Questions about decay chains...?
The naturally occurring radioisotopes uranium-238 and uranium-235 have decay chains that end with the stable isotopes lead-206 and lead-207, respectively. Natural minerals such as zircons contain these uranium and lead isotopes. Careful measurements of the relative amounts of the isotopes can be used to estimate the ages of such minerals.
a) how many seperate alpha decays are there in each decay chain?
b) For a mineral sample that is 4.5 billion years old, what would be the approximate ratio of the number of uranium-238 nuclei to the number of lead-206 nuclei? (Assume that the initial decay of uranium-238 is the slowest in the decay chain)
alpha decay means you lose 2 protons and 2 neutrons, a total mass of 4. you start out with a mass of 238;
238 - 4 = 234 - 4 = 230 - 4 = 226 - 4 = 222 - 4 = 218 - 4 = 214 - 4 = 210 - 4 = 206. i counted 8 decays there (8 alphas given off).
similarly, (235-207)/4 = 28/4 = 6 decays for the U-235.
U-238 has a half-life of 4.5E9, 4.5 billion years. suppose that your mineral sample started out with no lead-206. after 4.5 billion years, half the uranium decayed into lead-206, while the other half is still in its u-238 form, so ratio of u238 to pb206 is 1:1
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