In 238 grams of naturally occuring uranium metal there are approximately 6.02x10

Question

In 238 grams of naturally occuring uranium metal there are approximately 6.02x10^23 nuclei. Approximately 99.3% of Uranium metal consists of the radioactive isotope uranium-238. The half-life of U238 is 4.47 billion years. Using these fact, answer the following questions: a) Find the decay constant k of U238. b) Find the probability that a U238 nucleus will decay during a one second interval. c) Find the approximate number of nuclei of U238 in one gram of uranium metal. d) Find the approximate number of decays per second of U238 in one gram of uranium metal.

Explanation / Answer

(a) t1/2= In2/? ? = ln2/4.47 *10 ^9 = 5.02 X 10^-18 (b) Time taken to decay half of the nucleus = 1.38 X 10^17 probability that a U238 nucleus will decay during a half life = 1/2 probability that a U238 nucleus will decay during a one second = 1/(2*1.38 X 10^17) = 3.622 x 10^-18 (c)approximate number of nuclei of U238 in one gram of uranium metal = 6.023 X 10^23 X 0.993 /238 = 2.513 X 10^21 (d)the approximate number of decays per second of U238 in one gram of uranium metal = 2.513 X 10^21 / 2*1.38 X 10^17 = 9105

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