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Modeling Alpha and Beta Decay

A Carolina Essentials™ Activity

Overview

Students often use balanced nuclear reactions to model changes that occur in an unstable nucleus, but that doesn’t help students assess why the nucleus is unstable initially. In this activity, students use the band of stability and neutron-proton ratios to construct a simple predictive model to determine if an isotope will decay or not decay, and if the isotope does decay, whether the process is more likely to be alpha or beta decay. The activity does not address positron emission and gamma radiation.

Students calculate neutron-proton ratios for selected isotopes, determine if the isotope is stable or unstable, find the isotope’s location on the band of stability to determine decay type, and then write balanced nuclear equations for the isotopes that decay.

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Teacher Notes
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Student Worksheet
Grade & Discipline
9-12

Physical Science
Recommended for grades 9-12.

Time Requirements
Prep15 min
Activity45 min

Teacher Prep time: 15 min
Student Activity: 45 min

Safety Requirements
No PPE is required for the activity.

Overview

Students often use balanced nuclear reactions to model changes that occur in an unstable nucleus, but that doesn’t help students assess why the nucleus is unstable initially. In this activity, students use the band of stability and neutron-proton ratios to construct a simple predictive model to determine if an isotope will decay or not decay, and if the isotope does decay, whether the process is more likely to be alpha or beta decay. The activity does not address positron emission and gamma radiation.

Students calculate neutron-proton ratios for selected isotopes, determine if the isotope is stable or unstable, find the isotope’s location on the band of stability to determine decay type, and then write balanced nuclear equations for the isotopes that decay.

Save & Print
Teacher Notes
Save & Print
Student Worksheet

Phenomenon

side by side comparison of PET scan and MRI scan

Nuclear medicine is a branch of medicine that relies on the proper selection of radioactive isotopes to produce scans like those above and to treat many types of cancer. Why do you think nuclear decay can be a powerful and useful medical tool? Discuss responses with your students. Some students may have personal experience with diagnostic tools or treatment.

Essential Question

How can changes in the composition of the nucleus of an atom be predicted and modeled?

Activity Objectives

  1. Determine if an isotope is stable or unstable.
  2. Construct a model that predicts the type of nuclear decay expected for unstable nuclei.

Next Generation Science Standards* (NGSS)

HS-PS1-8. Develop models to illustrate the changes in the composition of the nucleus of the atom and the energy released during the process of fission, fusion, and radioactive decay.

Science and Engineering Practices

Developing and Using Models

  • Develop a model based on evidence to illustrate the relationships between systems or between components of a system.

Disciplinary Core Ideas

PS1.C: Nuclear Processes

  • Nuclear processes, including fusion, fission, and radioactive decays of unstable nuclei, involve release or absorption of energy. The total number of neutrons plus protons does not change in any nuclear process.

Crosscutting Concepts

Energy and Matter

  • In nuclear processes, atoms are not conserved, but the total number of protons plus neutrons is conserved.

Safety Procedures and Precautions

No PPE is required for the activity.

Teacher Preparation and Disposal

Copy the student pages or upload them to a class web page.

Student

Teacher

  1. Student: Calculate and record the number of neutrons and protons for all isotopes in the data table.
    Protons = atomic number (Z)
    Neutrons = isotope mass – atomic number
  1. Teacher: Review isotope notation with students so they recall that the top number is mass and the bottom number is charge (protons) for a block representation, and mass is the number following the element name in the long-hand notation.
  1. Calculate the neutron-proton ratio.
    Number of neutrons = x.xx or x.xx:1
    Number of protons 1
    Record the ratios in the data table.
  1. For this activity, round all calculations to 2 decimal places.
  1. Based on the background information about neutron-proton ratios and nuclear size, highlight the stable isotopes in the data table.
  1. Review the band of stability chart with students. Each small block represents a different isotope. Point out that isotopes of the same element may decay through different processes.
  1. Locate each isotope on the band of stability chart to confirm your decision about nuclear stability. For isotopes that decay, identify whether the nucleus decays by alpha or beta decay. Record the decay type in the chart.
  1. Remind students that a balanced nuclear equation shows conservation of charge and mass. The top numbers (mass) on both sides of the arrow must be equal, and the bottom numbers (charge) on both sides of the arrow must be equal. Use the charge to identify the daughter nuclide.
  1. For the isotopes that decay, write a balanced nuclear reaction.
  1. An interesting extension project is to assign students one of the imaging isotopes or treatment isotopes for additional research. Include how the isotope is made, how it is used or administered, and what specific diseases it is used to treat.

Data and Observations

Data Table

Isotope Neutrons Protons no: p+ Decay Type
Aluminum-27 14 13 1.08:1 Stable
Bromine - 82 47 35 1.34:1 Beta
Francium-211 124 87 1.43:1 Alpha
Iron-56 30 26 1.15:1 Stable
Lead-214 132 82 1.61:1 Beta
Platinum-175 97 78 1.24:1 Alpha
Iodine-131 78 53 1.47:1 Beta
Radium-226 138 88 1.57:1 Alpha
Silver-108 61 47 1.30:1 Stable
Carbon-14 8 6 1.33:1 Beta
Thorium- 234 144 90 1.60:1 Beta
Uranium-233 141 92 1.53:1 Alpha

Band of Stability

band of stability diagram

Source: Wikimedia Commons. Table isotopes en.svg.


Balanced Nuclear Equations

balanced nuclear equations

Analysis & Discussion

Construct a process diagram or flow chart that can be used to identify an isotope’s stability, and if unstable, how it will decay.

process diagram of an isotope's stability

Your teacher will assign you a medical isotope. Use your model to determine if the isotope is stable or unstable, and if unstable, how it will decay. Write the balanced nuclear equation for the decay of the isotope.

Student answers will vary. Use the chart from the National Isotope Development Center (NIDC) to assign elements, and check to see that students follow their flow charts.

*Next Generation Science Standards® is a registered trademark of Achieve. Neither Achieve nor the lead states and partners that developed the Next Generation Science Standards were involved in the production of, and do not endorse, these products.

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