Module 8
1. Module 8
1.25. Module Summary/Assessment
Module 8—Nuclear Decay, Energy, and the Standard Model of the Atom
Module Summary
In this module you studied the following questions:
- Which components make up the nucleus of an atom and what keeps them from coming apart?
- What is meant by alpha and beta decay?
- How is the conservation of mass and energy applied to nuclear decay?
- What is a half-life? How does it relate to dating organic and inorganic material?
- Why are nuclear fission and fusion reactions so powerful?
- How is it possible to probe the subatomic world in search of the fundamental particles that make up protons and neutrons?
- Which subatomic particles make up the proton and neutron?
- How do the discovery of antimatter and subatomic particles inform the latest models concerning the structure of matter?
In Lesson 1 you saw that an ionizing smoke detector depends on the unstable americium-241 nucleus in order to detect smoke and save lives. The nucleus is very small but it makes up nearly the entire mass of the atom. It is composed of smaller particles called nucleons: protons and neutrons. With the positively charged protons, Coulomb’s law from Module 3: Lesson 2 shows that there is a very strong repulsive electrostatic force between the protons. However, the protons are held in the nucleus by the even stronger nuclear force that holds nucleons together; but it only works over the extremely short distances found in the nucleus of an atom. Most larger nuclei with more than 83 protons are unstable and will decay spontaneously into smaller nuclei. This natural change from one substance to another is called transmutation and it can produce alpha and beta particles.
- Alpha decay
is characterized by the emission of an alpha particle (helium nucleus) from the nucleus of the parent atom.
- Beta negative decay
is characterized by the emission of a beta negative (electron) and electron antineutrino from the nucleus of the parent atom.
- Beta positive decay
is characterized by the emission of a beta positive (positron) and neutrino from the nucleus of the parent atom.
In Lesson 2 you learned that the rate of radioactive decay is described by the half-life of the radioactive isotope. This can be observed and analyzed both graphically, with an exponential regression curve, and mathematically as 
. Due to the constant decay rate the age of some ancient organic and inorganic substances can be determined by using radioactive dating. Radioactive dating is based on using radioactive isotopes in a sample, such as carbon-14. By comparing the remaining amount of parent nuclei to the amount that was originally in the sample and the known half-life of the isotope, it is possible to determine an age accurately.
In Lesson 3 you examined how nuclear reactions release large amounts of energy by changing mass into energy, called binding energy, using the famous equation, E = mc2. Nuclear reactions occur to increase the binding energy per nucleon and make the nucleus more stable. Small amounts of binding energy are released by alpha and beta decays.
Scientists and engineers are interested in nuclear fission and fusion reactions due to their ability to control the release of huge amounts of binding energy. Nuclear fission is currently used in nuclear power plants. In the process of fission a nucleus with more than 120 nucleons splits into two or more smaller nuclei with greater binding energy per nucleon. Nuclear fusion power is still in its infancy, with a couple of experimental designs being tested. In the process of fusion, a nucleus with fewer than 60 nucleons combines with another to form a larger nucleus with greater binding energy per nucleon. Both reactions, however, have positive and negative aspects.
Lesson 4 showed you that current particle accelerators are some of the most powerful machines ever built, capable of causing particle collisions at energy concentrations never before seen on Earth. Enormous amounts of energy are required to overcome the large binding energy per nucleon caused by the strong nuclear force. Information is gathered in the form of scattering patterns and paths of the emitted particles to find evidence of what happened inside the nuclei of the target atoms.
Based on particle scattering and track research, the subatomic world is revealing that it is composed of many different particles that form the current standard model: antimatter such as the positron, mediating particles such as photons and gluons, quarks that make up protons and neutrons. There are others that are theoretical, but physicists hope to find experimental evidence of them with the LHC. As theoretical physicists make new predictions, experimental physicists look for evidence to prove or disprove predictions. As new evidence is discovered, the theoretical physicists update theories and make new predictions, which the experimental physicists attempt to confirm in the never-ending circle of the scientific method.
Module Assessment
Question 1
Use the following information to answer this analytic question.
The Sun produces energy through nuclear fusion. In one particular reaction, energy is released when a hydrogen-2 nucleus fuses with a hydrogen-3 nucleus. This produces a helium-5 nucleus that is unstable and that decays to a helium-4 nucleus and a neutron. The fusion reaction chain is
The masses of two of these particles are given in the following table.
| Particle | Isotope Notation | Mass (10-27 kg) |
| Helium-4 |  |
6.64884 |
| Neutron |  |
1.67493 |
The decay of helium-5 to helium-4 and a neutron forms an isolated system. In this system, the mass defect is observed as an increase in kinetic energy.
A helium-5 nucleus, at rest, decays. Both the neutron and the helium-4 nucleus move away from the location of the decay. The helium-4 nucleus has a momentum of 1.903 06 × 10–20 N•s and a kinetic energy of 2.723 50 × 10–14 J.
- Determine the mass of a helium-5 nucleus.
Marks will be awarded based on the physics principles you provide, the formulas you state, the substitutions you show, and your final answer.
Question 2
Use the following information to answer the next question.
Radioactive isotopes (radioisotopes) are extremely important for some medical tests and procedures. A common radioisotope used for medical imaging is technetium-99. Technetium-99 is used because it releases 140 keV gamma rays that are easily detected outside of the body and doesn’t damage surrounding tissue. It has a short half-life and the human body easily excretes its daughter products. The short half-life that makes it safe also means that the hospital needs a constant supply.
To solve this problem, scientists developed a technetium-99 generator from molybdenum-99, a by-product of spent nuclear reactor fuel. The molybdenum-99 needs replacing weekly instead of daily shipments of technetium-99. The generator starts with molybdenum-99, which decays into technetium-99, which can be separated by a relatively easy chemical process.
As a learning exercise, a medical student is asked to monitor the decay of a molybdenum-99 sample of 100 g over a week. The student measures the following values.
| Time |
Mass Remaining |
0 |
100 |
10 |
90 |
20 |
81 |
30 |
73 |
40 |
66 |
50 |
59 |
60 |
53 |
70 |
48 |
80 |
43 |
90 |
39 |
100 |
35 |
110 |
31 |
120 |
28 |
130 |
26 |
140 |
23 |
150 |
21 |
160 |
19 |
170 |
17 |
- Graph the information.
- What is the half-life of molybdenum? Explain how you determined the half-life.
- What is the decay equation for molybdenum-99 into technetium-99?
- The decay of technetium-99 releases a 140 keV gamma ray. How much mass is changed into energy to create the gamma ray?
