Sciencium-380 has a half-life of 3 days. If you started with a 100 gram sample, how much Sciencium-380 will remain after 9 days?

Question

Sciencium-380 has a half-life of 3 days. If you started with a 100 gram sample, how much Sciencium-380 will remain after 9 days?

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Ngọc Khuê 2 months 2021-07-25T05:33:27+00:00 2 Answers 4 views 0

Answers ( )

    0
    2021-07-25T05:34:37+00:00

    Answer:

    12.5 grams

    Explanation:

    Solution:-

    – By definition, the half-life is the amount of time t that a substance of mass M   to decay to half its its initial mass.

    – We are given the mass of the Sciencium-380, M = 100 g

    – The half-life for the radioactive isotope is, h = 3 days

    – The amount of mass left after t = 9 days.

    – We will first estimate the number of half-lives that have passed in te duration of t = 9 years.

    – The number of half lives are:

                                        n = t / h

                                        n = 9 / 3

                                        n = 3

    For every half life the mass is halved or mathematically the mass ( m ) of a substance remaining after ” n ” number of half lives can be expressed as:

                                         m = M*0.5^n

    – Plug in the given values and evaluate the mass ( m ) of the substance after n = 3 half lives.

                       

                                         m = 100*0.5^3

                                         m = 12.5 grams.

    Answer: We are left with 12.5 grams of Sciencium after 3 half lives have passed.

    0
    2021-07-25T05:35:23+00:00

    Answer: 12.5 grams will remain.

    Explanation:

    The half life time means that if we start with a quantity A of a given subtance/material, after the half time we will have half that quantity, or A/2.

    We know that the half life of Sciencium-380 is 3 days.

    So if we have 100 grams, after 3 days we will have 100/2 = 50 grams.

    After other 3 days we will have 50/2 = 25 grams

    After other 3 days we will have 25/2 = 12.5 grams.

    So if we start with 100 grams, after 9 days we will have 12.5 grams.

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