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15 September, 03:04

How long will it take for 750 mg of a sample of radium-225, which has a half-life of about 15 days, to decay to 68 mg?

A. ≈ 50 days

B. ≈ 54 days

C. ≈ 48 days

D. ≈ 52 days

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Answers (1)
  1. 15 September, 04:32
    0
    For this case we have an equation of the form:

    y = A (b) ^ t

    Where,

    A: initial amount

    b: decrease rate

    t: time

    Substituting values:

    y = 750 (0.5) ^ ((1/15) * t)

    The number of days to reach 68 mg is:

    68 = 750 (0.5) ^ ((1/15) * t)

    Clearing t:

    (0.5) ^ ((1/15) * t) = (68/750)

    log0.5 ((0.5) ^ ((1/15) * t)) = log0.5 (68/750)

    (1/15) * t = log0.5 (68/750)

    t = 15 * log0.5 (68/750)

    t = 51.94

    Rounding:

    t = 52 days

    Answer:

    D. ≈ 52 days
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