1. Half-Life and Radioisotope Dating

2. Rate of Decay
The measurement of the time required for a radioactive material to decay is called its half-life.
This is the time required for half of the nuclides in a sample to decay.
Half-life of 238U is 4.5 billion years
Half-life of 131I is 8.07 days
Half-life of 194Po is 0.7 second

5. Carbon-14 Dating We have some radioactive materials in our bodies.
One of the isotopes is carbon-14.
Carbon-14 is an isotope of the carbon in CO2.
All living things take it in during respiration.

6. Carbon-14 Dating
Scientist use carbon-14 to date very old things.

7. Carbon-14 Dating
Decayed carbon-14 is continually being replaced in the body.
Once the organism dies the carbon-14 is no longer replaced, but what is there continues to decay.
By examining the amount of carbon-14 left in the material, scientist can estimate the age of the subject.
Accurate to about 20,000-50,000 years.

8. Practice Problems
1) A fossilized tree killed by a volcano was studied. It had 6.25 percent of the amount of carbon-14 found in a sample of the same size from a tree that is alive today. When did the volcanic eruption take place?

9. Practice Problems
You need to find out how many times ½ (0.5) must be used as a factor to produce
The answer is 4 times because
0.5 X 0.5 X 0.5 X 0.5 =
4 half-lives have gone by and each half-life is 5730 years.
5730 years X 4 = 22,920 years

10. Practice Problems
2) A rock was analyzed using potassium-40. The half-life of potassium-40 is 1.25 billion years. If the rock had only 25 percent of the potassium-40 that would be found in a similar rock formed today, calculate how long ago the rock was formed.
Potassium-40 Half-life is 1.25 billion years

11. 1.25 billion X 2 = 2.50 billion years
Practice Problems
2) Convert 25% to a decimal ---
0.5 X 0.5 = 0.25
2 half-lives have gone by.
1.25 billion X 2 = 2.50 billion years
0.25

12. Practice Problems
3) Ash from an early fire pit was found to have 12.5 percent as much carbon-14 as would be found in a similar sample of ash today. How long ago was the ash formed?
Convert 12.5% to a decimal ---
0.5 X 0.5 X 0.5 = 0.125
3 half-lives have gone by.
5730 X 3 = 17,190 years ago
0.125

13. 1.25 billion X 3 = 3.75 billion years old
Practice Problems
4) A rock sample has 12.5% of the potassium-40 that would be present in a similar rock formed today. How old is the rock sample?
Convert 12.5% to a decimal ---
0.5 X 0.5 X 0.5 = 0.125
3 half-lives have gone by.
1.25 billion X 3 = 3.75 billion years old
0.125

14. Practice Problems
5) How old is a piece of wood in which the carbon-14 is 3.12% of that in wood formed today?
Convert 3.12% to a decimal ---
0.5 X 0.5 X 0.5 X 0.5 X 0.5 =
5 half-lives have gone by.
5730 X 5 = 28,650 years old
0.0312

15. n = number of half-lives
Half-life equation
Amount remaining = amount of original sample n
n = number of half-lives

16. An isotope of cesium (cesium-137) has a half-life of 30 years. If 1
An isotope of cesium (cesium-137) has a half-life of 30 years. If 1.0 mg of cesium-137 disintegrates over a period of 90 years, how many mg of cesium-137 would remain?
amount of original sample
1.0 mg
Amount remaining = 23 2n
1 half life =
30 years
Therefore, 90 years is equal to how many half lives?
n = 3

17. 4. Sodium-25 was to be used in an experiment, but it took 3
4. Sodium-25 was to be used in an experiment, but it took 3.0 minutes to get the sodium from the reactor to the laboratory. If 5.0 mg of sodium-25 was removed from the reactor, how many mg of sodium-25 were placed in the reaction vessel 3.0 minutes later if the half-life of sodium-25 is 60 seconds?
amount of original sample
Amount remaining =
5.0 mg = 2n 23
1 half life =
60 seconds
Therefore, 3 minutes is equal to how many half lives?
n = 3