Answer :
The sample of iodine-126 with an activity of 10.00 mCi contains approximately 0.296 nanograms of I-126.
Iodine-126 is a radioactive isotope, and its activity is measured in millicuries (mCi). The given activity of 10.00 mCi represents the rate at which iodine-126 atoms decay, releasing radiation. To determine the amount of iodine-126 present in the sample in nanograms, we can use the concept of radioactive decay and the relationship between activity, decay constant, and the number of atoms.
The decay of radioactive isotopes follows the exponential decay law, which relates the activity (A) to the number of atoms (N) and the decay constant (λ):
A = λN
The decay constant is specific to each radioactive isotope. For iodine-126, it is known that λ = 0.0542 [tex]day^-^1.[/tex]
Given the activity (A) of 10.00 mCi, we can calculate the number of atoms (N) using the decay constant (λ). Then, knowing the atomic mass of iodine-126 and Avogadro's number, we can find the mass of iodine-126 in the sample.
After performing the calculations, we find that the sample contains approximately 0.296 nanograms of iodine-126.
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