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Nuclear Energy: Classroom Activities

Understanding the Half-Life of a Radioactive Element


Goal

To develop a better understanding of the basics of radioactive decay.

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Background Information

When radioactive particles decay they spontaneously lose energy by emitting particles. As a result of this process, the nucleus of the original atom becomes the nucleus of a product atom. These are called parent and daughter generations. Certain radioactive particles breakdown because of natural instability in their nuclei. Unlike the nuclear fission process, they do not require bombardment with neutrons. However, the waste materials from nuclear fission are radioactive and continue to breakdown to form new isotopes. There are three main types of decay, called alpha, beta, and gamma emissions. The time it takes for half the mass of the nucleus of a radioactive atom to decay is called the half-life. Some atoms break down relatively quickly, e.g. lead 210 (22 years) while others breakdown very slowly and have long half-lives e.g. rubidium (48.8 billion years).

Subatomic particles
The loss of subatomic particles from a radioactive element creates parent and daughter atoms.
Source: Mark Carpenter

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Activity Overview

Students run a simple model of the decay of a radioactive nucleus by using coins placed within a circle on a sheet of paper. They start with all the coins facing heads up. Every 30 seconds they turnover half of the coins to face tails up. They draw a graph to show the mass of decayed and non-decayed atoms over time. Students gain a basic understanding of the decay of radioactive elements.

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Materials and Equipment

32 of the same type of coin (e.g. pennies), large sheet of paper, clock.

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Activity

  1. Provide students the following table:
    Time
    (min)
    Mineral Non-decayed
    (heads up)
    Decayed
    (tails up)
    # Fraction Mass
    (g)
    # Fraction Mass
    (g)
    0:00 Formation 32 3232   0 032 0
    0:30 Half the atoms decay            
    1:00 Another half decays            
    1:30 Another half decays            
    2:00 Another half decays            
    2:30 Another half decays            
  2. Discuss with your students the following: Different elements have different half-lives. Elements that have very long half-lives decay very slowly. For example, the radioactive element rubidium takes approximately 48.8 billion years to lose half of its mass. Elements like this, with very slow rates of decay, are good for determining the ages of very old rocks. Uranium 235 has a half-life of 704,000 years.
  3. Ask students to draw a large circle on a sheet of paper to represent a mineral rock. Use thirty-two coins to represent radioactive atoms in the mineral.
  4. Have students measure and record the mass of one coin. Have them calculate the mass of thirty-two coins.
    Answers will vary depending on the mass of the coins used.
  5. Ask students to place all of the coins facing heads up in the mineral.
  6. Instruct students to run the model by turning over half of the coins to face tails up every 30 seconds. Continue this process for a total of 2 minutes and 30 seconds. The tails up coins represent the atoms produced by radioactive decay. For each 30 second time period, they should complete the appropriate row in the table.
  7. Ask students to create a graph that shows and describes the following relationships:
    1. The mass of non-decayed atoms over time.
      Graphs will vary depending on the mass of the coins used.
    2. The mass of decayed atoms over time.
      Graphs will vary depending on the mass of the coins used.
  8. Have students use their tables and graphs to answer the following:
    1. What is the ratio of non-decayed atoms to decayed atoms at one and a half minutes after the rock was formed?
      4:28
    2. How does this compare to the ratio after two and a half minutes?
      1:31 is more than four times smaller (17 compared to 131)
  9. Ask students the following: how old is a mineral with a fraction of non-decayed to decayed atoms of 115 ?
    The ratio of non-decayed to decayed atoms is the same as 230 which occurs at 2:00 minutes.

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