Iodine-131 is used to destroy thyroid tissue in the treatment of an overactive thyroid. the half-life of iodine-131 is 8.02 days. if a hospital receives a shipment of 200.0g of iodine-131, how much iodine-131 would remain after 32 days?

k = 0.693/t1/2

Sustitute into the equation below.
ln(No/N) = kt
No is 200.0g
N = what remains.
t is 32 days.

how did you get .693?

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To determine how much iodine-131 would remain after 32 days, we need to calculate the number of half-lives elapsed and use the half-life formula:

Amount remaining = Initial amount × (1/2)^(t / half-life)

Given:
Initial amount = 200.0 g
Half-life = 8.02 days
Time (t) = 32 days

First, let's calculate the number of half-lives elapsed:

Number of half-lives = t / half-life
Number of half-lives = 32 days / 8.02 days ≈ 3.99

Now, let's calculate the amount remaining:

Amount remaining = Initial amount × (1/2)^(number of half-lives)
Amount remaining = 200.0 g × (1/2)^3.99

To evaluate (1/2)^3.99, we can use a calculator:

Amount remaining ≈ 200.0 g × 0.0625
Amount remaining ≈ 12.5 g

Therefore, after 32 days, approximately 12.5 grams of iodine-131 would remain.