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28 November, 22:26

Suppose you found a material in which 12.5% of the original radioactive atoms were present. if the half-life is 47 years, how old is the material?

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  1. 28 November, 22:31
    0
    The answer is 141 years old.

    It can be calculated using the equation: (1/2) ⁿ = x

    x - decimal amount remaining,

    n - number of half-lives.

    x = 12.5% = 12.5%/100% = 0.125

    n = ?

    (1/2) ⁿ = 0.125

    log ((1/2) ⁿ) = log (0.125)

    n * log (1/2) = log (0.125)

    n = log (0.125) / log (1/2) = log (0.125) / log (0.50) = - 0.903 / - 0.301 = 3

    Number of half-lives is 3.

    Number of half-lives (n) is quotient of total time elapsed (t) and length of half-life (H).

    n = t/H

    t = n * H

    n = 3

    H = 47 years

    t = 3 * 47 years = 141 years
  2. 28 November, 22:53
    0
    3 half lives, 141 years

    (one half life: 50% left,

    two half lives: 25% left;

    3 half lives: 12.5% left)
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