Module 8

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

 

Module Introduction

 

In this module you will explore the nuclear world all the way down to the quarks that compose protons and neutrons. You will begin this journey at the edge of the nucleus by first understanding its composition and the forces that keep it together, as well as the energy that is associated with its decay and stability. These processes are applied in ionizing smoke detectors and radiometric dating.

 

Fission and fusion will be compared and contrasted in terms of changes to the number and type of nucleons that compose both parent and daughter material. They will also be described in terms of the large amount of energy associated with both reactions.

 

Next you will see how it is possible to probe the subatomic world in search of the fundamental particles that make up all of the subatomic particles, such as the proton and neutron. You will see how these investigations into antimatter, mediating particles, and quarks continue to inform the standard model, which describes current theory and models about the relationship between the fundamental forces and mediating particles. Your exploration will end, however, before the finish line as technology, theory, and model continue to evolve with new insight and evidence still being gathered in highly energetic laboratories around the world.

 

Specifically, you will be asked to apply your knowledge to answer the following questions:

• What is our current understanding of the atom?
  
  

• How do models, such as the standard model, evolve as new evidence and technology are applied at the atomic and subatomic levels?    

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Big Picture

 

The question marks on the balls in this photo represent the unknown. What do you suppose is inside each of them? How could you find out?

 

Now imagine they are so small that you can’t even see them with an electron microscope, never mind an optical one. Imagine they are held together by the strongest fundamental force in the universe, yet sometimes they spontaneously break down into smaller balls.

 

To study how they are arranged, you shoot other small balls at them and see how they scatter. Then you investigate the results when the balls spontaneously break down into smaller pieces. You apply this understanding to developing new and innovative technologies that can save lives, identify unknown chemicals, and generate enormous amounts of power.

 

The balls can be split apart and they can be fused together; and every ball has an opposite twin, what we would call its anti-ball. If any ball should ever meet its anti-ball, they would both be annihilated, releasing large amounts of energy.

 

With collisions of sufficient energy, the balls can be smashed open, revealing the inner particles. These inner particles can then be smashed again and again using higher and higher energy collisions to release the increasingly smaller, fundamental particles held together by incredible forces.

 

Along the way, theories and models evolve as you try to understand the composition of the balls and the fundamental forces that interact with them. Yet the question mark remains, symbolizing that you are still unable to verify all the parts in a theory that tries to capture the relationship between the fundamental particles of matter and the fundamental forces (such as gravity) that extend throughout the universe.

 

If you have not put it together already, the yellow balls represent atoms that are held together by a strong nuclear force. Atoms undergo alpha and beta decay and can release enormous amounts of energy when they split apart or fuse together. The regular matter that makes up these atoms is matched by antimatter, which will annihilate them if they meet. Massive particle accelerators are used to smash them, revealing protons that can be smashed again, revealing the fundamental quarks that make up hundreds of subatomic particles.

 

More experimentation and theory suggest the presence of other mediating particles thought to carry the fundamental forces, such as gravity and electromagnetism. Some of these particles have been observed, others have not; but, together, they all contribute to the ongoing investigation and understanding of what makes up matter.

 

By the end of Module 8 you will be able to describe the investigations and evidence that are part of the ongoing development of theories and models related to the fundamental structure of matter. As you are working in Module 8, you will explore the developing models of the atom in the context of the following questions.

• Which components make up the nucleus of an atom and what keeps them from coming apart?
  
  

• What are alpha and beta decay? How do they relate to the conservation of mass and energy?
  
  

• What is half-life and 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?
  
  

• How does the discovery of antimatter and subatomic particles inform the latest models concerning the structure of matter?

Module Assessment

 

Each lesson has a teacher-marked assignment, based on work completed in the lesson. In addition, you will be graded on your contributions to the Discuss section of each lesson.

 

You will also be asked to complete Self-Check or Try This questions, which you should place in your Physics 30 course folder. These are not formally assessed but are a valuable way to practise the concepts and skills of the lesson. These activities can provide you with reflective feedback on your understanding of the lesson work.

 

You will be marked for your lesson work on the following items:

• Module 8: Lesson 1 Assignment

• Module 8: Lesson 2 Assignment

• Module 8: Lesson 3 Assignment

• Module 8: Lesson 4 Assignment

At the end of the module you will complete a module assessment that consists of two Diploma Exam-style written-response questions. The first question will assess your ability to apply the principles of conservation of mass-energy and conservation of momentum to a fusion reaction and the second question will assess your knowledge of decay curves and half-lives of radioactive elements. See the Module Summary and Assessment page for more information. If you have any questions contact your teacher.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

In This Module

 

Lesson 1—The Nucleus and Radioactive Decay

 

In this lesson you will explore the nucleus and the process of decay in technologies such as the ionizing smoke detector.

• What components make up the nucleus of an atom and what keeps them from coming apart?
  

• What are alpha and beta decay?
  

• How is the conservation of energy and mass applied to nuclear decay?

Lesson 2—Decay Rates and Radioactive Dating

 

In this lesson you will explore the concepts of half-lives and the rate of decay in relation to dating rocks and organic material.

• What is a half-life?
  

• How are half-lives used to determine age?

Lesson 3—Fission and Fusion

 

In this lesson you will compare and contrast the characteristics of fission and fusion reactions in the context of power generation and research.

• Why do nuclear reactions release so much energy?
  

• What is nuclear fission?
  

• What is nuclear fusion?

Lesson 4—The Subatomic World

 

In this lesson you will learn about ongoing developments that inform the standard model for the structure of matter.

• How is it possible to probe the subatomic world?
  

• 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?

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Lesson 1—The Nucleus and Radioactive Decay

 

Get Focused

 

The typical household ionizing smoke detector uses nuclear reactions to detect smoke in the air. Inside such a detector is a small amount of radioactive americium-241. During normal operation, the large nucleus of this isotope spontaneously emits alpha particles, which ionize the air molecules between two charged plates generating a constant current. When smoke particles enter the detector, they prevent the alpha particles from ionizing the air and the current drops, triggering the alarm circuit and audible noise to warn anybody nearby.

 

The amount of radioactive material in an ionizing smoke detector is very small. This makes it safe for prolonged household use. However, manufacturers recommend that they be replaced every 10 years because the radioactive material operating the detector will eventually be depleted. Radioactive materials, such as americium-241, naturally break down, or decay, leaving a smaller nucleus as alpha particles and gamma radiation are emitted. Why does this happen? What makes a nucleus unstable enough to break down and emit smaller particles?

 

In this lesson you will answer the following essential questions:

• Which components make up the nucleus of an atom and what keeps them from coming apart?

• What are alpha and beta decay?

• How is the conservation of energy and mass applied to nuclear decay?

