2. The half-life of a radioactive element is important when considering its application in medicine. For example, iodine-131 is often used in the imaging of the thyroid. The reason is that iodine is readily absorbed by the thyroid gland. Another reason is the short half-life of iodine-131. I-131 gas has a half-life of 8.0 days.
a. If you started with 5 x 1010 iodine atoms, how many are left after approximately 1 month?
b. Why is it important that there will be very few I-131 left in your thyroid after 1 month of exposure?
a.
k = 0.693/t1/2
Substitute k into the below
ln(No/N) = kt
No = 5E10
N = ?
k from above
t = 1 month but change that to days if you use half life in days.
b.
Basically you don't want to get bombarded with radioactive rays longer than necessary.
To answer these questions, we need to understand the concept of half-life and how it relates to radioactive decay.
a) The half-life of iodine-131 is 8.0 days, which means that in 8.0 days, the amount of iodine-131 will be reduced by half. Let's calculate the number of iodine-131 atoms left after approximately 1 month.
1 month is equivalent to 30 days. To figure out how many half-lives occur in 30 days, we divide 30 by 8.0:
30 days / 8.0 days = 3.75 half-lives
Since we cannot have fractions of atoms, we need to consider how many half-lives have occurred:
After 1 half-life, half of the original amount remains.
After 2 half-lives, one-fourth (0.5 x 0.5 = 0.25) of the original amount remains.
After 3 half-lives, one-eighth (0.5 x 0.5 x 0.5 = 0.125) of the original amount remains.
Now, let's calculate the number of iodine-131 atoms left after 1 month:
5 x 10^10 atoms x 0.125 = 6.25 x 10^9 iodine atoms
Therefore, after approximately 1 month, there will be approximately 6.25 x 10^9 iodine-131 atoms left.
b) It is important that there will be very few I-131 left in your thyroid after 1 month of exposure because iodine-131 is radioactive and emits harmful radiation. This radiation can damage tissues and cells, potentially leading to adverse health effects such as cancer.
By using a short half-life isotope like iodine-131, the exposure to radiation is minimized. After 1 month, the amount of iodine-131 remaining is significantly reduced, reducing the radiation exposure and potential harm to the thyroid gland and the rest of the body. This is crucial for patient safety during medical procedures involving radioactive isotopes.