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A material has 32 atoms in all; 24 decayed and the rest undecayed. If the half-life of the radioactive material is 1000 years, what is the age of the material?

a. 1000 years
b. 2000 years
c. 3000 years
d. 4000 years

  • Science -

    The number of radioactive atoms has decayed to 8/32 = 1/4 of the original value. That takes two half lives.

  • Science -

    Why two half-lives?

  • Science -

    Angie, you can also work the problem as I showed you on the 30 mCi problem you had earlier.
    k = 0.693/1000 years = 6.93 x 10^-4
    ln(No/N) = kt
    [No is the number of atoms we started with; N = number of atoms today]
    ln(32/8) = 6.93 x 10^-4*t
    ln 4 = 6.93 x 10^-4*t
    1.386/6.93 x 10^-4 = t = 2,000 years.

  • Science -

    ok thanks

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