p43_035 - 03 × 10 20(b The decay rate is given by R = N =...

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35. (a) We assume that the chlorine in the sample had the naturally occurring isotopic mixture, so the average mass number was 35 . 453, as given in Appendix F. Then, the mass of 226 Ra was m = 226 226 + 2(35 . 453) (0 . 10 g) = 76 . 1 × 10 3 g . The mass of a 226 Ra nucleus is (226 u)(1 . 661 × 10 24 g / u) = 3 . 75 × 10 22 g, so the number of 226 Ra nuclei present was N =(76 . 1 × 10 3 g) / (3 . 75 × 10 22 g) = 2
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Unformatted text preview: . 03 × 10 20 . (b) The decay rate is given by R = Nλ = ( N ln 2) /T 1 / 2 , where λ is the disintegration constant, T 1 / 2 is the half-life, and N is the number of nuclei. The relationship λ = (ln 2) /T 1 / 2 is used. Thus, R = (2 . 03 × 10 20 ) ln 2 (1600 y)(3 . 156 × 10 7 s / y) = 2 . 79 × 10 9 s − 1 ....
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