Module 8

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

 

Try This

 

TR 7. Using the neptunium decay series in the decay series diagram above, trace the decay from uranium-233 to francium-221. Write the nuclear equations that represent this series of transmutations.

 

The Release of Energy During Nuclear Decay

 

A significant amount of energy is released during transmutations, which is clearly evident from the kinetic energy of the released alpha or beta particle. Einstein developed the equation for mass-energy equivalency the famous E=mc2. During a transmutation, a small amount of mass is changed directly into energy. This can easily be shown by calculating the mass of a uranium-235 atom from its constituent parts.

 

 

Note: The mass of the electrons is insignificant compared to the nucleons and is normally omitted.

 

 

So from your calculations, the atomic mass of uranium-235 should be 236 u. If you look it up in “Table 7.5” on page 881 of the physics textbook, you will find that it is actually 235.043 930 u. Why is there a difference? Where did the lost mass go?

 

The lost mass is called the mass defect—the mass has been changed into binding energy holding the nucleons together. This mass defect is where the energy for nuclear reactions comes from and explains where the strong nuclear force to hold the atom together comes from.

 

The law of conservation of energy was violated by this discovery as energy appears to be created. Therefore, the law has been amended to the law of conservation of mass-energy, since Einsten showed that mass and energy are equivalent. In fact, particle physicists often don’t bother with masses but use mass equivalent as measured in MeV/c2.

 

Mass defect = mass products − mass reactants

 

It is possible to calculate the amount of energy released in a nuclear reaction by comparing the mass of the parent versus the daughter particles.

 

Einstein’s Mass–Energy Equivalence

E = mc2   Quantity Symbol SI Unit energy released in a nuclear reaction per decay E J not eV mass defect—the mass converted to energy in a nuclear reaction = mproducts – mreactants m kg speed of light in a vacuum c m/s

 

Example Problem 5. What is the energy released when americium-241 transmutes?

 

From earlier we know the equation:

 

 

 

The masses were obtained from NIST, National Institute of Standards and Technology.

 

 

The transmutation of one americium-241 atom releases 9.04 × 10–13 J.

 

Self-Check

 

SC 3. a. What is the beta-positive decay reaction for sodium-22?

 

b. What is the energy released by the beta-positive decay of sodium-22?

 

 

Try This

 

 TR 8. Complete “Practice Problems” 1 to 3 on page 801 of your physics textbook. The masses can be found in “Table 7.5” on page 881 of the textbook.

 

Read

 

Read “Conservation Laws and Radioactive Decay” on page 798 of the textbook for an overview of the laws obeyed in nuclear reactions.

 

Try This

 

TR 9. Complete “Practice Problem” 1.(b) on page 803 of your physics textbook. You have already completed 1.(a) as TR 6.

 

 

Discuss

 

Marie and Pierre Curie studied radioactivity before it was known to be dangerous to living systems. As a result both suffered from radiation sickness and some of Marie’s lab notebooks are still dangerously radioactive today. Radiation sickness was also well documented among the survivors of the Hiroshima nuclear bomb (dropped August 6, 1945) and the Chernobyl reactor explosion (April 26, 1986).

 

The potential hazards of nuclear radiation are now understood and we know that precautions must be taken to protect living tissue from damage caused by radiation.

 

Research radiation sickness related to both of these disasters. Also see pages 808 and 809 of the textbook for information required to answer the following questions in the discussion forum.

 

D 1. Answer the following questions on nuclear radiation:

• What is radiation sickness? How does radiation cause damage to living tissue? Use the following vocabulary in your response: ionization/ionize, and chromosomes/genetic material.
  
  
• Which type of radiation is most dangerous and why?
  
  
• Contrast ionizing and non-ionizing radiation. Include real-life applications of each type.
  
  
• How is radiation exposure measured? How much is deemed safe?
  
  
• Where else in this course have we seen forms of ionizing radiation?

D 2. Post your summary to the discussion area set up by your teacher. Compare your summary to at least one other explanation produced by another student. Identify similarities and differences between your work and the work of other students. Remember to add the answer to this question to your course folder.

 

Module 3: Lesson 1 Assignment

 

Remember to submit your answer to D 3 to your teacher as part of your Module 8: Lesson 1 Assignment.

 

D 3. If you were to update your questions on nuclear radiation based on what you learned in D 2, what changes would you make? Submit your revised summary and comments on the changes that you made to your instructor as part of your assignment.

 

Discussion Scoring Guide

 

Module 8: Lesson 1 Assignment

 

Remember to submit the Module 8: Lesson 1 Assignment to your teacher.

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