Mathematical and Technological Literacy I Activity 3:  Radioisotope Dating

Please do the following at the beginning of every computer activity.

a. Open a new Word document.

b. Click on the Office Button in the upper left corner, then slide over "Save As".   Choose either "Word Document" to save your document as a Word 2007 document or "Word 97-2003 document" to save your document in an early version of Word.  If you are not sure which to choose, you should use "Word 97-2003 document".  Save the document to the desktop by setting the "Save in" textbox to "Desktop". (Saving to the desktop makes it easy to retrieve your work when you are finished.)  Your file name should be entitled something like "Group Activity 3".  Last, confirm the save as type in the last box.  (*.docx) is the suffix for a Word 2007 document.  (*.doc) is the suffix for early versions of Word.

Learning Goals for this Activity

1. You will learn about the essential characteristics of exponential decay.
2. You will learn to use logs to solve for time to reach a certain value.
3. You will be able to estimate the age of artifacts given the amount of a certain radioisotope with a known half life or decay rate.
4. You will understand the basic scientific concepts that underlay radioisotope dating.

1. Beryllium-11 is a radioactive isotope of the alkaline metal Beryllium.  Beryllium-11 decays at a rate of 4.9% every second. 

    a) Assuming you started with 100%, what percent of the beryllium-11 would be remaining after 10 seconds? Either copy and paste the table or show the equation used to answer the question. 

    b) How long would it take for half of the beryllium-11 to decay?  This time is called the half life.  (Use the "solve using logs" process to answer the question)  Show your work. 

2. Some of the most famous Cro-Magnon cave paintings are located in Lascaux, France. On the right is an image from Lascaux. Charcoal found in the cave has approximately 14% of the carbon 14 found in living wood. Carbon 14 decays approximately 1.202% every 100 years. a) Make a table in Excel that has in column A  years  in increments of 100 and in column B the percent of Carbon 14 remaining.  Use the table to approximate the age of the paintings.  (how long until there is only 14% of the original amount of Carbon 14 remaining?) b)  Now answer the same question using logs instead of a table.   Here you will need to define x as the number of 100 year increments--meaning x=3 would translate to 300 years.  Show your work.

Age of moon

3.  Rock samples brought back from the moon by Apollo astronauts have approximately 58% of the original amount of Uranium 238 present. Uranium decays at a rate of approximately 7.41% every 500 million years.  a) Make a table in Excel that has in column A million years after formation in increments of 500 and in column B the percent of Uranium 238 remaining.  Approximate how old the rocks are b)  Now answer the same question using logs instead of a table.  You will need to define x in the formula as the number of 500 million year increments--meaning if you get x=2, that would translate to 1000 million years.  Round your answer to the nearest million years.   Show your work c)  Use logs to find how many years since formation until there is only 20% of the Uranium remaining.  Show your work.  (To check the reasonability of your answer, use the spreadsheet you made in question 3a).