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A tumor is injected with 0.3 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?

User Egomesbrandao
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2 Answers

12 votes
12 votes

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.

User Zeroos
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3.2k points
9 votes
9 votes

Answer:

The time required is 60.3 days.

Step-by-step explanation:

initial amount, No = 0.3 g

rate, r = 1.15 % per day = 0.0115 per day

final amount, N = 0.15 g

Let the time is t.


N = No e^(-rt)\\\\0.15 = 0.3 e^(-0.0115 t)\\\\0.5 =e^(-0.0115 t)\\\\- 0.6931 = - 0.0115 t \\\\t = 60.3 days

User Trevor North
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3.1k points