Module 8: Lesson 1 Assignment

 

Your teacher-marked Module 8: Lesson 1 Assignment requires you to submit responses to the following:

• Lab—LAB 1, LAB 2, LAB 3, and LAB 4

• Reflect and Connect—RC 1, RC 2, RC 3, RC 4, RC 5, RC 6, and RC 7

• Discuss—D 3

The other questions in this lesson are not marked by the teacher; however, you should still answer these questions. The Self-Check and Try This questions are placed in this lesson to help you review important information and build key concepts that may be applied in future lessons.

 

After a discussion with your teacher, you must decide what to do with the questions that are not part of your assignment. For example, you may decide to submit to your teacher the responses to Try This questions that are not marked. You should record the answers to all the questions in this lesson and place those answers in your course folder.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Explore

 

The Nucleus

 

What's in the nucleus of the atom? Recall from Module 7: Lesson 3 that the nucleus is very small compared to the entire volume of the atom. This fact was confirmed by Rutherford in his alpha particle scattering experiments. The nucleus is only about 10−14 m across, while the entire atom may be as much as 10 000 times wider. Even though it is very small, the nucleus makes up almost the entire mass of the atom. The large particles found inside the nucleus are called nucleons.

 

There are two types of nucleons: protons and neutrons. Protons carry a charge of +1; neutrons have no net charge. In a neutral atom, the number of protons is always balanced by the number of electrons. An ion is created when there is an unequal number of protons and electrons, producing a net positive or negative charge.

 

The Periodic Table

 

The periodic table provides important reference information on each element. The periodic table is ordered by atomic number, the number of protons in the nucleus. An element is uniquely determined by the number of protons it has—an atom with 92 protons is uranium, regardless of the number of neutrons or electrons present. If protons are added or taken away, the element is no longer uranium.

 

The number of neutrons in a nucleus is not given on the periodic table, although the atomic mass can be used to calculate the number of neutrons in the most common isotopes. The number of electrons in an atom is equal to the number of protons and is important for chemists. The number of electrons is important for beta-positive decay.

 

In previous science courses you used the periodic table to calculate how many of each type of nucleon was in the nucleus. For example, the atomic mass of sodium, which is 22.99, was rounded to 23—the total number of nucleons. Because sodium has 11 protons (the atomic number), it must have 12 neutrons to add up to an atomic mass of 23.

 

The atomic mass number is the number of nucleons in the nucleus. If the atomic mass number of sodium is 23, why is the atomic mass on the periodic table 22.99?

 

Isotopes

 

Different atoms of the same element may have different numbers of neutrons and therefore different atomic masses. Uranium nuclei, for example, have various masses due to variations in the number of neutrons. The various masses are called isotopes. Hydrogen exists in three isotopes, with the nuclei having zero, one, or two neutrons. There are many isotopes of uranium. The atomic mass value listed on the periodic table is the mean atomic mass of the element that is abundant in nature, which is the value used by chemists who deal with large numbers of atoms at a time. Physicists tend to deal with individual atoms so the isotope’s atomic mass is indicated as a number after the element’s name. For example, look at the following table.

 

Isotope	Name	Atomic Mass	Number of Protons	Number of Neutrons
H-1	Hydrogen 1	1	1	0
H-2	Hydrogen 2 (deuterium)	2	1	1
H-3	Hydrogen 3 (tritium) unstable	3	1	2

 

Isotopes of one element all have the same chemical properties, since they have the same number of protons. The nuclear stabilities may differ dramatically, however. Lead, for example, has 35 isotopes, only four of which are stable.

 

Symbolic Notation

 

Because of the various isotopes of an element such as hydrogen, the chemical symbol H does not provide sufficient information about the nucleus.

 

The Nuclide Symbol

A = Z + N   Quantity Symbol SI Unit atomic mass number— the number of nucleons A -- atomic number Z -- neutron number N -- chemical symbol X --

 

Using this notation, the three isotopes of hydrogen H-1, H-2 and H-3 are expressed as , , and .

 

As demonstrated with hydrogen, isotopes can be written with the element name followed by the mass number as well as with nuclide symbols. For example, uranium-238 is the isotope .

 

Self-Check

 

SC 1. How many neutrons are in lead-204?

 

 

Try This

 

TR 1. Complete “Practice Problems” 1 and 2 on page 791 of your physics textbook.

 

The Atomic Mass Unit

 

The average mass of a hydrogen atom is 1.01. It is reported in atomic mass units (u), which are defined as exactly of the mass of the carbon-12 atom.

 

1 u = 1.660539 × 10–27 kg

 

The value for the atomic mass unit was determined using a mass spectrograph, which is very similar to J.J. Thomson’s charge-to-mass ratio experiment you studied in Module 7: Lesson 1.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Try This

 

TR 2. A singly ionized carbon atom is accelerated by a parallel-plate apparatus and passes through a velocity selector with a magnetic field strength of 0.950 T and an electric field strength of 5.60 × 105 V/m. The ion then passes into a mass spectrograph with a magnetic field of 1.50 T and the sensor detects a radius of 4.89 × 10–2 m.

1. What is the velocity of the carbon ion as it passes through the velocity selector?

2. What is the mass of the carbon ion as determined by the mass spectrograph?

3. If the carbon ion has an atomic mass of 12, what is the value of 1 atomic mass unit?

Read

 

The preceding information can also be found in your physics textbook on pages 790 and 791. “Table 16.1” on page 792 lists the masses of subatomic particles in both kilograms (kg) and atomic mass units (u).

 

Nuclear Decay

 

There is one question about the nucleus that has yet to be addressed. If the nucleus is a ball of positively charged protons, why don’t these like charges fly apart? Recall from Module 3: Lesson 2 that Coulomb’s law of electrostatic forces would indicate that the positive protons should repel each other, leading to a breakdown of the nucleus. In fact, some atoms do break down because of this electrostatic force. This is called nuclear decay.

So, while there is evidence of some nuclear decay, what stops the atom from totally breaking apart from repelling protons?

 

Nuclear Forces

 

The nucleus is held together by what physicists call the strong nuclear force. This fundamental force of nature counters the electrostatic force of repulsion that would exist between the protons in the nucleus. For example, the gravitational attraction between two protons 5 cm apart is 7 × 10–36 N, while the electrostatic force of repulsion at the same distance is 9 N. Just making up the difference between these two fundamental forces would require a nuclear force that is 1037 times stronger than gravity. The strong nuclear force is massive compared to the gravitational force; but the gravitational force extends throughout the universe, whereas the strong nuclear force can act only over distances that are—relative to the size of the nucleus (~10–14 m)—extremely small.

 

So, why are some atoms stable and others unstable? And what is the purpose of all these neutrons? The strong nuclear force is almost independent of electric charge but acts only over a very short distance. It exists between any nucleon pair, whether it’s a proton-proton, neutron-neutron, or proton-neutron. Even though the strong nuclear force is powerful, the electrostatic repulsive force has a longer range of action. This means that one proton is repelled by every other proton in the nucleus but is attracted only to its nearest neighbours.

