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.