Final answer:
To calculate how long it takes for half of the Iodine-125 to decay, a decay rate of 1.15% per day translates to a decay constant of 0.0115 per day. Using the half-life formula T(1/2) = ln(2)/k, it is estimated that it will take approximately 60 days for half of the Iodine-125 to decay.
Step-by-step explanation:
The student's question about the half-life of Iodine-125 requires knowledge about the decay rate and involves a mathematical calculation. To find out how long it will take for half of the Iodine-125 to decay, we can use the concept of half-life, which is the time it takes for half of a radioactive substance to decay. Iodine-125 has a different half-life than Iodine-131, but the calculation method remains the same.
To calculate the half-life, we can use the decay rate formula specific for first-order decay, which is T(1/2) = ln(2)/k, where T(1/2) is the half-life and k is the decay constant. However, as we're given a decay rate in percentage, we'll convert this into the decay constant first. The decay constant (k) can be calculated from the daily decay rate by using the formula k = decay rate per day / 100. Thus, k = 1.15 / 100 = 0.0115 per day. Now, we can substitute this into the half-life formula to find the half-life of Iodine-125.
Using T(1/2) = ln(2)/k, we get T(1/2) = ln(2)/0.0115 ≈ 60.2 days. Therefore, it will take approximately 60 days for half of the Iodine-125 to decay.