Gold Seal Lesson:
Half-Life Nuclear Decay

Copernicus Education Gateway

 

Subject:

Science

Grade:

 

 

9-12

 

 

ICLE Standards:

 

 

Mathematics: Model real-world problems with a variety of functions. Represent and analyze relationships using tables, verbal rules, equations, and graphs.

Physical Science: Develop an understanding of structure and properties of matter.

 

 

Performance Task:

 

 

Cliff is an archaeologist for the U.S. Department of Agriculture. As part of his job he must survey and excavate possible sites of ancient inhabitants on federal properties slated for disturbance, such as a hiking trail through a National Forest. On several occasions he has uncovered what appears to be an Indian burial mound. Cliff must determine the age of the biological artifacts and often uses carbon dating. Carbon dating utilizes the fact that 1/2 of all carbon-14 isotopes decay by half every 5730 years.

This activity is a simulation of exponential decay where you will plot the half lives of carbon-14 isotopes represented by M&M candies and find the unknown time elapsed to get a given quantity of atoms, when 2n = number of half lives.

Materials needed:

  • Calculator

  • 50 pieces of M&M candy

  • graph paper

  • paper cups

  1. Place 50 pieces of M&M candies in a paper cup. Each M&M candy represents 1 atom of carbon.

  2. When the teacher gives the signal, remove 1/2 of the M&M candies and put them into another paper cup. Since the candy represents carbon-14, the removal of 1/2 of the pieces represents a time elapse of 5730 years.

  3. Record the years elapsed and the number of candies remaining in the chart below.

  4. Each time the teacher gives the signal, remove 1/2 of your candy pieces and record the number remaining along with the time elapses, which is calculated by adding 5730 years each time.
    Note to the teacher: Continue giving the signal until the time elapse is 28,650 years

  5. Construct a graph of the decay of carbon-14 by labeling the y-axis Atoms and the x-axis Time.

  6. What can you conclude from your graph?

  7. Predict the amount of time it will take 14 grams of Carbon 14 (6.02x1023 atoms) to decay to leave only 1.5 x 1023 by using the following procedure:

  1. Divide the original number of atoms by the remaining number of atoms to obtain a ratio of atoms.

  2. Determine the number of half-lives where n = number of half-lives and 2n = ratio of atoms found in "a". Use the log function n (log 2) = log (ratio found in "a") to solve for n.

  3. Calculate the amount of time passed:


Optional
Research the Shroud of Turin and write a position paper on the validity of carbon dating to determine its authenticity.

Note to the teacher: This activity has students simulate exponential decay using M&M candies. It can be used to demonstrate the connection between mathematics and physical science. Carbon dating is an application of exponential decay that is often used to date biological artifacts.

 

 

Knowledge / Skills:

 

 

Plan and apply real or hypothetical models and constructions to facilitate investigation and learning and the solution to practical problems.  (xs2)

Understand the technique of measuring geologic ages by absolute dating of rocks/fossils using known decay rates of radioactive isotopes.  (s95)

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions.  (m1)

Understand the best procedures for statistical data collection, organization, and display.  (m5)

Understand the use of variables in expressions such as 4x, x+2, and 2x-1, solve for the variable, and know how to represent expressions such as "twice the number" or "four more than the number" using variables.  (m7)

Gather information from a variety of sources, including electronic sources, and summarize, analyze, and evaluate its use for a report.  (ela3)

Use expository writing skills in subjects other than English language arts.  (ela58)

 

 

Rubric:

 

 

3 Points  =  The student can accurately record the number of atoms remaining and can accurately calculate and record the time intervals. His/her graph is accurate and neat and his/her paper demonstrates an understanding of the utilization of carbon dating and half-life concepts. All questions are answered correctly.

 

 

2 Points  =  The student has difficulty with the table and graphing, but is successful with some coaching. He/she needed assistance in answering the questions. The student's paper demonstrates an understanding of carbon dating and half-life concepts. His/her graph is accurate and complete.

 

 

1 Point  =  The student did no complete the assignment. The table was incomplete and the graph was improperly done. His/her paper demonstrates little understanding of carbon dating and half-life concepts. The questions were not answered accurately.

 

 

0 Points  =  The student did not complete the task and shows little, if any, understanding of the science or math concepts. Little effort was applied.

 

 

Keywords:

 

 

CHEMISTRY
CARBON
NUCLEAR CHEMISTRY                 
EARTH SCIENCE
EARTH
EARTH HISTORY

 

 

Grades:

 

 

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [X] - 10 [X] - 11 [X] - 12 [X]

 

 

ICLE Application:

 

 

D

 

 

 

 

 

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