Final-Answer:
To calculate how much iodine-131 will be left after 21.3 days, we can use the radioactive decay formula:
[N(t) = N0 cdot e^{-lambda t}]
Where:
- (N(t)) = the quantity of the substance at time (t)
- (N0) = the initial quantity of the substance
- (lambda) = decay constant
- (t) = time in days
- (e) = mathematical constant approximately equal to 2.71828
The decay constant,(lambda), can be calculated using the half-life,(t{1/2}), as follows:
[ lambda = frac{0.693}{t{1/2}]
Given:
- Half-life (t{1/2}) = 8.02 days
- Initial quantity (N0) = 215.25 g
- Time (t)= 21.3 days
First, calculate the decay constant:
[ lambda = frac{0.693}{8.02} approx 0.0865]
Then, substitute the known values into the radioactive decay formula:
[N(21.3) = 215.25 cdot e^{-0.0865 times 21.3}]
[N(21.3) = 215.25 cdot e^{-1.84345}
[N(21.3) = 215.25 cdot 0.1587]
[N(21.3) ≈ 34.18]
After approximately 21.3 days, there will be about 34.18 grams of iodine-131 left.
So, after 21.3 days, approximately 34.18 grams of iodine-131 will be left.
