One of the reasons why thermonuclear weapons have to be serviced regularly is the nuclear decay of the tritium, ³H, that they contain. Suppose you are monitoring the decay of tritium.
What mass of a tritium sample initially of mass 1.00 g will remain after 5.0 a (1 a = 1 year)? The decay constant of tritium is 0.0564 a^–1.

ANTICIPATE The half-life of tritium (TABLE 10B.3) is 12.3 years, and so you should expect that more than half of the sample will remain after only 5 years.

PLAN The total mass of isotope in a sample is proportional to the number of nuclei of that isotope that the sample contains; therefore, the time dependence of the mass of a radioactive isotope follows the same radioactive decay law as the number of nuclides in the sample. That is, because m ∝ N, in place of Eq. 3 you can write m = m₀e^–kt, where m is the total mass of the radioactive isotope at time t and m₀ is its initial mass.

Transcribed Image Text:

TABLE 10B.3 Half-Lives of Radioactive Isotopes* Nuclide tritium carbon-14 carbon-15 potassium-40 cobalt-60 strontium-90 iodine-131 cesium-137 radium-226 uranium-235 uranium-238 fermium-244 *d = day; a = year. Half-life, t1/2 12.3 a 5.73 ka 2.4 s 1.26 Ga 5.26 a 28.1 a 8.05 d 30.17 a 1.60 ka 0.71 Ga 4.5 Ga 3.3 ms