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    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
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    What have you tired?

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    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
    Hint:
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    t=-\dfrac{\ln{\frac{A}{A_0}}}{ \lambda }
 
 
 
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