Consider an initially pure 26 g sample of 67Ga an isotope th

Consider an initially pure 2.6 g sample of 67Ga, an isotope that has a half-life of 78 h. (a) What is its initial decay rate? s-1 (b) What is its decay rate 39 h later? s-1

Solution

(a)

initial decay rate = 0.693/t(1/2)

t(1/2) = half life period = 78 h = 78*60*60 s

lambda = 0.693/(78*60*60)

lambda = 2.47*10^-6 s^-1   <<<<<-----answer

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(b)

after t = 38 h

N = N0*e^-lambda*t

N = 2.6*e^-(2.47*10^-6*38*3600)

N = 1.85

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after t = 38 h

N2 = N*e^(lambda1*t1/2)

N2 = N1/2

0.5 = e^-(lambda1*76*3600)

lambda 1 = 2.53*10^-6 s^-1 <<<<<-----answer