PLEASE HELP ME WITH THIS ONE QUESTION The half-life of Barium-139 is 4.96 x 10^3 seconds. A sample contains 3.21 x 10^17 nuclei. How

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PLEASE HELP ME WITH THIS ONE QUESTION
The half-life of Barium-139 is 4.96 x 10^3 seconds. A sample contains 3.21 x 10^17 nuclei. How much of the sample is left after 1.98 x 10^4 seconds?

a) 8.03 x 10^16 nuclei

b) 4.01 x 10^16 nuclei

c) 2.02 x 10^16 nuclei

d) 1.61 x 10^17 nuclei

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Calantha 6 months 2021-07-26T09:02:38+00:00 1 Answers 3 views 0

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    2021-07-26T09:04:07+00:00

    Answer:

    c) 2.02 x 10^16 nuclei

    Explanation:

    The isotope decay of an atom follows the equation:

    ln[A] = -kt + ln[A]₀

    Where [A] is the amount of the isotope after time t, k is decay constant, [A]₀ is the initial amount of the isotope

    [A] = Our incognite

    k is constant decay:

    k = ln 2 / Half-life

    k = ln 2 / 4.96 x 10^3 s

    k = 1.40×10⁻⁴s⁻¹

    t is time = 1.98 x 10^4 s

    [A]₀ = 3.21 x 10^17 nuclei

    ln[A] = -1.40×10⁻⁴s⁻¹*1.98 x 10^4 s + ln[3.21 x 10^17 nuclei]

    ln[A] = 37.538

    [A] = 2.01×10¹⁶ nuclei remain ≈

    c) 2.02 x 10^16 nuclei

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