 

Force	Relative Strength	Range
strong nuclear	1	≈10–14 m (nucleus)
electromagnetic	0.0073	∞
weak nuclear	10–9	≈10–18 m (nucleon)
gravitational	10–38	∞

 

As protons are added to a nucleus (moving down in the periodic table to heavier elements), more neutrons need to be added to balance out the additional repulsive electrostatic forces. At some point, however, adding neutrons no longer helps. All nuclei with more than 83 protons are unstable and will decay spontaneously, like americium-241 in the smoke detector, which has 95 protons.

 

Try This

 

Complete “Practice Problems” 1 and 2 on page 792 of the textbook.

 

Scientists working with radioactive substances discovered that helium gas was invariably present in their experiments. Rutherford proposed that the helium gas was produced by the radioactive substances and that the alpha particle, known to be produced by radioactive materials, was simply a helium nucleus missing its electrons. When Rutherford experimented with radon, he found that radon spontaneously split into an alpha particle (a helium nucleus) and a polonium atom. This natural change from one element to another is called transmutation. The original element is known as the parent element and the new element is called the daughter element.

 

Watch and Listen

 

Watch an animation of the parent carbon-14 decay into the daughters nitrogen-14, electron, and electron antineutrino in this Natural Transmutations/Decay Animation.

 

Since the transmutation of radon to polonium produced an alpha particle, it is called alpha decay. If the particle emitted is a beta particle, it is called beta decay. The term decay refers to a larger particle splitting into smaller particles.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Reflect and Connect—Three Types of Nuclear Radiation

 

Rutherford classified the three types of naturally occurring nuclear radiation according to penetrating ability. Listed from least to greatest penetrating ability, the three types are alpha, beta, and gamma rays.

 

When americium-241 decays, it releases alpha particles energetic enough to ionize gas molecules. This fact is used in the ionizing smoke detector where ionized gas molecules are used as conductors between two electrodes, establishing a current in the detector. When smoke particles enter the detector they block the alpha particles, which stops the ionization of the air causing the current in the gas to drop, triggering the alarm.

 

You can explore the effect that smoke and other barriers have on radiation using a Geiger counter, a device that measures the number of alpha particles, beta particles, and gamma radiation emitted by an isotope. Either the type of barrier or the radioactive isotope can be manipulated. The responding variable is the amount (per unit time) of each type of radiation reaching the Geiger counter.

 

Open the Geiger Counter simulation. This simulation uses a Geiger counter to measure the number of alpha and beta decay particles emitted from an isotope in a five-second time interval.

 

Module 8: Lesson 1 Assignment

 

Remember to submit your answers to RC 1, RC 2, RC 3, RC 4, RC 5, RC 6, and RC 7 to your teacher as part of your Module 8: Lesson 1 Assignment. You will be using the Geiger Counter simulation for these Reflect and Connect questions.

 

RC 1. On the Geiger Counter simulation, select Americium-241 as the isotope and select “air” as the barrier. Start the count and complete the data table below. How do you know what type of decay is occurring?

 

Alpha
Beta
Gamma

 

 

 

 

 

 

 

RC 2. Switch the barrier to “smoke,” start the counter, and complete the data table below. How is a Geiger counter like a smoke detector?

 

Alpha
Beta
Gamma

 

 

 

 

 

 

 

RC 3. Switch the isotope to “no isotope,” start the counter, and complete the data table. How can you account for any radioactivity when there is no isotope?

 

Alpha
Beta
Gamma

 

 

 

 

 

 

 

RC 4. Select uranium-238 as the isotope and air as the barrier. Start the counter and record the number of alpha particles detected. Move the Geiger counter away from the isotope and start the count again. Record the new activity. Complete the table below by continuing to move the Geiger counter away from the isotope.

 

Distance (mm)	Alpha Count
10
20
50
100
200
300
400

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RC 5. Graph the recorded count versus distance of separation. Does the intensity of the radiation obey the inverse square rule? Explain how this graph could be used to find the minimum safe distance from a radioactive source.

 

 

RC 6. Experiment with different types of barriers. Which material is the best shield from decay radiation?

 

RC 7.  Repeat RC 4 for cobalt-60. Make a table to organize your data for beta and gamma decays. Graph the information as in RC 5. What relationship do you see?

 

Try This

 

TR 4. Read the description of each particle below, and explain why Rutherford’s ranking of emitted radiation particles by penetrating power makes sense in terms of the structure of each particle.

• alpha (α) particle: a helium nucleus made up of 2 neutrons and 2 protons;  symbol or
  
  

• beta (β) particle: a very high-speed electron; symbol or
  
  

• gamma (γ) particle: a high-energy photon (higher energy than X-rays);  symbol

The Process of Nuclear Decay

 

The decay process must obey the following laws of physics:

1. conservation of charge
   
   

2. conservation of nucleons
   
   

3. conservation of mass-energy

The first two laws will be used to complete and balance nuclear decay equations while the third will be applied later when you investigate the concept of mass defect and binding energy.

 

There are several types of decay that can be simulated with this Nuclear Decay Gizmo. Use the gizmo to study alpha and beta decay. Watch for the concepts of conservation of charge and nucleon number as you complete the following activity. Activate the animation on the lower right of the graphic.

 

Alpha Decay (α)

 

The alpha decay of uranium-238 can be represented with an equation and animation. The default display for the Nuclear Decay Gizmo is for the alpha decay of a uranium-238 nucleus.

 

Module 8: Lesson 1 Assignment

 

Remember to submit your answers to LAB 1 and LAB 2 to your teacher as part of your Module 8: Lesson 1 Assignment. 

 

LAB 1. On the Nuclear Decay Gizmo, select “Show Equation.” Press the “play” button and add the missing information to the following equation:

 

 

LAB 2. Vary the “starting element” on the simulation and observe alpha decay for several other isotopes.

1. Is the atomic mass (number of nucleons) conserved on both sides of the equation? How can you tell?
   
2. Is the atomic number (number of protons or positive charges) conserved on both sides of the equation?
   
3. What particle is always produced in alpha decay?

In LAB 2 you observed uranium-238 as the parent element and thorium-234 as the daughter element.

 

According to the conservation laws, alpha decay can be represented by the following equation.

Quantity Symbol SI Unit X – parent element X -- Y- daughter element Y -- α- alpha particle α

The atomic mass number (A) and the atomic number (Z) are conserved in nuclear decay reactions.

 

Example Problem 1. Use the americium-241 from the smoke detector to answer the following questions.

1. What is the alpha decay equation?
   
   
   
   

2. What is the parent element and what are the daughter elements?
   
   

   The parent element is americium-241. The daughter elements are neptunium-237 and helium-4.
   
   

3. How does this decay equation obey the law of conservation of charge?
   
   

   The law of conservation of charge is obeyed because there are 95 protons before the transmutation and 95 protons (93+2) after the transmutation. Electrons are not involved in this transmutation.
   
