1. Absolute Dating of Rocks and Strata

2. Absolute Dating
Calculating the age of rocks, fossils, or strata in years.
Gives a numerical value.
Example: A rock is found to have an absolute age of 300 million years.

3. Radiometric Dating
Radiometric dating uses radioactive decay of minerals in rocks and fossils to determine a rock or fossil’s absolute age.
Isotope: Element with the same number of protons and electrons but different number of neutrons.
Primary radioactive isotopes used in geology are:
Carbon 14 decays to Nitrogen 14
Uranium 238 decays to Lead 206
Uranium 235 decays to Lead 207
Thorium 232 decays to Lead 208
Rubidium 87 decays to Strontium 87
Potassium 40 decays to Argon 40

4. Absolute Age is Determined by Half-Life of Radioactive Isotopes
Half-Life: The time it takes for one half of the radioactive material to decay.
Parent Material (element): The original radioactive isotope before decay.
Daughter Material (element): The element the radioactive isotope decays to.
Example: Carbon 14 is the Parent. Nitrogen 14 is the Daughter because Carbon 14 decays to Nitrogen 14.

5. Common Half-Lives Carbon 14 decays to Nitrogen 14 in 5,730 Years
Primarily Used for dating organic objects. Limited to about 80,000 years old.
Uranium 238 decays to Lead 206 in 4.5 Billion years
Uranium 235 decays to Lead 207 in 713 Million years
Thorium 232 decays to Lead 208 in 1.4 Billion Years
Rubidium 87 decays to Strontium 87 in 48.8 Billion years
Potassium 40 decays to Argon 40 in 1.3 Billion Years

6. Radiocarbon Dating
Can only be used for rocks containing organic material.
Carbon 14 produced in upper atmosphere and is incorporated into living matter through carbon dioxide.
As a result, all living things contain some Carbon 14.
Decaying Carbon 14 is continually replaced when organism is alive but stops being replaced at death.
We can measure ratio of Carbon 14 to nonradioactive Carbon 12 to determine a date of death.
Thus, the ratio of Carbon 14 to Carbon 12 tells us how old something is.

7. Carbon 14 Decay Graph

8. Half-Life Calculations
Number of Half-Lives
Fraction Remaining
Percentage of Parent Remaining
Percentage of Daugher
1/1
100% 0% 1
1/2
50% 2
1/4
25%
75% 3
1/8
12.5%
87.5% 4
1/16
6.25%
93.75% 5
1/32
3.125%
96.875% 6
1/64
1.583%
98.417% 7
1/128
0.781%
99.219% n
1/(2n)
100/(2n)
100% - % Parent

9. Example Problems
What is the fraction of parent material remaining after 3 half-lives?
Answer: 1/(23) = 1/8
What is the percentage of parent material remaining after 5 half lives?
Answer: 100/(25) = 3.125%
What is the percentage of daughter material after 4 half-lives?
Answer: Find Percent Parent first. 100/(24) = 6.25%.
Then find Percent Daughter by subtracting percent parent from % = 93.75%

10. Try These
What is the half-life of a g sample of nitrogen-16 that decays to 12.5 g of nitrogen-16 in 21.6 seconds?
All isotopes of technetium are radioactive, but they have widely varying half-lives. If an g sample of technetium- 99 decays to g of technetium-99 in 639,000 years, what is its half-life?
If a radioactive isotope has a half-life of 100 years, how many years would it take for a 20 gram sample to decay down to 5 grams?
Gold-198 has a half-life of 2.7 days. How much of a 96 g sample of gold-198 will be left after 8.1 days?

11. Answers
7.2 Seconds % is left after 3 half lives. So seconds/3 = 7.2 Seconds
213,000 years. First: Figure out how many half lives: 800/2 =400, 400/2 = 200, 200/2 =100. So 3 half-lives have occurred. Then, 639,000 years/3= 213,000 years.
200 years. Figure out how many half-lives: 2 half-lives. Then, 100 years x 2 = 200 years.
12 grams. Figure out how many half lives: 8.1 Days/2.7 days = 3, so 3 half lives. 3 half lives = 1/8 of parent remaining. 96g x1/8 = 12.