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Answer :
Final answer:
To calculate the activity of an I-131 source after 2 days, we use the radioactive decay formula with the known half-life of I-131. By applying the formula, we can confirm that option (a) 59.8mCi is the correct answer as it is the only value that represents a decrease in activity consistent with the isotope's decay rate.
Explanation:
If the initial activity of an I-131 source measures 100mCi, the activity after 2 days can be determined using the radioactive decay formula and the half-life of I-131, which is approximately 8 days.
The decay formula is given by:
A = A0e−λt
Where:
- A is the activity after time t,
- A0 is the initial activity,
- λ is the decay constant (found using the half-life of the isotope),
- t is the time elapsed.
The decay constant λ can be calculated as:
λ = ln(2) / half-life
Thus, for I-131:
λ = ln(2) / 8 days
After 2 days, the activity A can be calculated as follows:
A = 100mCi * exp(-ln(2) * 2 / 8)
This calculation will give us an activity less than 100mCi. To find the exact answer, we can plug this into a calculator. However, in a multiple-choice question such as this one, we can use process of elimination and our understanding that the activity should decrease over time due to decay. Therefore, answer (a) 59.8mCi is the one that makes sense given the half-life. All other options are greater than the expected amount of decay after 2 days.
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