   

4. How does this decay equation obey the law of conservation of nucleons?
   
   

   The law of conservation of nucleons is obeyed because there are 241 nucleons before the transmutation and 241 nucleons (237+4) after the transmutation.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Try This

 

Complete “Practice Problems” 1 to 3 on page 800 of your physics textbook.

 

Beta Decay (β)

 

The beta decay of carbon-14 can be represented with an equation and animation. Open Nuclear Decay Gizmo and change the “type of decay” to “beta decay.”

 

LAB 3. On the simulation, select “show equation.” Press the “play” button and add the missing information to the equation:

 

 

LAB 4. Vary the “starting element” on the simulation and observe beta decay for several other isotopes.

1. What happened to the neutron?
   
   
2. Is the atomic mass conserved on both sides of the equation?
   
   
3. Is the atomic number conserved on both sides of the equation? Where did the new proton come from?
   
   
4. Which particle is always produced in beta decay?

In LAB 3, you observed carbon-14 as the parent element and nitrogen-14 as the daughter element.

 

In beta-negative decay, a neutron converts into a proton, electron, and antineutrino. The proton is retained by the nucleus, keeping the atomic mass constant while increasing the atomic number and, thus, changing the type of element. The emitted electron is called a beta particle to distinguish it from the electrons around the nucleus. According to the conservation laws, beta decay can be represented by the following equation.

Quantity Symbol SI Unit X – parent element X -- Y - daughter element Y -- β - beta particle β - antineutrino --

atomic mass number (A) and the atomic number (Z) are conserved in nuclear decay reactions

 

The antineutrino listed in the preceding equation was not included in the simulation.

 

Read

 

Read about the neutrino on page 804 of the textbook.

 

Example Problem 2. Amercium-241 is produced by a beta decay of plutonium-241.

1. Write the beta decay reaction for plutonium-241.
   
   
   
   

2. What is the parent element and what are the daughter elements?
   
   

   The parent element is plutonium-241. The daughter element is americium-241. (Electrons and antineutrinos are not elements.)

   
   

3. How does this decay equation obey the law of conservation of charge?
   
   

   The law of conservation of charge is obeyed because there are 94 protons before the transmutation and after there are 95 protons in the americium but negative one on the electron [95+ (−1) = 94]. [A neutron (q = 0) changes into a proton (q = 1) and an electron (q = −1).]
   
   

4. How does this decay equation obey the law of conservation of nucleons?
   
   

   The law of conservation of nucleons is obeyed because there are 241 nucleons before the transmutation and 241 nucleons after the transmutation. (The beta particle and the antineutrino are ejected from the americium 241 atom.)

Try This

 

TR 6. Complete “Practice Problem” 1 with Example 16.8 and “Practice Problem” 1 with Example 16.9 on page 803 of your physics textbook. Remember that each reaction also produces a beta particle and an antineutrino.

 

Read

 

Read about antimatter and the positron on pages 804 and 805 of the textbook. Note in Example 16.10 the extra electron that must be taken into account in the mass defect.

 

Self-Check

 

SC 2. How does the weak nuclear force relate to beta decay (both positive and negative decay)?

 

 

In beta-positive decay, a proton converts into a neutron and a positron. The neutron is retained by the nucleus, keeping the atomic mass constant while decreasing the atomic number and thus changing the type of element. The beta particle emitted is called a positron. According to the conservation laws, beta-positive decay can be represented by the following equation. Note: the parent atom has Z electrons to be electrically neutral, when the proton changes into a neutron and positron there is Z-1 electrons in the daughter nucleus. An electron is released to drift away but this is not shown in the equation. This will affect the mass defect equations you will see later.

Quantity Symbol SI Unit X – parent element X -- Y- daughter element Y -- - beta particle (positron) β - neutrino v --

atomic mass number (A) and the atomic number (Z) are conserved in nuclear decay reactions

 

Example Problem 3. Write the beta-positive decay equation for nickel-56.

 

 

The Neutrino and Antineutrino

 

The neutrino and antineutrino are a matter-antimatter pair. The existence of an antineutrino was hypothesized when the kinetic energy of a beta particle following beta decay was lower than expected. It was predicted that some other particle was carrying this energy away before the particle could be detected. This was later proven to be true.

 

Gamma Decay (γ)

 

Often, the alpha and beta decay processes leave the daughter nucleus in an excited state, with the nucleons spread apart. Similar to that of an electron in an energy level, the nucleons will rearrange to form a more stable ground state and releases very high frequency gamma radiation as a result.

 

According to the EMR spectrum, gamma radiation has extremely high energy, which corresponds to a high frequency and a short wavelength. It has no mass or charge, therefore producing no changes in the atomic number or atomic mass of the nucleus. There is no transmutation with the emission of gamma radiation. Gamma rays are represented by the symbol (γ).

 

The nucleus may be left in an excited state after alpha or beta decay. In the nuclear equation, this excited state is represented with an asterisk (*). The nucleus then experiences gamma decay to return to a ground state.

 

Read

 

Read pages 806 and 807 of your physics textbook for an example of a gamma decay chain and equation as well as a radioactive decay series.

 

Decay Series

 

Many of the daughter nuclei produced by alpha and beta decay are still unstable and, as such, will undergo further transmutation. In such cases a decay series is used to illustrate the successive decays until a stable nucleus is produced. Search the Internet for examples of decay series. In most, each dot in this series represents a new nucleus. Both alpha and beta decay form part of each series as the parent material undergoes successive decay in both forms until a stable nucleus is reached.

 

The Direction of Alpha and Beta Decay in the Diagram

 

 

First, focus on why alpha and beta decay are drawn in the direction shown. Recall that alpha decay (the release of a nucleus) involves a decrease in atomic mass number (by four) and a decrease in protons (by two). On the chart, therefore, you need to move down four and left two to get to the new mass number and atomic number. 

 

Notice on page 807 of your physics textbook that the alpha decays are red arrows. Also notice that the horizontal axis increases by one atomic number and the vertical axis increases by four atomic mass numbers per line.

 

Beta decay results in no change to the atomic mass number, so there is no movement up or down on the grap; but it results in an increase in the atomic number, so there is a movement of one unit to the right. Still on page 807 of the textbook, notice that a horizontal blue arrow that is two units long must, therefore, represent two beta decays in succession.

 

Example Problem 4. Using the decay series on page 807 of your textbook, write the nuclear decay equations that represent the transmutation of protactinium-234 to radium-226 (from the radium decay series).

 

Find the dot for protactinium-234, and read off the chemical symbol and atomic number, . Do the same for its daughter element,  (uranium-234 in this case). Set up the nuclear equation; then use the concepts of conservation of charge and nucleons to balance the equation by adding either an alpha particle or beta particle. (You could just add the particle by referring to the decay type shown in the diagram; but you should still check that the equation is balanced.) If the decay is beta, remember to add the antineutrino.

 

Continue to follow the decay chain in this way until all of the equations have been written.

