1. Rates of Nuclear Decay
These stone tools from the archaeological site in Cactus Hill, Virginia, are at least 15,000 years old.
Scientists estimated the age of the site based on rates of nuclear decay.

2. Half-life
Unlike chemical reaction rates, which vary with the conditions of a reaction, nuclear decay rates are constant.

3. Half-life
A half-life is the time required for one half of a sample of a radioisotope to decay.

4. Half-life
The half-life for the beta decay of iodine-131 is 8.07 days.

5. Half-life
The half-life for the beta decay of iodine-131 is 8.07 days.

6. Half-life
The half-life for the beta decay of iodine-131 is 8.07 days.

7. Half-life
The half-life for the beta decay of iodine-131 is 8.07 days.

8. Half-life
Every radioisotope decays at a specific rate. Half-lives can vary from fractions of a second to billions of years.

9. Decay Series of Uranium-238
Uranium-238 decays through a complex series of radioactive intermediates, including radon (Rn) gas. Interpreting Diagrams What is the stable end product of this series?
Stable Isotope

10. Problem #1: The half-life of Zn-71 is 2. 4 minutes. If there are 100
Problem #1: The half-life of Zn-71 is 2.4 minutes. If there are g at the beginning, how many grams would be left after 7.2 minutes has elapsed?
Solution:
7.2 min ÷ 2.4 min per half-life = 3 half-lives
100.0 g ÷ 2 = 50.0 g
50.0 g ÷ 2 = 25.0 g
25.0 g ÷ 2 = 12.5 g remain after 3 half-lives.

11. Problem #2: Os-182 has a half-life of 21. 5 hours
Problem #2: Os-182 has a half-life of 21.5 hours. How many grams of a 10.0 gram sample would have decayed after exactly two half-lives?
Solution:
10.0 g ÷ 2 = 5.00 g
5.00 g ÷ 2 = 2.50 g remain after 2 half-lives.
10.0 g – 2.50 g = 7.50 g decayed

12. Problem #3: After 24 days, 2. 00 mg of an original 32
Problem #3: After 24 days, 2.00 mg of an original mg sample is left. What is the half-life of the substance?
Solution:
32.00 mg ÷ 2 = mg
16.00 mg ÷ 2 = 8.00 mg
8.00 mg ÷ 2 = 4.00 mg
4.00 mg ÷ 2 = 2.00 mg remain after 4 half-lives.
24 days / 4 half-lives = 6 days / half-life

13. Problem #4: A bone contains radioactive carbon-14 with a half-life of 5,000 yrs. The bone is thought to have had 20.0 mg of 14C when the animal died and it now has 2.5 mg of 14C left. How old is the bone?
Solution:
20.0 mg ÷ 2 = 10.0 mg
10.0 mg ÷ 2 = 5.0 mg
5.0 mg ÷ 2 = 2.5 mg after 3 half-lives.
(3 half-lives) x (5,000 yrs/half-life) = 15,000 yrs

14. Transmutation Reactions
The conversion of an atom of one element to an atom of another element is called transmutation.
Transmutation can occur by radioactive decay.
Transmutation can also occur when particles bombard the nucleus of an atom.

15. Transmutation Reactions
The first artificial transmutation reaction involved bombarding nitrogen gas with alpha particles.
The first artificial transmutation reaction involved bombarding nitrogen gas with alpha particles, as illustrated here. Interpreting Diagrams What particles were formed?

16. Transmutation Reactions
The elements in the periodic table with atomic numbers above 92, the atomic number of uranium, are called the transuranium elements.
All transuranium elements undergo transmutation.
None of the transuranium elements occur in nature, and all of them are radioactive.

17. Transmutation Reactions
Transuranium elements are synthesized in nuclear reactors and nuclear accelerators.
Fermilab is a major accelerator center located in Batavia, Illinois. The main accelerator is a ring that has a radius of 1.0 km.