The disintegration of a radioisotope, such as I-131 to Xe-131, is another example of a first-order reaction.
It has a half-life of 8.0 days.
I-131 -> Xe-131 + e
If you start with 1.40 g I-131, how many grams of I-131 will be left after the following days?
PLEASE HELP!!!!
12 years ago
10 years ago
A vial contains radioactive iodine-131 with an activity of 3.7 mCi per milliliter. If the thyroid test requires 2.9 mCi in an "atomic cocktail," how many milliliters are used to prepare the iodine-131 solution?
11 months ago
To solve this problem, we need to use the formula for calculating the amount of substance remaining after a certain time in a first-order reaction:
N(t) = N(0) * e^(-kt)
Where:
N(t) = amount of substance remaining after time t
N(0) = initial amount of substance
k = rate constant of the reaction
t = time
The half-life of the reaction is given as 8.0 days, which means that after 8.0 days, the amount of I-131 will be reduced to half of its initial value.
Let's calculate the rate constant, k, using the equation:
k = ln(2) / t_1/2
Plugging in the given value of the half-life (t_1/2 = 8.0 days), we can calculate the rate constant:
k = ln(2) / 8.0
k ≈ 0.0866 (rounded to four decimal places)
Now we have the rate constant, we can use the formula to calculate the amount of I-131 remaining after a specific number of days.
Example: If we want to know how much I-131 remains after 10 days:
N(t) = N(0) * e^(-kt)
N(10) = 1.40 g * e^(-0.0866 * 10)
N(10) ≈ 1.40 g * e^(-0.866)
N(10) ≈ 1.40 g * 0.4189
N(10) ≈ 0.585 g
Therefore, after 10 days, approximately 0.585 grams of I-131 will remain.
You can repeat this calculation for any specific number of days to find the amount of I-131 remaining. Just replace t with the desired number of days in the equation.