If the half-life of iodine-131 is 8 day, how much would remain undecayed after 8 day if we started with 38 grams?
How much at 16 days?
24 days?
32 days?
To do these problems you start by taking the amount you start with in this case 38 grams and divide it by the time. I'll show you how to do one and hopefully you can do the rest
38grams/8 days = 2grams/day
(1/2)^2gams/day = .25
38 grams x .25 = 9.5g remaining after 8 days
amount = 38 (1/2)^(t/8)
clearly after 8 days , we would have 38(1/2)^1 = 19 g
after 16 days:
amount = 38(1/2)^(16/8
= 38(1/2)^2
= 38/4 or 9.5 g
repeat for the other two cases
To calculate the amount of radioactive substance remaining after a given time, you can use the formula:
Amount remaining = Initial amount × (1/2)^(time/half-life)
In this case, the half-life of iodine-131 is 8 days, and the initial amount is 38 grams.
1. After 8 days:
Amount remaining = 38 grams × (1/2)^(8/8)
Amount remaining = 38 grams × (1/2)^1
Amount remaining = 38 grams × 1/2
Amount remaining = 19 grams
Therefore, after 8 days, 19 grams of iodine-131 would remain undecayed.
2. After 16 days:
Amount remaining = 38 grams × (1/2)^(16/8)
Amount remaining = 38 grams × (1/2)^2
Amount remaining = 38 grams × 1/4
Amount remaining = 9.5 grams
Therefore, after 16 days, 9.5 grams of iodine-131 would remain undecayed.
3. After 24 days:
Amount remaining = 38 grams × (1/2)^(24/8)
Amount remaining = 38 grams × (1/2)^3
Amount remaining = 38 grams × 1/8
Amount remaining = 4.75 grams
Therefore, after 24 days, 4.75 grams of iodine-131 would remain undecayed.
4. After 32 days:
Amount remaining = 38 grams × (1/2)^(32/8)
Amount remaining = 38 grams × (1/2)^4
Amount remaining = 38 grams × 1/16
Amount remaining = 2.375 grams
Therefore, after 32 days, 2.375 grams of iodine-131 would remain undecayed.