Element X is a radioactive isotope such that every 9 years, its mass decreases by half. Given that the initial mass of a sample of Element X

Question

Element X is a radioactive isotope such that every 9 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 70 grams, how long would it be until the mass of the sample reached 56 grams, to the nearest tenth of a year?

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Khánh Gia 6 months 2021-07-31T11:03:36+00:00 1 Answers 20 views 0

Answers ( )

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    2021-07-31T11:04:52+00:00

    Answer:

    2.9 years

    Step-by-step explanation:

    Given that :

    Half-life t1/2 = 9 years

    Initial mass = I = 70 grams

    A = final mass = 56 grams

    t = time taken to reach final amount

    Using the exponential half life relation :

    A = I(0.5)^t/t1/2

    56 = 70(0.5)^t/9

    56/70 = 0.5^t/9

    0.8 = 0.5^t/9

    Log 0.8 = log 0.5^t/9

    −0.096910 = −0.301029 * t/9

    t/9 = 0.096910 / 0.301029

    t/9 = 0.3219291

    t = 0.3219291 * 9

    t = 2.8973619

    t = 2.9 years

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