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.