ch42-p025 - 25. (a) The decay rate is given by R = N, where...

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If M is the mass of the sample and m is the mass of a single atom of gallium, then N 0 = M / m . Now, m = (67 u)(1.661 × 10 – 24 g/u) = 1.113 × 10 – 22 g and N 0 = (3.4 g)/(1.113 × 10 – 22 g) = 3.05 × 10 22 . Thus, R 0 = (8.89 × 10 – 3 h – 1 ) (3.05 × 10 22 ) = 2.71 × 10 20 h – 1 = 7.53 × 10 16 s – 1 . (b) The decay rate at any time t is given by RR e t = 0 λ where R 0 is the decay rate at t = 0. At t = 48 h, λ t = (8.89 × 10 – 3 h – 1 ) (48 h) = 0.427 and Re = × −− 7 53 10 4 91 10 16 1 0 427 16 .. . . ss 1
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