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Nuclear Decay A level

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    • Thread Starter

    The question is

    Technetium-99 (Tc-99) is a radioisotope tracer with a decay constant of 0.12 hr^-1 . It emits 140 keV gamma photons and is commonly used in nuclear medicine to study the functionality of body organs and systems. A patient undergoing a bone scan is injected with Tc-99 with activity 800MBq. After how long will the total amount of gamma energy emitted from the patient every second fall to 1.0 micro jules

    What have you tired?

    Moved to Physics

    This is your problem:
    \lambda = 7.2s^{-1}
    A_0=8 \times 10^8 Bq
    E_{photon}=1.4 \times 10^5 eV

    Now, A=A_0e^{-\lambda t} for the activity of the substance A after time t

    We need the time when activity is less than 1 microjoule.
    1 \mu J = 1 \times 10^{-6} J = 6.25 \times 10^{12} eV
    So we calculate how many decays per second we need for this energy to be true, if each decay gives off a single photon and we need  6.25 \times 10^{12} eV;
    A = \frac{ 6.25 \times 10^{12}}{1.4 \times 10^5}
    Now we have A, A_0 and \lambda
    Take logs of both sides
    t=-\dfrac{\ln{\frac{A}{A_0}}}{ \lambda }
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