Calculus disaster

posted by .

Uranium ore has two main isotopes, mostly U-238 with just a trace amount of U-235. In a sample of Uranium ore, 99.85% of the atoms are U-238 atoms and 0.15% are U-235 atoms.

Before the Uranium can be used in a nuclear power plant, the proportion of U-235 must be increased to 15% (thus reducing the proportion of U-238 to 85%). This is done by a process called gas diffusion. The ratio of the masses of these two isotopes is U-238 to U-235 = 1.013. Each cycle of the gas diffusion process decreases U-238 by 1.3%. How many cycles are required to reduce the U-238 to 85%?

  • Calculus disaster -

    You want to go from 99.85% U-238 to 85%.

    Each cycle of the process decreases the U-238 fraction by a ratio 1-0.013 = 0.987. Let the number of processing cycles required be N.
    0.850/0.9985 = 0.8513 = 0.987^N

    Solve for N.

    N = Log0.8513/Log0.987 = 12.3

    Call it 13, for a margin of safety

    This is not a calculus problem. Precalc, maybe.

  • Calculus disaster -

    178

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Chemistry

    Uranium-235 can be separated from U-238 by fluorinating the uranium to form UF6 (which is a gas) and then taking advantage of the different rates of effusion and diffusion for compounds containing the two isotopes. Calculate the ratio …
  2. 11th grade

    How many uranium atoms are there in 9.5 g of pure uranium?
  3. 11th grade AP Chemistry

    Pretend you are a nuclear scientist and try to answer this bonus question. Uranium -235 (235U) is used as a fuel in nuclear power plants. However, natural uranium contains mostly U -238 (238U) and very little uranium -235. Therefore, …
  4. AP Chem

    Pretend you are a nuclear scientist and try to answer this bonus question. Uranium -235 (235U) is used as a fuel in nuclear power plants. However, natural uranium contains mostly U -238 (238U) and very little uranium -235. Therefore, …
  5. Chemistry 1046

    Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated in the rock as it hardens and then decays with first-order kinetics and a half-life of 4.5 billion years. A rock contains 65.7% of the …
  6. Chemistry

    Uranium-235 can be separated from U -238 by fluorinating the uranium to form UF 6 which is a gas) and then taking advantage of the different rates of effusion and diffusion for compounds containing the two isotopes. Calculate the ratio …
  7. Chemistry

    Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated in the rock as it hardens and then decays with first-order kinetics and a half-life of 4.5 billion years. A rock is found to contain …
  8. Chemistry

    If we ignore the small fraction of U-234, natural uranium has a concentration of 99.28 atom% of U-238 and 0.72% U-235. Their half-lives are, respectively, 4.68*109 and 7.038*108 years. (a) In the future, will the U-238 percentage be …
  9. Science

    Uranium-238 is less stable than oxygen-16. What accounts for this difference?
  10. science

    The half-life of uranium-235 is 713 million years. Suppose a fossil originally had 26 grams of uranium-235. A geologist had the fossil tested and found that it now has only 3.25 grams of uranium-235. Approximately how old is the fossil?

More Similar Questions