1. Module 8

1.12. Page 3

Lesson 2

Module 8—Nuclear Decay, Energy, and the Standard Model of the Atom

 

Try This

 

TR 1. Complete “Practice Problem” 2 on page 813 of the textbook.

 

TR 2. Complete “Practice Problems” 1 and 2 on page 814 of the textbook.

 

Radioactive Dating

 

Using nuclear decay to determine age is only possible because radioactive decay is a predictable process. It can be used to determine the age of rocks, fossils, and artifacts. This method is called radiometric dating.

 

Module 8: Lesson 1 Assignment

 

Remember to submit your answer to LAB 8 to your teacher as part of your Module 8: Lesson 1 Assignment. 

 

Open the Half-life simulation again.

 

LAB 8. On the drop-down menus, select “Isotope A” and “Theoretical decay.” Set the number of atoms to 128 and click play.

  1. According to the graph, what is the approximate half-life of isotope A?

  2. Select the “TABLE” tab. According to the data table, what is the exact half-life of isotope A?

  3. Suppose you analyzed a sample of isotope A that contained 25 radioactive isotope A atoms and 103 stable daughter atoms. Approximately how old is the sample?

  4. About how old is a sample of isotope A with 75 radioactive atoms and 53 daughter atoms?

  5. Click reset. Change the number of atoms to 50 and click play. Does this change the half-life of isotope A? Confirm this by experimenting with other starting numbers. Does this mean that radioactive dating does not depend on the amount of radioactive nuclei at the start? Explain.

Summary

 

The isotopes that are useful for measuring the age of rocks and fossils have very long half-lives. As previously mentioned, the carbon-14 used to date organic material has a half-life of 5730 years, while uranium-235, used to date rocks, has a half-life of 704 million years.

 

Module 8: Lesson 1 Assignment

 

Remember to submit the answer to LAB 9 as part of your Module 8: Lesson 1 Assignment to your teacher for marks. 

 

Open the Half-life simulation again.

 

LAB 9. Set the number of atoms to 100 and check that “Isotope B” and “Theoretical decay” are selected. Click play and view the results on the “GRAPH” tab. To model how scientists might date an artifact, imagine that the y-axis represents the percentage of radioactive atoms and that each second on the x-axis represents 1000 years. Assume this is true.

  1. What is the age of an artifact with 50% radioactive atoms of isotope B?

  2. What is the estimated age of a sample with 25% radioactive atoms of isotope B? 12%? 6%?

  3. About how old is a sample with 72% radioactive atoms of isotope B?
Read

 

Read “Radioactive Decay Rates” on pages 811 to 816 of your physics textbook.

 

Self-Check

 

SC 1. The half-life of strontium-90 is 28 years. If 60 g of strontium-90 is currently in a sample of soil, how much will be in the soil in 84 years?

 

SC 2. The half-life of strontium-90 is 28 years. If 100 g of strontium-90 is currently in a sample of soil, how much will be in the soil in 65 years?

 

SC 3. Tritium (hydrogen-3), a by-product of the CANDU nuclear power reactor, has a half-life of 12.3 years. How much time is required for its radioactivity to reach 1/4 its original level?

 

Check your work.
Self-Check Answers

 

Contact your teacher if your answers vary significantly from the answers provided here.

 

SC 1.

 

Given

 

 

Note: a or y are acceptable units for years.

 

Required

 

the remaining amount of strontium-90 in 84 years

 

Analysis and Solution

 

Determine the number of half-lives in 84 years.



Determine the remaining amount of strontium-90.

 

Paraphrase

 

The amount of strontium-90 remaining in the soil in 84 years is 7.5 g.

 

SC 2.

 

Given

 

 

Required

 

the remaining amount of strontium-90 in 65 years

 

Analysis and Solution

 

Determine the number of elapsed half-lives in 65 years.



Determine the amount of remaining strontium-90.

 

 

Paraphrase

 

The amount of strontium-90 remaining in the soil in 65 years is 21 g.

 

SC 3.

There are two ways of solving this question.

 

Method 1: How many ½ are there in ¼?

 

 

Therefore, two half-lives have passed.

 

 

The elapsed time is 24.6 years.

 

Method 2: Logarithms

 

This method is optional. If you have seen logarithms in math class, you can use them here. In Physics 30 all questions like this should have whole-number answers for the number of half-lives.

 

 

 

Determine the time for two half-lives.

 

 

Paraphrase

 

The elapsed time is 24.6 years.