60. (a) The rate of heat production is
3 3 3
dE ln 2 (1.00 kg)fi
= RiQi = 1NiQi = Qi
dt T1/2i mi
i=1 i=1 i=1
(1.00 kg)(ln 2)(1.60 × 10-13 J/MeV) (4 × 10-6)(51.7MeV)
=
(3.15 × 107 s/y)(1.661 × 10-27 kg/u) (238 u)(4.47 × 109 y)
(13 × 10-6)(42.7MeV) (4 × 10-6)(1.31 MeV)
+ +
(232 u)(1.41 × 1010 y) (40 u)(1.28 × 109 y)
= 1.0 × 10-9 W .
(b) The contribution to heating, due to radioactivity, is P = (2.7 × 1022 kg)(1.0 × 10-9 W/kg) =
2.7 × 1013 W, which is very small compared to what is received from the Sun.
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