 

Physics 30 Learn EveryWare © 2009 Alberta Education

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.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Lesson Summary

 

In this lesson you focused on the following questions:

• Which components make up the nucleus of an atom and what keeps them from coming apart?
  
  
• What are alpha and beta decay?
  
  
• How is the conservation of energy and mass applied to nuclear decay?

The nucleus is very small, only about 10–14 m across, but it makes up nearly the entire mass of the atom. The nucleus is composed of smaller particles called nucleons. The protons and neutrons are both nucleons. The number of protons defines the element. The physical characteristics, such as atomic mass, vary due to the number of neutrons present. Two atoms, each with an identical number of protons but a different number of neutrons, are called isotopes. Each isotope has a unique atomic mass. The atomic mass unit (u) is defined as exactly of the mass of the carbon-12 atom (1 u = 1.66 × 10–27 kg).

 

The nucleus is held together by what physicists call the strong nuclear force, which must be overcome to change the number of nucleons in the atom.

 

Some nuclei are unstable and decay. This natural change from one substance to another is called transmutation. Alpha decay is defined by the production of an alpha particle ( ) during the decay of a parent nucleus into a daughter nucleus. The general equation for alpha decay is .

 

Beta decay is defined by the production of a beta particle () during the transmutation. The general equation for beta decay is . Beta-positive decay is defined by the production of a positron () (antimatter electron) during transmutation. The general equation for beta-positive decay is .

 

In all three decay processes, charge and atomic mass number are conserved. Mass itself (atomic mass units, grams or kg) is not conserved, since in each process some mass is converted to energy according to the relationship E = mc2.

 

All transmutations produce significant amounts of energy in the form of kinetic energy of the emitted particles and sometimes the production of high frequency gamma radiation. Einstein’s mass-energy equivalency (E = mc2) relates the mass defect in transmutations to the amount of energy released. Comparing these values supports the conservation of energy principle.

 

The alpha, beta, and gamma particles are a form of ionizing radiation. Ionizing radiation is dangerous because it has enough energy to ionize DNA and change chromosomes, which can lead to cancer or, in high doses, radiation sickness and death.

 

Lesson Glossary

 

antimatter: a form of matter that has properties opposite to its normal-matter counterpart

 

antineutrino: a tiny subatomic particle with no charge emitted with  in beta decay

 

alpha particle: two protons and two neutrons bound together to form a stable particle identical to a helium nucleus

 

atomic mass: the weighted mean atomic mass number of the element’s natural isotopes

 

This number is given on the periodic table.

 

atomic mass number (A): the number of nucleons in an atom’s nucleus

 

atomic number (Z): the number of protons in the nucleus

 

The atomic number uniquely identifies the element.

 

beta particle: an electron emitted by the nucleus when a neutron splits into a proton and electron during the beta decay process

 

daughter element: the element produced by a decay process

 

isotope: an atom that has the same number of protons but a different number of neutrons and, therefore, a different atomic mass number

 

nucleon: a proton or neutron

 

neutrino: a tiny subatomic particle with no charge emitted with a positron in beta-positive decay

 

neutron: a neutral particle found in the nucleus

 

parent element: the original element in a decay process

 

positron: the antimatter to an electron

 

It is the same type of particle but has an opposite charge. Unlike electrons, positrons are scarce.

 

proton: a positively charged particle found in all nuclei

 

transmutation: decay or change into a different element

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Lesson 2—Decay Rates and Radioactive Dating

 

Get Focused

 

Heading west on Highway 3 near the Crowsnest Pass, you will find one of Alberta’s most famous and most photographed trees. This limber pine, called the Burmis Tree, is more than 300 years old. It was a seedling in the late 1600s and died in 1978. It toppled over 20 years later in 1998. It has since been restored to its original position and is symbolic of the resiliency needed to survive in the unforgiving environment of the eastern Rocky Mountain slopes of Alberta.

 

The appeal of this natural landmark is its extreme age. Its gnarled branches have withstood more than 300 Alberta winters and countless days of high winds, drought, intense heat, and chilling cold. How could you know that this tree really is that old? How could you know when, and for how long, a tree has lived? How could you accurately determine when it died?

 

The unstable nuclei of the carbon isotopes in the tree, or any carbon-based organism, provide a built-in clock that can be observed to determine its age. When the tree was alive, the process of photosynthesis extracted radioactive carbon-14 from the atmosphere and fixed it into the tissue of the tree. When it died, the process stopped. As you observed in Module 8: Lesson 1, the carbon-14 nuclei will undergo beta decay to form nitrogen-14. Due to this decay, the amount of carbon-14 in the tissue decreases over time. By comparing the current amount of carbon-14 in the tissue to that of the carbon-14 that was present when the organism formed, it is possible to determine an age. Of course, this is only possible if you first know how fast, or at what rate, the carbon-14 nuclei in the tree decayed.

 

In Lesson 2 you will explore the rate of decay and its application in radioactive dating.

 

In this lesson you will focus on answering the following essential questions:

• What is a half-life?
• How are half-lives used to determine age?

Module 8: Lesson 2 Assignment

 

Your teacher-marked Module 8: Lesson 2 Assignment requires you to submit responses to the following:

• Lab—LAB 1, LAB 2, LAB 3, LAB 4, LAB 5, LAB 6, LAB 7, LAB 8, and LAB 9
• Reflect and Connect—RC 1 and RC 2

The other questions in this lesson are not marked by the teacher; however, you should still answer these questions. The Self-Check and Try This questions are placed in this lesson to help you review important information and build key concepts that may be applied in future lessons.

After a discussion with your teacher, you must decide what to do with the questions that are not part of your assignment. For example, you may decide to submit to your teacher the responses to Try This questions that are not marked. You should record the answers to all questions in this lesson and place those answers in your course folder.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Explore

 

Half Life

 

The half-life of a radioactive isotope is defined as the amount of time it takes for half of the radioactive particles to decay. Consider a container with 128 unstable nuclei. Over time, some of the nuclei decay, forming daughter nuclei and related decay particles. Eventually, half of the nuclei will have decayed into daughter nuclei. In this example, after a certain amount of time had passed, 64 nuclei decayed to daughter nuclei, leaving 64 of the original parent nuclei.

 

The amount of time it takes for this to happen is defined as the half-life of the unstable parent nuclei. The half-life of other nuclei will be different. For example carbon-14, which is used to date organic material, has a half-life of 5730 years. While iodine-131, used in the medical diagnosis of thyroid problems, has a half-life of 192 hours.

 

 

Module 8: Lesson 2 Assignment

 

Remember to submit the answer to LAB 1, LAB 2, LAB 3, LAB 4, LAB 5, LAB 6, and LAB 7 to your teacher as part of your Module 8: Lesson 2 Assignment.

 

A simulation will be used to explore the rate of radioactive decay and the concept of half-life. Open the Half-life simulation. Use the controls on the right side of the simulation to activate the animation.

