That at any given instant a sample of radioactive uranium contains many, many different isotopes of atoms that are not uranium.

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Chapter 27, Problem 13QAP

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That at any given instant a sample of radioactive uranium contains many, many different isotopes of atoms that are not uranium.

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•3 @ A thermal neutron (with approximately zero kinetic energy) is absorbed by a 23U nucleus. How much energy is transferred from mass energy to the resulting oscillation of the nucleus? Here are some atomic masses and the neutron mass. 237U 237.048 723 u 239U 239.054 287 u 238U 238.050 782 u 240U 240.056 585 u 1.008 664 u

*•58 Two radioactive materials that alpha decay, 238U and 232Th, and one that beta decays, "K, are sufficiently abundant in granite to contribute significantly to the heating of Earth through the de- cay energy produced. The alpha-decay isotopes give rise to decay chains that stop when stable lead isotopes are formed. The isotope 4"K has a single beta decay. (Assume this is the only possible decay of that isotope.) Here is the information: Stable Decay Half-Life End Parent Mode (y) Point (MeV) (ppm) 238U 232Th 4.47 x 10° 206рЬ 51.7 1.41 x 1010 208Pb 42.7 13 1.28 x 10° 40Ca 1.31 4 In the table Q is the total energy released in the decay of one par- ent nucleus to the final stable end point and f is the abundance of the isotope in kilograms per kilogram of granite; ppm means parts per million. (a) Show that these materials produce energy as heat at the rate of 1.0 x 10-9 W for each kilogram of granite. (b) Assuming that there is 2.7 x 102 kg of granite in a 20-km-thick spherical shell at…

•49 SSM Generally, more massive nuclides tend to be more un- stable to alpha decay. For example, the most stable isotope of ura- nium, 28U, has an alpha decay half-life of 4.5 x 10° y. The most stable isotope of plutonium is 24Pu with an 8.0 x 10' y half-life, and for curium we have 248Cm and 3.4 x 10 y. When half of an original sam- ple of 238U has decayed, what fraction of the original sample of (a) plu- tonium and (b) curium is left?