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).
Break the calculations down
Sure! Let's break down the calculations for each question:
20. Iodine-125:
- Half-life = 60 days
- After 1 year (365 days), there are 365/60 = 6.08 half-lives
- Remaining amount = Initial amount * (1/2)^6.08
- Initial amount = 0.020 g
- Remaining amount = 0.020 * (1/2)^6.08 ≈ 0.001 g
- Therefore, approximately 0.001 g of iodine-125 remains in the prostate gland after one year.
21. Barium-122:
- Half-life = 2 minutes
- Time to set up experiment = 10 minutes
- Number of half-lives during setup = 10/2 = 5 half-lives
- Remaining amount = Initial amount * (1/2)^5
- Initial amount = 10.0 g
- Remaining amount = 10.0 * (1/2)^5 = 10.0 * (1/32) = 0.3125 g
- Therefore, approximately 0.3125 g of Barium-122 remains at the point when you begin the experiment.
22. Carbon-14:
- Initial amount = 200 mg
- Remaining amount = 50 mg
- Half-life = 5730 years
- Number of half-lives = log(50/200) / log(0.5) = -1.386 / -0.301 = 4.6 half-lives
- Age of the bone = 5730 years * 4.6 = 26,358 years
- Therefore, the bone is approximately 26,358 years old.