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:
First, calculate how many half-lives have passed in one year:
1 year = 365 days
Half-life = 60 days
Number of half-lives = 365 days / 60 days = 6.08 (approximately 6)
Now, calculate the amount of iodine-125 remaining after 6 half-lives:
Remaining amount = Initial amount * (1/2)^6
Remaining amount = 0.020 g * (1/2)^6
Remaining amount = 0.020 g * (1/64)
Remaining amount = 0.0003125 g
Therefore, after one year, only 0.0003135 g of iodine-125 remains in the prostate gland.
For question 21:
Since the half-life of Barium-122 is 2 minutes, and the experiment is set up for 10 minutes, this means 5 half-lives have passed during the setup time.
Calculate the remaining amount of Barium-122 after 5 half-lives:
Remaining amount = Initial amount * (1/2)^5
Remaining amount = 10.0 g * (1/2)^5
Remaining amount = 10.0 g * (1/32)
Remaining amount = 0.3125 g
Therefore, 0.3125 g of Barium-122 remains at the point when the experiment begins.
For question 22:
Since the initial amount of Carbon-14 in a living jawbone is 200 mg, and the remaining amount is 50 mg, this means 3 half-lives have passed (since 200 mg reduced to 100 mg after the first half-life, then to 50 mg after the second half-life).
Calculate the age of the bone using the formula:
Age = Number of half-lives * Half-life
Age = 3 * 5730 years
Age = 17190 years
Therefore, the bone is approximately 17190 years old.