2 = 0.1lambda2​=0.1 hr−1^{-1}−1. If a sample initially contains N1(0)=1000N_1(0) = 1000N1​(0)=1000 atoms and N2(0)=0N_2(0) = 0N2​(0)=0 atoms, what is the population of N2N_2N2​ at time t=10t = 10t=10 hours?