1. Preview Section 1 The Nucleus Section 2 Nuclear Decay
Section 3 Nuclear Reactions
Section 4 Particle Physics

2. The student is expected to:
TEKS
5A research and describe the historical development of the concepts of gravitational, electromagnetic, weak nuclear, and strong nuclear forces
5H describe evidence for and effects of the strong and weak nuclear forces in nature
8C describe the significance of mass-energy equivalence and apply it in explanations of phenomena such as nuclear stability, fission, and fusion

3. What do you think? What holds a nucleus together?
What particles exist within the nucleus?
What force(s) exist between these particles?
Are these forces attractive or repulsive?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting students’ ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
Help students consider the electrical repulsion between protons and then ponder what might be holding the nucleus together.

4. The Nucleus
The chemical symbol for an element is written like the one shown to the left. What information is provided by this symbol?
The atomic number (Z) or number of protons is 13.
The mass number (A) or number of protons + neutrons is 27.
The number of neutrons (N) is 14 (27 – 13).
The element is aluminum.

5. Isotopes
Isotopes are atoms of the same element with different atomic masses.
The number of neutrons is different.
Most carbon nuclei have 6 protons and 6 neutrons and an atomic mass of 12.
Called carbon-12
Others have 5 neutrons (carbon-11), 7 neutrons (carbon-13), or 8 neutrons (carbon-14).
Be sure students understand that the number after the atom name is the number of nucleons, e.g. carbon-11 has 6 protons + 5 neutrons.

6. Isotopes
Click below to watch the Visual Concept.
Visual Concept

7. Nuclear Mass
The density of the nucleus is approximately 2.3  1017 kg/m3.
Mass is measured in unified mass units (u).
1 u is one-twelfth the mass of one atom of carbon-12.
1 u =  kg
Protons and neutrons each have a mass of approximately 1 u.

8. Nuclear Mass Find the energy equivalent of 1 u in both J and eV.
(For c, use the value  108 m/s.)
Answers:
 J,  106 eV or MeV
With more significant figures, 1 u = MeV.
The mass of subatomic particles is often expressed in MeV.
E = mc2 = (  kg)(  108 m/s)2 =  J
Since 1 eV =  J, this also equals  106 eV.

9. Nuclear Mass
This table provides the mass and rest energy of atomic particles in kilograms, unified mass units, and MeV.

10. Nuclear Stability
What type of electric force would exist in the nucleus shown?
Protons would repel other protons very strongly because the distance between them is small.
Neutrons would produce no forces.
What holds the nucleus together?
A force called the strong force:
a powerful attractive force between all particles in the nucleus
Does not depend on charge
Exists only over a very short range
The strong force is an attractive force between protons and protons, protons and neutrons, and neutrons and neutrons. It exists only when the particles are very tightly packed, as in the nucleus, and is zero when they are farther apart.

11. Nuclear Stability
As more protons are added to the nucleus, more repulsion exists.
Larger and larger nuclei require more neutrons, and more strong force, to maintain stability.
Look at a periodic table to find out which elements have approximately a 1:1 ratio between neutrons and protons, and which elements have the highest ratio of neutrons to protons.
Lighter elements have approximately equal numbers. Heavier elements such as lead have have nearly 1.5:1 rations of neutrons to protons. (This is shown visually on the graph on the next slide.) Emphasize that more neutrons are needed to help stabilize the nucleus. Be sure students understand why this is the case. (The repulsive force exists between all protons in the nucleus because the electrostatic force is long range. The strong force is very short range; it only exists between neighboring particles. As the number of protons increases, the number of neutrons has to increase even more to add enough attractive force to maintain stability.)

12. This graph has a dot for each nucleus that is stable
This graph has a dot for each nucleus that is stable. It also has a reference line (red) showing where the ratio between neutrons and protons is 1:1.
Point out the following:
Heavier elements require more neutrons than protons for stability.
Lighter elements have nearly a 1:1 ratio.
No nuclei greater than Z = 83 (Bismuth) are stable. They are radioactive and will decay. (Nuclear decay is covered in the next section of this chapter.)

