Carbon Dating and Radioactive Materials

Carbon Dating

Learning Intentions

• Understand what carbon dating is.

• Understand how we can use carbon-14.

• Calculate the age of substances from the percentage of carbon-14 from graphs.

• Understand what objects can be carbon dated and why.

What is Carbon Dating?

• Carbon-14 is used for carbon dating.

• It is a radioactive isotope that emits beta radiation.

• It has a half-life of 5730 years.

• It can be used to age organic objects up to 60,000 years old.

• The ratio of carbon-12 and carbon-14 is measured to date objects by working backwards.

Carbon Composition of Living Things

• All living things contain carbon.

• Only 1 in every 10,000,000,000 carbon atoms is carbon-14.

• Carbon-14 is radioactive and emits beta particles with a half-life of 5730 years.

• This property allows dating of organic objects up to 60,000 years old.

Graph Interpretation

• A graph showing the percentage of Carbon-14 remaining over time is used to calculate the age of an object.

  • The x-axis represents time in years.

  • The y-axis represents the percentage of Carbon-14.

How to Use Carbon Dating

• Use the provided graph to calculate the half-life of items by analyzing carbon-14 percentages.

Practice Problems

• Calculate the ages of:

  • Bow

  • Skull

  • Wooden branch
    *Dinosaur fossil

  • Rock

• The percentage of carbon-14 found in a wooden bow is 88%. What is the age of the bow?

• The percentage of carbon-14 found in a skull is 11%. What is the age of the skull?

• The percentage of carbon-14 found in a tree is 93%. What is the age of the tree?

• The percentage of carbon-14 found in a dinosaur fossil is 0%.

  • What does a 0% reading mean?

  • What problems does this pose for carbon dating?

• Carbon-14 cannot be used to check the age of a rock.

  • Why?

  • What method is used instead?

• Given that the age of a rock found using uranium dating is 10 million years, calculate a very rough estimate of the age of the dinosaur fossil.

Additional Information

• Living animals take in small amounts of radioactive carbon-14.

• After death, the amount of carbon-14 decreases due to decay.

• The remaining carbon-14 in bones estimates the age of a skeleton.

• Carbon-14 is a beta emitter with a half-life of 5720 years.

Decay Equation

• ^{14}C \rightarrow Ne

Sample calculation

• A bone contains 10 units of carbon-14, while an identical bone in a living animal contains 160 units.

• Calculate the age of the skeleton using the concept of half-life.

• Explain why this method is unreliable for skeletons less than 100 years old.

Half Life and Isotopes

• Compare the half-lives of two isotopes.

• Determine which isotope is safer and why.

• Consider potential uses for these isotopes.

lodine Isotopes

• Graphs showing the activity of lodine-131 and lodine-135 over time (in hours) are displayed.

True or False Quiz

1. The activity of a source reduces to one-sixteenth of its original value after four half-lives. (True)

2. The radioactive isotope sodium-25 has a half-life of 1 minute. What fraction of it remains after 3 minutes? (D) 1/8

3. Technetium-99m Half-Life Calculation

• Technetium-99m, used as a medical tracer, has a half-life of 6 hours.

• A sample gives a count rate of 2400 counts per second at 11:00 am on Monday.

  • How many half-lives will it take for the count to drop to 300 counts per second?

  • How long will it take for the count to drop to 300 counts per second?

  • What day and time will it be when the count is 300 counts per second?

• 2400 \rightarrow 1200 \rightarrow 600 \rightarrow 300
  One half-life
  One half-life
  One half-life

• 3 Half lives x 6 hours = 18 Hours

• 11am Mon – 5 pm Mon – 11pm – Mon – 5 am Tues

1. Xenon-133 Half-Life Problem

• Xenon-133, a radioactive gas used for diagnosing lung problems, has its activity fall to 1/8 of its original value in 15 days.

• Question: What is its half-life?

• Solution:

  • 1/2 * 1/2 * 1/2 = 1/8

  • 3 Half lives = 15 days. Half life = 5 days.

1. Sodium-24 Count Rate Calculation

• The half-life of the radioactive isotope sodium-24 is 15 hours.

• A sample has a count rate of 240 counts per minute (cpm).

• Question: What will its count rate be 60 hours later?

• Solution:

  • (15) Hours

  • (30) Hours

  • (45) Hours

  • (60) Hours

• Answer: A 15 cpm

1. Silver Isotope Count Rate Over Time

• A radioactive isotope of silver has a half-life of 20 minutes.

• A sample gives a count rate of 6400 counts per second at 9 am.

• Question: At what time will the count rate be about 200 counts per second?
  Solution

• 9am 9:20 am 9:40 am 10 am 10:20 am 10:40 am

1. A sample of bone from a living animal contains carbon-14. Its activity is 80 counts per minute. The half-life of carbon-14 is 5730 years. How old is an antler with activity of 20 counts per minute?

• Solution:

• 80 40 20

• = 2 Half lives = 2 x 5730 = 11460 Years

Review

• Understand what is carbon dating

• Understand how we can use carbon-14.

• Calculate the age of substances from the % of carbon-14 from graphs.

• Understand what objects can be carbon dated like this and why.

Radioactive Decay

• A radioactive substance decaying by gamma emission is placed in front of a detector.

Radioactive Elements Table

Detector Readings

• Plot the data points and draw a decay curve for this substance.

• Use the graph to find the half-life of this substance.

Half-Life Definition

• Explain the meaning of the term 'half-life'.

Applications of Radioactive Materials

1. Monitoring the thickness of aluminum sheet in a factory.

   • Choice:

   • Reason:

2. Monitoring internal organs in the body.

   • Choice:

   • Reason: