The iodine-131 nuclide has a half-life of 8 days. If you originally have 625-g sample, how many grams will you have after 2 months(approximately 64 days)?
To find out how many grams of iodine-131 you will have after 2 months, we need to determine the number of half-lives that occur within that time period.
The half-life of iodine-131 is 8 days, so the number of half-lives in 64 days can be calculated by dividing the total time by the half-life:
Number of half-lives = 64 days / 8 days = 8 half-lives.
Every half-life, the amount of the substance is reduced by half. Therefore, after 8 half-lives, the remaining quantity will be:
Remaining quantity = (Initial quantity) x (0.5)^(Number of half-lives)
= 625 g x (0.5)^8
Calculating this expression:
Remaining quantity = 625 g x (0.00390625)
ā 2.44140625 g
Therefore, after approximately 64 days, you will have around 2.44 grams of iodine-131 remaining.
To determine the amount of iodine-131 remaining after 64 days, we can use the formula:
Amount remaining = Initial amount * (1/2)^(number of half-lives)
First, let's calculate the number of half-lives that occur in 64 days. Since the half-life of iodine-131 is 8 days, we divide 64 by 8:
Number of half-lives = 64 days / 8 days per half-life = 8 half-lives
Now, let's substitute the values into the formula:
Amount remaining = 625 g * (1/2)^(8)
Next, calculate the amount remaining:
Amount remaining = 625 g * (1/256) = 2.441 g
Therefore, after approximately 64 days, you will have approximately 2.441 grams of iodine-131 remaining.
8 half-lives
625 * (1/2)^8