The time elapsed between packaging and delivery is approximately 182.6 minutes, which is equivalent to 3.04 hours.
To solve this question, we can use the formula for radioactive decay:
A = A0 * e^(-kt)
Where:
A = Final amount
A0 = Initial amount
k = Decay constant
t = Time elapsed
Let's determine the decay constant, k. We can do this by using the formula:
t1/2 = (ln 2) / k
Where t1/2 is the half-life of the isotope.
Given that the nuclear half-life of Fluorine-18 is 110 minutes, we can substitute this value into the equation:
110 min = (ln 2) / k
Solving for k:
k = (ln 2) / 110 â 0.00631 min^-1
Now, we can use the formula for radioactive decay to find the time elapsed. We know that the sample delivered to the hospital was 35.2 mg, while the original sample was 250 mg. Therefore, the fraction that remained after delivery is:
(amount remaining / initial amount) = A / A0 = 35.2 / 250 = 0.1408
Substituting this value, along with the other values we have, into the radioactive decay formula:
0.1408 = e^(-0.00631t)
Taking the natural logarithm on both sides, we get:
ln(0.1408) = -0.00631t
Solving for t, we find:
t = -ln(0.1408) / 0.00631 â 182.6 minutes
Therefore, the time elapsed between packaging and delivery is approximately 182.6 minutes, which is equivalent to 3.04 hours. Hence, the answer is 3.04 hours.
Learn more about Radioactive decay from the link given below:
brainly.com/question/17983159
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