Iodine-131 is used I'd diagnosing certain medical problems because of the short half-life, which is 8.02 days. Assume the hospital lab uses for 4.52g of iodine-131 in a month. What mass of this radioisotope remains in patients after 32 days?
Amount/dosage=e^(-.693*32/8.02)
put this into your google search window:
e^(-.693*32/8.02)=
multiply that by the original dose, 4.52 grams, and you have it.
To determine the mass of iodine-131 that remains in patients after 32 days, we need to consider its half-life and the amount used in a month.
First, let's calculate the number of half-lives that have occurred in 32 days.
Since the half-life of iodine-131 is 8.02 days, we can divide 32 by 8.02:
32 days ÷ 8.02 days/half-life ≈ 3.99 half-lives
Now, we know that each half-life reduces the amount of iodine-131 by half. Therefore, we need to calculate the remaining amount using the half-life formula:
Remaining mass = Initial mass × (1/2)^(number of half-lives)
Given that 4.52 grams of iodine-131 are used in a month, we can use this value as the initial mass.
Remaining mass = 4.52 g × (1/2)^(3.99)
Calculating this expression, we find:
Remaining mass ≈ 4.52 g × 0.0625
Remaining mass ≈ 0.28 g
Therefore, approximately 0.28 grams of iodine-131 would remain in patients after 32 days.