43. (a) The sample is in secular equilibrium with the source and the decay rate equals the production rate.
56
Let R be the rate of production of Mn and let be the disintegration constant. According to
the result of problem 41, R = N after a long time has passed. Now, N =8.88 × 1010 s-1, so
R =8.88 × 1010 s-1.
(b) They decay at the same rate as they are produced, 8.88 × 1010 s-1.
(c) We use N = R/. If T1/2 is the half-life, then the disintegration constant is = (ln 2)/T1/2 =
(ln 2)/(2.58 h) = 0.269 h-1 =7.46 × 10-5 s-1, so N =(8.88 × 1010 s-1)/(7.46 × 10-5 s-1) =1.19 ×
1015.
56 56
(d) The mass of a Mn nucleus is (56 u)(1.661×10-24 g/u) = 9.30×10-23 g and the total mass of Mn
in the sample at the end of the bombardment is Nm =(1.19×1015)(9.30×10-23 g) = 1.11×10-7 g.
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