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3 March, 01:39

A half-life is the time it takes an amount of substance to decay to one-half of its original amount. For example, the sample is one-half after the first half-life but one-quarter (i. e., one-half of one-half) after the second half-life. If the half life of uranium-235 is 700 million years, how long does it take for 10.0 grams to decay to 2.5 grams? Express your answer in billions of years.

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  1. 3 March, 04:15
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    I'm failing to understand how it isn't 1.4 billion years. From 10g to 5g would be 700 million years. Then, from 5g to 2.5g would be another 700 million years.
  2. 3 March, 05:10
    0
    2.10 * 10⁹ yr

    Step-by-step explanation:

    The half-life of U-235 is the time it takes for half the U to decay.

    After one half-life, half (50 %) of the original amount will remain.

    After a second half-life, half of that amount (25 %) will remain, and so on.

    We can construct a table as follows:

    No. of Fraction Amount

    half-lives t / (yr * 10⁶) remaining remaining/g

    1 700 ½ 10.0

    2 1400 ¼ 5.00

    3 2100 ⅛ 2.50

    4 2800 ¹/₁₆ 1.25

    We see that 2100 * 10⁶ yr is three half-lives, and the amount of U-235 remaining is 2.50 g.

    It takes 2.10 * 10⁹ yr for the U-238 to decay to 2.50 g.
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