can you help me with this .
20 Iodine – 125 emits gamma rays when it decays to Tellerium-125 and has a half-life of 60 days. If a 0.020 g pellet of iodine – 125 is implanted into a prostate gland, how much iodine – 125 remains there after one year?
21. Barium – 122 has a half-life of 2 minutes. Suppose you obtain a sample weighing 10.0 g and it takes 10 minutes to set up an experiment. How many grams of Barium – 122 will remain at the point when you begin the experiment?
22. A normal adult jawbone contains 200 mg of Carbon-14 in a living person. If scientists found a jawbone that only had 50mg of Carbon-14, how old is the bone? (The half-life of C-14 is 5730 years).
For question 20:
Given:
- Half-life of Iodine-125 = 60 days
- Initial mass of Iodine-125 implanted = 0.020 g
- Time period = 1 year = 365 days
To find out how much Iodine-125 remains after one year, we can use the formula for radioactive decay:
Amount remaining = Initial amount * (1/2)^(Time elapsed / Half-life)
Plugging in the values, we get:
Amount remaining = 0.020 g * (1/2)^(365 / 60) = 0.020 g * (1/2)^6.08 ≈ 0.020 g * 0.0156 ≈ 0.000312 g
Therefore, after one year, approximately 0.000312 grams of Iodine-125 remains in the prostate gland.
For question 21:
Given:
- Half-life of Barium-122 = 2 minutes
- Initially obtained sample mass = 10.0 g
- Time taken to set up the experiment = 10 minutes
To find out how much Barium-122 remains when the experiment begins, we can calculate the number of half-lives that have elapsed during the setup time:
Number of half-lives = Time elapsed / Half-life = 10 min / 2 min = 5 half-lives
As each half-life reduces the amount of Barium-122 by half, the remaining amount after 5 half-lives is:
Amount remaining = Initial amount * (1/2)^5 = 10.0 g * (1/2)^5 = 10.0 g * 0.03125 ≈ 0.3125 g
Therefore, when you begin the experiment, approximately 0.3125 grams of Barium-122 will remain.
For question 22:
Given:
- Initial amount of Carbon-14 in a living person's jawbone = 200 mg
- Amount of Carbon-14 in the found jawbone = 50 mg
- Half-life of Carbon-14 = 5730 years
To find out how old the bone is, we can use the formula for radioactive decay:
Amount remaining = Initial amount * (1/2)^(Time elapsed / Half-life)
Plugging in the values we have:
50 mg = 200 mg * (1/2)^(Time elapsed / 5730)
Dividing both sides by 200, we get:
0.25 = (1/2)^(Time elapsed / 5730)
Now, to find the time elapsed, we take the logarithm of both sides:
log(0.25) = log[(1/2)^(Time elapsed / 5730)]
log(0.25) = (Time elapsed / 5730) * log(1/2)
Time elapsed = log(0.25) * 5730 / log(1/2)
Using a calculator, we can find the value of Time elapsed as approximately 11460 years. Therefore, the bone is approximately 11460 years old.