13. Nuclear Stability and Ratio of Neutrons and Protons
Click below to watch the Visual Concept.
Visual Concept

14. Binding Energy
The nucleons (protons and neutrons) have a greater mass when unbound than they do after binding to form a nucleus.
Called binding energy
This energy is released when the binding occurs, and must be absorbed to separate the nucleons.
Mass defect is the difference between the unbound mass of the neutrons, protons, and electrons and the final mass of the atom after binding has occurred.

15. Classroom Practice Problem
The mass of the individual particles in an atom is the mass of the protons, neutrons, and electrons.
For the mass of the protons and electrons combined, simply multiply the atomic number times the mass of a hydrogen atom (1 electron bound to 1 proton).
Find the binding energy (in u and MeV) for a helium atom with two protons and two neutrons. The atomic mass of helium-4 is u.
Answer: u or MeV
For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow students some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful.
The mass defect is (2 hydrogen atoms + 2 neutrons) - (helium-4) or [(2)( u) + (2)( u)] u = u.
This is equivalent to ( u)( MeV/u) = MeV.

16. Now what do you think? What holds a nucleus together?
What particles exist within the nucleus?
What forces exist between these particles?
Are these forces attractive or repulsive?
What happens to each of these forces when the particles are farther and farther apart?
What is meant by the term binding energy?
The strong force attracts the nucleons to each other while the electric force is pushing the protons apart. The strong force only exists for particles very close to each other and becomes zero when they are separated. The electric force is an inverse square relationship with distance.
Binding energy is the energy required to separate an atom into its constituent parts.

17. The student is expected to:
TEKS
8D give examples of applications of atomic and nuclear phenomena such as radiation therapy, diagnostic imaging, and nuclear power and examples of applications of quantum phenomena such as digital cameras

18. What do you think?
Often scientists use radioactive carbon dating to determine the age of fossils.
What does the term radioactive mean?
Are all atoms radioactive?
If not, how are radioactive atoms different from those that are not radioactive?
How can radioactivity be used to determine the age of a fossil?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting students’ ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
Students may have heard of carbon dating or radioactive dating as a method for determining the age of fossils. Try to find out what they know and understand about radioactivity in general.

19. Nuclear Decay
When nuclei are unstable, particles and photons are emitted.
The process is called radioactivity.
It occurs because the nucleus has too many or too few neutrons.
Three types of radiation can occur:
Alpha
Beta
Gamma

20. Alpha Decay ()
An alpha particle (2 protons and 2 neutrons) is emitted from the nucleus.
 particles are helium-4 nuclei.
A new element is formed by alpha decay.
Example of alpha decay:
The uranium atom has changed into a thorium atom by ejecting an alpha particle.

21. Radioactive Decay
These rules are used to determine the daughter nucleus when a parent nucleus decays.
Note how these rules apply in the alpha decay of uranium-238:
238 =
92 =

22. Beta Decay An electron or positron is emitted from the nucleus.
A positron is the same as an electron but with an opposite charge.
A positron is the antiparticle of an electron.
Since there are no electrons or positrons in the nucleus, how can beta decay occur?
A neutron is transformed into a proton and an electron, and then the electron is ejected.
A proton is transformed into a positron and a neutron, and then the positron is ejected.

23. Beta Decay
It was discovered that, during beta decay, momentum and energy were not conserved.
The ejected electron did not have as much forward momentum as the recoiling nucleus.
In 1930, Wolfgang Pauli proposed the existence of a particle that was not detectable at the time.
In 1956, Pauli’s neutrino () was detected.
The neutrino and its antiparticle, the antrineutrino (), are emitted during beta decay.
Electrons are accompanied by antineutrinos.
Positrons are accompanied by neutrinos.
Explain that when the neutrino or antineutrino are taken into account, energy and momentum are conserved during beta decay.
The neutrino provides a good example of a theoretical scientific prediction that was not demonstrated experimentally until a later date. (Many scientists did not accept Pauli’s proposal until the experimental evidence confirmed it.) A similar example is the discovery of electromagnetic waves, which were predicted theoretically by James Clerk Maxwell in 1864 and then discovered experimentally by Heinrich Hertz in 1887.

