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25 October, 04:21

If a radioactive isotope that was injected into your bloodstream has a half-life of 5 hours, how many hours do you have to wait before the amount of this isotope in your body is 1/16 its original amount?

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Answers (2)
  1. 25 October, 07:53
    0
    20 hours

    Explanation:

    Using

    R/R' = 2ᵃ/ᵇ ... Equation 1

    Where R = Original amount of radioactive isotope, R' = Amount of radioactive isotope after disintegration, a = Total disintegration time, b = half life.

    Note: The Fraction of original amount of radioactive isotope is 1.

    Given: R = 1, R' = 1/16, b = 5 hours

    Substitute into equation 1

    1 / (1/16) = 2ᵃ/⁵

    16 = 2ᵃ/⁵

    2⁴ = 2ᵃ/⁵

    Equation the base

    4 = a/5

    a = 4*5

    a = 20 hours

    Hence the time = 20 hours
  2. 25 October, 07:54
    0
    Total time = 20 hours

    Explanation:

    Half life is the amount of time it takes for a substance to decay tohalf of it's original amount.

    Half life = 5 hours.

    We have to obtain the number of half lives to get the time required.

    1st half life = 1/2

    2nd half life = 1/4

    3rd half life = 1/8

    4th half life = 1/16

    So ffour half lives.

    Total time = number of half lives * Time of half life

    Total time = 4 * 5

    Total time = 20 hours
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