32P is a radioactive isotope with a half-life of 14.3 days. If you currently have 30.3 g of 32P, how much 32P was present 2.00 days ago?

1 Answer

  • Radioactive decay is a first-order process and is described by this equation.

    A = Ao e^(-kt) ……… where A is the activity at time t, Ao is the initial activity, k is the decay consant, and t is the elapsed time

    The equation can also be written as …

    ln A = -kt + ln Ao

    The decay constant, k, is determined from the half-life.

    k = ln 2 / t½ = 0.693 / 14.3 day = 0.0485 day⁻¹

    A = Ao e^(-kt)

    Ao = A / e^(-kt)

    Ao = 30.3 / e^(-0.0485 x 2.00)

    Ao = 33.4 g

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