Radioactive iodine-131 decays (beta emitter) to form Xenon-131. Iodine-131 has a half-life of 8.07 days. If a thyroid gland absorbed 20.0 microcuries of I-131 today, how many microcuries would remain after 30.0 days. Microcuries are disintegrations per second of isotope decay.
20 * .5^(30/8.07)
Another way.
ln(No/N) = kt
No = 20 ug
N = ?
k = 0.693/half life in days
t = 30 days
To determine how many microcuries of Iodine-131 (I-131) would remain after 30.0 days, we need to use the concept of half-life.
The half-life of I-131 is given as 8.07 days.
1. Start by calculating the number of half-lives that have passed in 30.0 days. Since the half-life of I-131 is 8.07 days, divide 30.0 by 8.07 to get the number of half-lives:
Number of half-lives = 30.0 days / 8.07 days ≈ 3.71 half-lives
2. Now, we can use the concept of half-life to calculate the remaining amount of I-131. Each half-life reduces the amount of radioactive material to half its original value.
Remaining amount = Initial amount × (1/2)^(number of half-lives)
Initially, the thyroid gland absorbed 20.0 microcuries of I-131. Therefore,
Remaining amount = 20.0 microcuries × (1/2)^(3.71 half-lives)
3. Finally, calculate the remaining amount of I-131 by evaluating the equation above:
Remaining amount ≈ 20.0 microcuries × (1/2)^3.71 ≈ 4.10 microcuries
So, after 30.0 days, approximately 4.10 microcuries of I-131 would remain in the thyroid gland.