Thanks SHoW all steps: Problem Molybdenum-99 decays to form \"metastable\" techn

Question

Thanks SHoW all steps: Problem Molybdenum-99 decays to form "metastable" technetium-99 (tero through beta decay. This isotope has a very long lifetime (half-life of 6 hours) compared to other nuclear isomers that undergo gamma decay. The gamma rays emitted when c decays are easily detected, which makes this species ideal for a variety of medical imaging applications such as singlephoton emission computed tomography. At the beginning of this millennium, the decommissioning of two nuclear reactors created a critical shortage of 9 Tc, and this shortage remains to be addressecd (Science 331 (2011): 227). Imagine you are performing ni aging experiment with ei which you need 2 hours to obtain the image after injecting the isotope into the patient. How much of the 99Tc will have decayed during this time? Step-by-step solution Step 1 ofa In this case, the half life of Tc-99 can be considered a first order elementary reaction. Expression for the hal-life t2 is as follows: 27

Explanation / Answer

given half life of 99 Tc ( tecnitium 99) is t1/2 = 6 hours

Let initial amount of 99Tc in patients body be No
then after time T amount of Tc inside patients body is given by
N = No*exp(-lambda*t)
where lambda = ln(2)/t1/2 = ln(2)/6 = 0.115524 per hour
so, for t = 2hr
N/No = exp(-2*0.115524) = 0.7937

hence amount of Tc which has decayed in 2 hours = (No - N) = No - 0.7937No = 0.2063No ( where No is the intial amount of Tc inside the patient)

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