Question

use the chart above to answer the following questions:

1. if we start with 8000 grams of radium - 226, how much would remain after 3,200 years?
2. if we have 5000 grams iodine - 131 how much remains after 10 half - lives? how long does it take the sample to decay?
3. if we start with 20 atoms of plutonium - 239, how many would remain after 48,240 years?
4. if we start with 60 grams of uranium - 238, how many remain after 4,470,000,000 years?
5. if we start with 24 atoms of iodine - 131, how many remain after 32 days?
6. if we have 800 grams plutonium - 239 how much remains after 6 half - lives? how long does it take the sample to decay?
7. if a 100 gram sample of radon has decayed to 12.5 grams how many half - lives have passed? how long did it take to decay?
8. if you have a 2700 gram sample of c - 14 and 12 half - lives have passed how much of your original sample remains. how much times has passed?
9. how long does it take a 100 gram sample of radon - 222 to decay to 0.390g? how many half - lives have passed?

Explanation:

13.

Step1: Calculate number of half - lives

The half - life of radium - 226 is 1600 years. The time passed $t = 3200$ years. The number of half - lives $n=\frac{t}{T_{1/2}}=\frac{3200}{1600}=2$.

Step2: Calculate remaining amount

The formula for the remaining amount of a radioactive substance is $N = N_0\times(\frac{1}{2})^n$, where $N_0 = 8000$ grams and $n = 2$. So $N=8000\times(\frac{1}{2})^2=8000\times\frac{1}{4}=2000$ grams.

Step1: Calculate remaining amount

Using the formula $N = N_0\times(\frac{1}{2})^n$, with $N_0 = 5000$ grams and $n = 10$. So $N=5000\times(\frac{1}{2})^{10}=5000\times\frac{1}{1024}\approx4.88$ grams.

Step2: Calculate time passed

The half - life of iodine - 131 is 8 days. The time passed $t=n\times T_{1/2}=10\times8 = 80$ days.

Step1: Calculate number of half - lives

The half - life of plutonium - 239 is 24120 years. The time passed $t = 48240$ years. $n=\frac{t}{T_{1/2}}=\frac{48240}{24120}=2$.

Step2: Calculate remaining amount

Using $N = N_0\times(\frac{1}{2})^n$, with $N_0 = 20$ atoms and $n = 2$. So $N=20\times(\frac{1}{2})^2=20\times\frac{1}{4}=5$ atoms.

Answer:

2000 grams

14.