24. Beta Decay What new element is formed by the beta decay of carbon-14?
The new element is nitrogen-14.
The electron is shown with a mass number of zero and an atomic number of -1.
The total of the mass numbers and atomic numbers are still equal.
Point out that the decay of carbon-14 includes an antineutrino because this particle always accompanies the electron.

25. Gamma Decay
During alpha and beta decay, the nucleons left behind are often in an excited state.
When returning to ground state, the nucleus emits electromagnetic radiation in the form of a gamma ray.
The nucleus remains unchanged except for its energy state.

26. Types of Radioactive Decay

27. Alpha, Beta, and Gamma Radiation
Click below to watch the Visual Concept.
Visual Concept

28. Nuclear Decay Series
During nuclear decay, the daughter may be unstable as well, causing further decays.
What element would be formed by thorium-232 undergoing 6 alpha and 4 beta decays?
Answer: lead-208
Ask students to spend a few moments finding the result of the 10 decays. The order of the decays is not important at this time. It will be shown on the next slide.

29. Point out that the thorium-232 starts out far from the stability curve and must undergo many steps in order to reach the lead-208 position and be stable.

30. Classroom Practice Problems
Find the missing item (X) in these reactions:
Answer:
For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow students some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful.
Help students apply the rules about mass number and atomic number to determine the answers. After you show them how the first problem is solved, let them move on to the second problem.
Also ask students which type of decay each equation describes. (The first is beta decay; the second is alpha decay.)

31. Measuring Nuclear Decay
The rate of decay is different for each nucleus.
N/t = -N
N is the number of nuclei, t is the time, and  is the decay constant.
 differs for every element.
The rate of decay is called the activity.
The negative sign occurs because the number of nuclei is decreasing.
SI unit: becquerel (Bq) or decays/s

32. Half-Life
Half life is the time required for half of the nuclei to decay.
Half-lives can be very short (nanoseconds) or very long (millions of years).
Half-life is inversely related to the decay constant.
The equation is derived using calculus and involves the natural log of 2 (0.693).

33. Half-Life Carbon-14 is radioactive with a half-life of 5715 years.
The figure shows a decay curve for carbon-14.
Does the total number of nuclei change? No
How much time has passed at T1/2?
5715 years
How much time has passed at 2T1/2?
years
How many blue circles will there be at 3T1/2 ?
one

34. Radioactive Carbon Dating
All living things have about the same ratio of carbon-14 to carbon-12.
Carbon-14 is radioactive, and carbon-12 is not.
After death, the ratio drops because the carbon-14 decays into nitrogen-14, while the carbon-12 is stable and remains.
When the ratio is half the starting ratio, 5715 years have passed since death occurred.
The ratio of carbon-14 to carbon-12 is about 1.3 to 1 trillion. Carbon-14 represents a very small fraction of the carbon present in living things.
Emphasize that carbon-12 does not change in the body because it is not radioactive; only the carbon-14 decays (and thus the ratio between the two changes). This method of dating only works for living organisms.

35. Classroom Practice Problems
A sample of barium-144 contains  10 9 atoms. The half-life is about 12 s.
What is the decay constant of barium-144?
How many atoms would remain after 12 s?
How many atoms would remain after 24 s?
How many atoms would remain after 36 s?
Answers:
0.058 s-1
2.5  109 atoms, 1.2  109 atoms, 6.2  108 atoms

36. Half-Life
Click below to watch the Visual Concept.
Visual Concept

37. Now what do you think?
Often scientists use radioactive carbon dating to determine the age of fossils.
What does the term radioactive mean?
Are all atoms radioactive?
If not, how are the radioactive atoms different from those that are not radioactive?
How can radioactivity be used to determine the age of a fossil?
Radioactive means that an unstable nucleus emits particles or energy due to its instability. Many atoms are stable due to the right proportion of protons and neutrons (and thus are not radioactive). Remind students that, as seen in the last section, all atoms with more than 83 protons are unstable.
Carbon dating measures the amount of carbon-14 remaining in once-living things and uses the half-life to determine the time of death.