 

LAB 1. In the simulation there is a chamber of 128 radioactive atoms represented by red spheres. Click Play () and observe. Over time, describe what happens to the relative amount of parent nuclei (red) and daughter nuclei (grey).

 

LAB 2. Reset the simulation and select the “BAR CHART” tab. Click play and observe. Compare the rate of change from parent to daughter nuclei throughout the decay process. Is the rate of particle decay constant through time? If not, did it speed up or slow down over time?

 

LAB 3. Reset the simulation and select the “GRAPH” tab. Click play and observe. Sketch the half-life curve. (You can find a blank graph, like the one that follows, in your Module 8: Lesson 2 Assignment.)

 

 

LAB 4. Select a different isotope from the drop-down menu and observe its decay graph. Does it have exactly the same shape as the other isotope decay curve? What does this suggest about the nature of decay?

 

LAB 5. The rate of decay of a radioactive isotope is described by its half-life. On the simulation, ensure that the half-life is set to 20 seconds and select “Theoretical decay” from the second drop-down menu. Check that the initial number of atoms is 128. Select the “TABLE” tab and click play.

1. At 20 seconds, how many of the original 128 radioactive atoms remained?
   
   
2. How many remained at 40 seconds? 60 seconds? 80 seconds? 100 seconds? What is the pattern?

LAB 6. If there are 100 radioactive atoms with a half-life of 30 seconds, how many radioactive atoms will remain after one half-life (30 seconds)? How many will remain after two half-lives (60 seconds)? three half-lives? Use the simulation to check your answers.

 

LAB 7. The half-life of a radioactive isotope is defined as the amount of time it takes for half of the radioactive particles to decay. Start with 128 particles and a half-life of 30 seconds. (“Theoretical decay” should still be selected.) Select the “GRAPH” tab and click play. Turn on the half-life probe and ensure it is on the y-axis of the graph. (You can "grab" and drag the probe by clicking on one of the purple triangles or the line between.)

1. What is the time value and number of radioactive particles at the beginning of the interval measured by the probe? What is the time value and number of radioactive particles at the end of this interval? How are these two numbers related to the definition of half-life?
   
   
2. Drag the probe to different parts of the graph. Does the same pattern persist?

The mathematical expression for the graph of parent nuclei versus time gives the following equation for determining the number of original parent nuclei in a radioactive sample after a given time interval.

Quantity Symbol SI Unit amount of parent material remaining N activity/percentage/mass decay/second amount of parent material at the start No activity/percentage/mass decay/second number of half-lives elapsed unitless time t seconds/hours/days/years half life t1/2 seconds/hours/days/years

Activity is usually measured in decays per second, or becquerels (Bq); however, mass and percentages can also be used to indicate the relative amount of parent material. Since these units appear on both sides of the equation, they will mathematically cancel one another.   Graphical representation of radioactive decay.     The half-life can be measured from the time axis from the point where half of the nuclei have transmuted. In this case, 50 nuclei are left after 25 seconds.

 

Example Problem 1. A radioactive sample has an activity of 3.2 × 103 Bq. The isotopes in the sample have a half-life of 24 hrs. What will be the activity of this sample after five days have passed?

 

Given

 

 

Required

 

the amount of activity after five days

 

Analysis and Solution

 

Determine the number of half-lives that have elapsed.

 

 

Determine the amount remaining.

 

 

Paraphrase

After five days, the sample will have an activity of 1.0 × 102 Bq.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Try This

 

TR 1. Complete “Practice Problem” 2 on page 813 of the textbook.

 

TR 2. Complete “Practice Problems” 1 and 2 on page 814 of the textbook.

 

Radioactive Dating

 

Using nuclear decay to determine age is only possible because radioactive decay is a predictable process. It can be used to determine the age of rocks, fossils, and artifacts. This method is called radiometric dating.

 

Module 8: Lesson 1 Assignment

 

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

 

Open the Half-life simulation again.

 

LAB 8. On the drop-down menus, select “Isotope A” and “Theoretical decay.” Set the number of atoms to 128 and click play.

1. According to the graph, what is the approximate half-life of isotope A?
   
   
2. Select the “TABLE” tab. According to the data table, what is the exact half-life of isotope A?
   
   
3. Suppose you analyzed a sample of isotope A that contained 25 radioactive isotope A atoms and 103 stable daughter atoms. Approximately how old is the sample?
   
   
4. About how old is a sample of isotope A with 75 radioactive atoms and 53 daughter atoms?
   
   
5. Click reset. Change the number of atoms to 50 and click play. Does this change the half-life of isotope A? Confirm this by experimenting with other starting numbers. Does this mean that radioactive dating does not depend on the amount of radioactive nuclei at the start? Explain.
   

Summary

 

The isotopes that are useful for measuring the age of rocks and fossils have very long half-lives. As previously mentioned, the carbon-14 used to date organic material has a half-life of 5730 years, while uranium-235, used to date rocks, has a half-life of 704 million years.

 

Module 8: Lesson 1 Assignment

 

Remember to submit the answer to LAB 9 as part of your Module 8: Lesson 1 Assignment to your teacher for marks. 

 

Open the Half-life simulation again.

 

LAB 9. Set the number of atoms to 100 and check that “Isotope B” and “Theoretical decay” are selected. Click play and view the results on the “GRAPH” tab. To model how scientists might date an artifact, imagine that the y-axis represents the percentage of radioactive atoms and that each second on the x-axis represents 1000 years. Assume this is true.

1. What is the age of an artifact with 50% radioactive atoms of isotope B?
   
   
2. What is the estimated age of a sample with 25% radioactive atoms of isotope B? 12%? 6%?
   
   
3. About how old is a sample with 72% radioactive atoms of isotope B?

Read

 

Read “Radioactive Decay Rates” on pages 811 to 816 of your physics textbook.

 

Self-Check

 

SC 1. The half-life of strontium-90 is 28 years. If 60 g of strontium-90 is currently in a sample of soil, how much will be in the soil in 84 years?

 

SC 2. The half-life of strontium-90 is 28 years. If 100 g of strontium-90 is currently in a sample of soil, how much will be in the soil in 65 years?

 

SC 3. Tritium (hydrogen-3), a by-product of the CANDU nuclear power reactor, has a half-life of 12.3 years. How much time is required for its radioactivity to reach 1/4 its original level?

 

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Watch and Listen

 

Explore half-lives using this Half-Life tutorial.

 

Self-Check

 

You may check your understanding of half-lives by completing the assessment questions in the Half-life simulation.

 

SC 4. A student studying radioactivity makes the following measurements from a radioactive sample.

