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?
08 days: g,
16 days: g,
20 days: g,
24 days: g,
30 days: g
32 days: g
47 days: g
k = 0.693/t1/2
Then ln(No/N) = kt
No = 1.41 g
N = ?
k = from above
t = 8 days for #1.
The others are done the same way. Solve for N.
Hhf
To calculate the grams of I-131 remaining after a given number of days, we need to use the concept of half-life.
The half-life of a substance is the time it takes for half of the substance to decay. In this case, the half-life of I-131 is 8.0 days.
To find the amount of I-131 remaining after a certain number of half-lives, we can use the formula:
Amount remaining = Initial amount * (1/2)^(number of half-lives)
Now let's calculate the grams of I-131 remaining for each given number of days:
1) After 8 days:
Number of half-lives = 8 / 8.0 = 1
Amount remaining = 1.40 g * (1/2)^1 = 0.70 g
2) After 16 days:
Number of half-lives = 16 / 8.0 = 2
Amount remaining = 1.40 g * (1/2)^2 = 0.35 g
3) After 20 days:
Number of half-lives = 20 / 8.0 = 2.5
Amount remaining = 1.40 g * (1/2)^2.5 ≈ 0.248 g
4) After 24 days:
Number of half-lives = 24 / 8.0 = 3
Amount remaining = 1.40 g * (1/2)^3 = 0.175 g
5) After 30 days:
Number of half-lives = 30 / 8.0 = 3.75
Amount remaining = 1.40 g * (1/2)^3.75 ≈ 0.087 g
6) After 32 days:
Number of half-lives = 32 / 8.0 = 4
Amount remaining = 1.40 g * (1/2)^4 = 0.087 g
7) After 47 days:
Number of half-lives = 47 / 8.0 ≈ 5.875
Amount remaining = 1.40 g * (1/2)^5.875 ≈ 0.024 g
So, the grams of I-131 remaining after the given number of days are:
- 08 days: 0.70 g
- 16 days: 0.35 g
- 20 days: 0.248 g
- 24 days: 0.175 g
- 30 days: 0.087 g
- 32 days: 0.087 g
- 47 days: 0.024 g