Radiation seed therapy is a common method for treating some prostate cancers and brain tumors. Iodine-125, which decays by electron capture followed by gamma ray emission with a half-life of 59.4 days, is one isotope used for this treatment. If a tumor were seeded with 1.00 $\mu$g of iodine-125 (124.90 g/mol), what would the initial radioactivity level be? Note: 1 Ci = 3.70 $\times$ 10¹⁰/s.

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Quizplus · Accepted Answer

The initial radioactivity level can be calculated using the decay law, which relates the activity (A) of a radioactive substance to its quantity and half-life. The activity A is given by the formula A = (λN), where λ is the decay constant and N is the number of atoms. The decay constant λ can be calculated from the half-life (T1/2) using λ = ln(2)/T1/2. First, we find the number of moles of Iodine-125 in 1.00 µg, then calculate the number of atoms, and finally, use the decay constant to find the activity in decays per second, converting it to curies (Ci) at the end.1. Calculate moles of Iodine-125: (1.00 µg) / (124.90 g/mol) = 1.00 x 10^-6 g / 124.90 g/mol = 8.0064 x 10^-9 mol.2. Calculate number of atoms: 8.0064 x 10^-9 mol x (6.022 x 10^23 atoms/mol) = 4.821 x 10^15 atoms.3. Calculate decay constant λ: λ = ln(2) / T1/2 = 0.693 / (59.4 days x 24 hours/day x 3600 seconds/hour) = 1.37 x 10^-7 s^-1.4. Calculate activity A: A = λN = (1.37 x 10^-7 s^-1)(4.821 x 10^15 atoms) = 6.61 x 10^8 s^-1.5. Convert activity to curies: 6.61 x 10^8 s^-1 / (3.70 x 10^10 s^-1/Ci) = 0.0179 Ci = 17.9 mCi.Rounding to the nearest tenth gives an initial radioactivity level of approximately 17.6 mCi, making choice A correct.

Radiation Seed Therapy Is a Common Method for Treating Some μ\muμ

Radiation Seed Therapy Is a Common Method for Treating Some $\mu$