38. The student is expected to:
TEKS
8C describe the significance of mass-energy equivalence and apply it in explanations of phenomena such as nuclear stability, fission, and fusion
8D give examples of applications of atomic and nuclear phenomena such as radiation therapy, diagnostic imaging, and nuclear power and examples of applications of quantum phenomena such as digital cameras

39. What do you think?
Nuclear power and nuclear weapons are important and frequently-discussed issues in the world today.
How does a nuclear reactor produce energy?
What is nuclear about it?
What problems are associated with nuclear power?
Do atomic bombs and hydrogen bombs differ in the way they produce energy?
If so, how are they different?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting students’ ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
Find out what knowledge the students bring with them about nuclear power and nuclear weapons. Check the depth of their knowledge by asking questions about why these energy sources use the term “nuclear.”

40. Nuclear Changes
For nuclear changes to occur naturally, energy must be released.
Binding energy must increase.
Lighter elements must combine, and heavier elements must reduce in size.
The greatest stability is for atoms with mass numbers between 50 and 60.

41. Fission
Fission occurs when a large nucleus absorbs a neutron and splits into two or more smaller nuclei.
Example of fission:
It only occurs for heavy atoms.
The * indicates an an unstable state that lasts for about a trillionth of a second.
X and Y can be different combinations of atoms that have a total atomic number of 92.

42. Fission A typical fission reaction is shown above.
The products, Ba and Kr, have more binding energy than the uranium.
As a result, energy is released.
Each fission yields about 100 million times the energy released when burning a molecule of gasoline.
Note that the sum of the mass numbers and atomic numbers is the same on each side of the equation.

43. Chain Reaction
On the average, 2.5 neutrons are released with each fission.
These neutrons are then absorbed and cause more fissions.
A chain reaction occurs.

44. Nuclear Fission Click below to watch the Visual Concept.

45. Nuclear Reactors
Reactors manage the fission rate by inserting control rods to absorb some of the neutrons.
Nuclear power plants and navy vessels use fission reactions as an energy source.
Reactors produce radioactive waste, and disposal is one difficulty.
Presently 20% of the U.S. electric power is generated by nuclear reactors.
Atomic bombs use uncontrolled fission.
The PhET web site has a simulation that may be useful at this time.
Choose “Simulations,” then choose ““Quantum Phenomena,” and then choose “Nuclear Physics.”
This simulation allows the user to observe fission, chain reactions, and a nuclear reactor.

46. Fusion Light elements can combine and release energy as well.
Hydrogen atoms have less binding energy per nucleon than helium atoms.
Fusion is the source of a star’s energy.
Hydrogen atoms fuse to form helium atoms.
Much energy is released with each fusion.
Hydrogen bombs use uncontrolled fusion.
First tested in 1952 but never used in war

47. Fusion as an Energy Source
Fusion reactors are being developed.
Advantages of fusion reactors:
The fuel source, hydrogen from water, is cheap.
The products of fusion are clean and are not radioactive.
Disadvantages of fusion:
It requires extremely high temperatures of roughly 108 K to force atoms to fuse.
It is difficult to keep the hydrogen atoms contained at this temperature.

48. Nuclear Fusion
Click below to watch the Visual Concept.
Visual Concept

49. Now what do you think?
Nuclear power and nuclear weapons are important and frequently-discussed issues in the world today.
How does a nuclear reactor produce energy?
What is nuclear about it?
What problems are associated with nuclear power?
Do atomic bombs and hydrogen bombs differ in the way they produce energy?
If so, how are they different?
Nuclear reactors use fission. They split nuclei with neutrons to produce energy. The byproducts are generally radioactive and have very long half-lives, so disposal of spent fuel and other waste is difficult.
Atomic bombs and hydrogen bombs both use nuclear reactions to produce huge amounts of energy. Atomic bombs use fission, and hydrogen bombs use fusion.