 

Time (s)	Decays (Bq)
0.0	100.00
1.0	75.79
2.0	57.43
3.0	43.53
4.0	32.99
5.0	25.00
6.0	18.95
7.0	14.36
8.0	10.88
9.0	8.25
10.0	6.25
11.0	4.74
12.0	3.59

1. What is the independent variable?
   
   
2. What is the dependent variable?
   
   
3. Graph the information.
   
   
4. What type of relationship is shown on the graph?
   
   
5. From your graph what is the half life of the sample?
   
   
6. After how many seconds will there be less than 1.0 Bq?
   
   
7. Will the decays ever reach zero?

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Reflect and Connect

 

 

In order to determine the age of a sample using radioactive dating, we will assume that the amount of carbon-14 in the ancient wood, when it died, was identical to the amount of carbon-14 in a similar sample of living wood today. In other words, the amount of carbon-14 in the atmosphere has not changed significantly in the past 5000 years. In reality scientists and archaeologists carefully adjust for variations in atmospheric carbon-14 by comparing values to known values from ice cores, deep-sea sediments, and tree growth rings (dendrochronology).

 

Module 8: Lesson 2 Assignment

 

Remember to submit your answers to RC 1 and RC 2 to your teacher as part of your Module 8: Lesson 2 Assignment. 

 

RC 1. Predict the percentage of remaining carbon-14 (half-life = 5730 years) in an ancient wood sample that is known to be 2500 years old.

 

RC 2. Explain how this prediction could be used to measure the accuracy of radiocarbon dating.

 

Module 8: Lesson 2 Assignment

 

Remember to submit the Module 8: Lesson 2 Assignment to your teacher.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Lesson Summary

 

In this lesson you focused on the following questions:

• What is a half-life?
  
• How are half-lives used to determine age?

In this lesson you learned that the half-life of a radioactive isotope is defined as the amount of time it takes for half of the radioactive nuclei to decay. Graphing the amount of parent nuclei versus time gives the following mathematical expression for the number of original parent nuclei in a radioactive sample after a given time interval.

 

 

Both the graphical representation and the mathematical expression can be used to determine the age of a radioactive sample. Radioactive dating is based on comparing the remaining amount of parent nuclei to the amount that was originally in the sample. Using this and the known half-life of the material, it is possible to accurately determine its age.

 

Lesson Glossary

 

activity or decay rate: the number of nuclei in a sample that decays in a given time interval

 

becquerel (Bq): the unit of radioactivity equal to one decay per second

 

half-life: the time it takes for half the radioactive nuclei in a sample to decay

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Lesson 3—Fission and Fusion

 

Get Focused

 

In the Big Picture at the beginning of the module molecules, atoms, protons, and particles were characterized as different sized balls. The Sun is powered by two very small balls colliding to produce a slightly larger ball and release a huge amount of energy. In the case of fusion, multiple hydrogen nuclei join together to form a heavier helium nucleus, accompanied by the release of massive amounts of energy. It would be an ideal source of power if it could be sustained in a reactor on Earth, such as the one seen in the photograph. Such a reactor would combine multiple hydrogen nuclei to form helium, which is environmentally clean and biologically harmless.

 

However, fusion reactions involving hydrogen need to have sustained temperatures ranging from 45–400 million degrees Kelvin. In the Tokamak reactor vessel, plasma is heated in a doughnut-shaped vessel called a torus. Magnetic fields are used to contain the superheated plasma, preventing it from contacting the vessel walls.

 

Although very promising in theory, current fusion technology can only sustain the reaction for a few seconds while producing only slightly more energy than it consumes. Significant technological advances need to be made before fusion becomes a practical energy source, one that is clean, safe, and abundant.

 

Watch and Listen

 

Watch this video about the Joint European Tours Nuclear Fusion Research Facility (“The Starmakers”) to see the latest reactor technology in action.

 

In Lesson 3 you will compare and contrast the characteristics of fission and fusion reaction.

 

In this lesson you will focus on answering the following essential questions:

• Why do nuclear reactions release so much energy?
  
• What is nuclear fission?
  
• What is nuclear fusion?

Module 8: Lesson 3 Assignment

 

Your teacher-marked Module 8: Lesson 3 Assignment requires you to submit responses to the following:

• Lab—LAB 1, LAB 2, LAB 3, LAB 4, and LAB 5
• Reflect and Connect—RC 1 

The other questions in this lesson are not marked by the teacher; however, you should still answer these questions. The Self-Check and Try This questions are placed in this lesson to help you review important information and build key concepts that may be applied in future lessons.

After a discussion with your teacher, you must decide what to do with the questions that are not part of your assignment. For example, you may decide to submit to your teacher the responses to Try This questions that are not marked. You should record the answers to all questions in this lesson and place those answers in your course folder.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Explore

 

The Energy of Nuclear Reactions

 

Nuclear reactions involve vast amounts of energy, either creating massive fireballs in a chain reaction or slowly releasing significant amounts of energy over many years in a nuclear reactor. Recall from Module 8: Lesson 1 that particles (nucleons) make up a nucleus that is held together by a strong nuclear force. Both nuclear fission and fusion reactions change the number of nucleon particles, so work must be done against the strong nuclear force during any nuclear reaction.

 

The amount of work required to separate all the nucleons in a given atom is referred to as the binding energy. It is equal to the difference between the energy of all the nucleons when they are free compared to when they are contained in the nucleus.

 

Ebinding = Enucleons – Enucleus

 

Dividing the binding energy of the nucleus by the number of nucleons making it up gives a value for the binding energy of each nucleon.

 

 

Stable nuclei have greater binding energy per nucleon than unstable nuclei. Nuclei with atomic masses in the range of 58–62 (iron-nickel) are the most stable, with the highest binding energy per nucleon. Smaller atoms, such as hydrogen-2, have a very small amount of binding energy per nucleon, making them less stable. At the same time much larger atoms, such as uranium-238 also have a reduced binding energy per nucleon making it unstable. In order to become more stable, very small nuclei can become larger by combining in the process of fusion, and very large nuclei can become smaller by breaking down into smaller nuclei in the process of fission. The result in either process is to move toward a medium-sized stable nucleus with the greatest amount of binding energy per nucleon.

 

For both fission and fusion reactions, the energy released is equal to the difference between the total binding energy of the original nucleus or nuclei and the final binding energy of the nucleus or nuclei.

 

 

For both fission and fusion, the binding energy of the final (resulting) atom(s) is much larger than the binding energy of the initial atom(s), leading to both a more stable nucleus and the release of a large amount of energy.

 

The change in binding energy also corresponds exactly to the change in mass between the original and new nuclei, according to Einstein’s mass-energy equivalency (E = mc2). In this respect, the energy released in a nuclear reaction is based on the change in mass before and after the reaction.

 

 

According to this equation, even a very small change in mass multiplied by the square of the speed of light (9 × 1016) will result in a large release of energy.

 

Nuclear Fission

 

 

The Canadian CANDU nuclear reactor uses the fission of uranium-235 as an energy source. In this reactor a free neutron is absorbed by a uranium nucleus causing it to become unstable and break apart into two smaller nuclei accompanied by the release of several more neutrons.

