Half-Life and Radiometric Dating

Rate of Decay

The time required for half the nuclei in a sample of a radioisotope to undergo radioactive decay is called its half-life. This is the time required for half of the

nuclides in a sample to decay. Half-life of U-238 is 4.5 billion years Half-life of I-131 is 8.07 days Half-life of Po-194 is 0.7 second

Red dots are radioactive atoms

Blue dots are stable atoms that have undergone decay

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.

Carbon-14 Dating

Scientist use carbon-14 to date very old things were once alive.

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 that which remains 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.

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?

Practice Problems

You need to find out how many times ½ (0.5) must be used as a factor to produce 0.0625.

The answer is 4 times because

0.5 X 0.5 X 0.5 X 0.5 = 0.0625

4 half-lives have gone by and each half-life is 5730 years.

5730 years X 4 = 22,920 years

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

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

Practice Problems3) 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

Practice Problems4) 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

Practice Problems5) 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 = 0.03125

5 half-lives have gone by.

5730 X 5 = 28,650 years old

0.0312

Half-life equation

Amount remaining = amount of original sample 2n

n = number of half-lives

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 remaining =amount of original sample

2n

1.0 mg

231 half life = 30 years

Therefore, 90 years is equal to how many half lives?

n = 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 remaining =amount of original sample

232n5.0 mg =

1 half life = 60 seconds

Therefore, 3 minutes is equal to how many half lives?

n = 3