50. The student is expected to:
TEKS
5A research and describe the historical development of the concepts of gravitational, electromagnetic, weak nuclear, and strong nuclear forces
5H describe evidence for and effects of the strong and weak nuclear forces in nature

51. What do you think?
When the idea of the atom was first conceived, it was thought to be a fundamental particle, indivisible and indestructible. We now know differently.
List every particle you can think of that is smaller than an atom.
If you know the properties of these particles, list them as well.
Which of the particles on your list are fundamental?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting students’ ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
Students should know the basic particles but will probably not realize how many other particles there are. Students have probably heard of quarks but may not understand what they are. After students have listed their particles, point out that there could have been over 300 particles on the list. They might believe that all of the particles on their list (such as protons and neutrons) are fundamental.

52. Fundamental Forces
There are four fundamental interactions or forces in nature:
strong
electromagnetic
weak
gravitational
They exert force using the exchange of mediating particles.
Photons are the mediating particle exchanged between electrons.
This causes repulsion.

53. Fundamental Forces Strong force Electromagnetic force Weak force
Holds protons and neutrons together in the nucleus
Electromagnetic force
Creates forces between charged particles
Holds atoms and molecules together
Weak force
A nuclear force that controls radioactive decay
Gravitational force
The weakest force
Gravitons (the mediating particle) not yet discovered
Ask students: Which force holds the solar system or galaxy together? (gravitational)
Which force is acting when we pick up a book? (electromagnetic force between molecules in our fingers and molecules in the book)

54. Fundamental Forces Remind students that 1 fm is 10-15 m.
The strong force holds neutrons and protons together in the nucleus.
The electromagnetic force is responsible for the forces between charges, and holds atoms and molecules together.

55. Classification of Particles
All particles are classified as leptons, hadrons, or mediating particles.
Over 300 particles are known.
Leptons are thought to be fundamental.
Electrons are leptons.

56. Classification of Particles
Hadrons are composed of smaller particles called quarks.
Quarks are thought to be fundamental.
Protons and neutrons are hadrons.
Two types of hadrons: baryons and mesons
Hadrons interact through all four of the fundamental forces, while leptons do not participate in strong force interactions.
Baryons and mesons are distinguished by their internal structure, as shown on slides 8 and 9. The next slide lists the names and charges of the quarks and antiquarks.

57. There are 6 quarks and their respective antiquarks
There are 6 quarks and their respective antiquarks. They differ in mass and charge. Protons and neutrons are composed of up and down quarks.

58. Classification of Particles
Protons and neutrons are baryons.
What combination of up and down quarks would make a proton and a neutron?
Two up quarks (+4/3) and one down quark (-1/3) gives a proton a charge of +1.
One up quark (+2/3) and two down quarks (-2/3) gives a neutron a charge of zero.
You may need to go back to the previous slide to show students the charges of the quarks. They can also refer to the table in their textbooks.

59. Combinations of Quarks
Baryons and mesons are distinguished by their internal structure.
The particles above are a proton, a neutron, a pion, and a kaon.
Mesons are unstable, and are not constituents of everyday matter.

60. The Standard Model of Particle Physics
Click below to watch the Visual Concept.
Visual Concept

61. The Standard Model
The Standard Model is the current model used in particle physics.
How many fundamental particles are there in the standard model?
Six quarks, six leptons, and an antiparticle for each (24 total)
This diagram summarizes much of the material from this section. The four fundamental forces are on the left, each with its own mediating particle. Matter made of quarks participates in all four interactions, while leptons do not participate in the strong interaction. In addition to the electron, the other leptons in the chart are the muon, the tau, and a neutrino associated with each. Each particle shown on the right also has an antiparticle.

62. Evolution of the Four Forces
This diagram shows the evolution of the four forces. Scientists believe that when the universe began, there was only one force. They have discovered the “electroweak” force.

63. Quarks and their Charges
Click below to watch the Visual Concept.
Visual Concept

64. Now what do you think?
When the idea of the atom was first conceived, it was thought to be a fundamental particle, indivisible and indestructible. We now know differently.
List every particle you can think of that is smaller than an atom.
If you know the properties of these particles, list them as well.
Which of the particles on your list are fundamental?
What are the four fundamental forces and what particle mediates each?
Answers are available on the standard model chart (slide 11). Remind students that there are still many open questions in particle physics, and encourage them to explore these topics further.