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Homework Help: Estimate the age of the Earth

  1. Dec 11, 2015 #1
    1. The problem statement, all variables and given/known data
    The half life of U-238 is approximately 4.4 billion years, while U-235 is approximately 700,000,000.

    A Uranium ore has 0.75% U-235.
    Assuming there was an even amount of both types of Uranium when the Earth was formed, estimate the age of the Earth.

    2. Relevant equations
    N = N0 - kt

    N = amount after time t
    N0 = amount at time=0
    k = decay constant
    t = time
    3. The attempt at a solution
    I don't do a lot of derivation at my school, but I want to get a lot better at it.

    N = N0 - kt

    dN / dt = -kt

    dN = -kt dt

    ∫ - kt dt (definite integral from t to t0

    = -k(t - t0)

    I'm not really sure to go from here.
  2. jcsd
  3. Dec 11, 2015 #2
    Maybe they are asking for a crude estimate?
    So 1.4 My ago there was four times as much U-235, about 3 %.
    And 4.2 My ago there was 64 times as much. But back then there was also twice as much U-238, so the U-235 content was about 25 %.

    PS: Should be Gy. Thanks SteamKing
    Last edited: Dec 11, 2015
  4. Dec 11, 2015 #3


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    What you are missing is that the rate of decay is proportional to the amount of substance on hand at any one time:


    Knowing the rate of decay allows you to calculate the half-life of the substance:

  5. Dec 11, 2015 #4


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    If by 'My' you mean billions (109) of years.
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