 

If the free neutrons encounter more uranium atoms they will be absorbed again, causing further fission and the production of more neutrons capable of continuing the process. If enough uranium is present in a small enough area (critical mass), the probability of a neutron causing another uranium atom to split is very high and a chain reaction will occur. This would cause the release of a massive amount of energy in a very short period of time, producing a nuclear explosion. In a nuclear reactor, by contrast, the uranium atoms are spread out in fuel rods and some of the released neutrons are blocked by control rods in order to slow down the chain reaction. When the reaction rate is slow, a smaller amount of energy is released over a long period. In essence, a nuclear reactor is a nuclear bomb going off in a controlled manner over a prolonged period. When all or most of the uranium-235 atoms in the fuel have been spent, the reactor cools, at which point new fuel would have to be inserted to ensure continued energy production.

 

Example Problem 1. How much energy is released by the fission of one U-235 atom?

 

 

Given

 

The atomic masses come from “Table 7.5” and “7.6” on page 881 of your physics textbook.

 

 

Required

 

the amount of energy released

 

Analysis and Solution

 

Determine the mass defect.

 

 

Change the mass defect into kilograms.

 

 

Determine the amount of energy released.

 

 

Paraphrase

The energy released by the fission of one uranium-235 atom is 2.78×10–11 J.

 

This value may seem small by comparison, but in a single kilogram of uranium there are enough fissionable uranium atoms to produce 7.09 × 1013 J of nuclear energy, which is approximately 1.6 million times greater than the chemical energy within one kilogram (≈1.4 litres) of gasoline.

 

Read

Read “Comparing Chemical Energy with Nuclear Energy” on page 820 of the textbook.

 

Watch and Listen

 

When dealing with nuclear reactors the rate of the reaction must be controlled to prevent a chain reaction. In the fission of uranium, each uranium nucleus decays spontaneously, which is a very slow reaction. This decay also occurs when a uranium nucleus absorbs a neutron in a nuclear reactor, which can be slow or fast depending on the position of the control rods. It is slowed down when the ejected neutrons are absorbed by inserting control rods, or it is sped up by removing the control rods, which lets the ejected neutrons strike other uranium nuclei, thus continuing the chain reaction. In the following animation you will see how a chain reaction spreads exponentially.

 

Three animationss are available to explain nuclear reactions. Do an Internet search using the term “atomic archive.” This should take you to a website that explores the histrory, science, and more of the invention of the atomic bomb. When you get to the website, use the website’s search function to locate “Nuclear Chain Reaction Animation.” This animation will show how, in a nuclear bomb, the chain reaction is engineered to occur as rapidly as possible to produce the largest explosion possible.

 

Next, find “Nuclear Fission Animation.” This animation shows the reactants and products of a uranium-based nuclear fission reaction, like the one that powers nuclear power reactors.

 

Finally, find “Nuclear Fusion Animation.” Fusion reactions release much more energy than fission reactions; however, this is also what makes them hard to control. This animation shows the reactants and products of a deuterium (H-2) and tritium (H-3) fusion, which produces a helium nucleus and a neutron. This is the main form of fusion that powers Earth’s Sun.

 

If you're having trouble finding any of the animations, click on “Media” in the top navigation bar on the website, and then on “Animations” on the page that appears.

 

Try This

 

TR 1. Complete “Practice Problems” 1 to 3 on page 819 of the textbook.

 

Nuclear Fusion

 

Nuclear fusion is similar to nuclear fission in that the binding energy of the products is much higher than the starting nuclei. The process to achieve this, however, is based on combining nuclei rather than breaking them down. At temperatures greater than 100 million Kelvin, the small nuclei of tritium and deuterium will combine to form larger, more stable helium atoms while releasing an amount of energy proportional to the change in mass (mass defect) or equal to the difference in binding energies before and after the reaction.

 

 

Nuclear fusion powers the Sun, which has enough hydrogen to maintain its present rate of energy production for another 6 billion years. On Earth, hydrogen is abundant in the water, which, in theory, could provide a seemingly infinite supply of clean, safe nuclear energy.

 

Watch and Listen

 

Watch the video “Sun Flares,” which is about solar flares. The video demonstrates the energy released by the nuclear fusion on the surface of the Sun. When the Sun’s magnetic field fluctuates it allows massive amounts of plasma to arc off into space. The arcs are often larger in diameter than Earth.

 

Commercial fusion reactors could provide phenomenal amounts of non-polluting electrical energy. The EFDA (European Fusion Development Agreement) sponsors JET (Joint European Torus), a commercial fusion reactor development site. EFDA scientists are researching how to safely recreate the reaction that powers the Sun to produce electricity on Earth. They used the information gathered from the JET project to design a large reactor called ITER, which is scheduled to begin operation in 2016. It will be the biggest fusion furnace ever built, twice as large as any previously built, and will produce plasma at temperatures of hundreds of millions of degrees Celsius. The video “Inside a Reactor” shows the inside of the JET reactor during a plasma experiment.

 

Read

 

Read “Fusion” on pages 821 to 823 of your physics textbook. Page 821 provides more extensive detail on the reactions occurring on the Sun and includes references to the products released (neutrinos, positrons or antielectrons, and gamma rays).

 

Try This

 

TR 2. Read “Example 16.16” and complete “Practice Problem" 1 on page 822 of the textbook.

 

How does a nuclear fission reactor work? Why are they so dangerous if they get out of control? What caused the Chernobyl nuclear accident? Open this nuclear reactor simulation, take your operator test and see if you can run the reactor efficiently. You can also discover how you could accidentally cause an explosion. (Be sure to open the “Information” tab in the simulation.)

 

After completing the nuclear reactor simulation, post your response to the following Lab questions in the discussion area of your class. You may need to return to the simulation.

 

Module 8: Lesson 3 Assignment

 

Remember to submit your answer to LAB 1, LAB 2, LAB 3, LAB 4, and LAB 5 to your teacher part of your Module 8: Lesson 1 Assignment. 

 

LAB 1. Which variables control the reactor temperature and how does an operator adjust them?

 

LAB 2. Describe the combination of variables that leads to the quickest meltdown.

 

LAB 3. Describe the combination of variables that prevent the reactor core from generating heat.

 

LAB 4. Which type of control rod is most effective and why?

 

LAB 5. Which type of coolant works best for safely generating electricity?

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

 

Reflect and Connect

 

Nuclear energy comes in one of two varieties:

1. fission of large nuclei like uranium-235
   • 

2. fusion of small nuclei like tritium and deuterium
   • 

The fission of uranium-235 is widely used in reactors, such as the CANDU reactor. Fusion does not produce the unstable and biologically dangerous daughter nuclei of fission. Fusion produces stable helium atoms. Research is being conducted to find a technological solution to sustain the fusion reaction. However, a sustained and practical use of fusion is yet to be achieved, but it holds great promise as an infinite source of clean, environmentally safe energy.

 

Module 8: Lesson 3 Assignment

 

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

 

RC 1. Complete the following table comparing and contrasting various issues related to nuclear fusion and fission.

 

 

Issue	Fusion	Fission
How is the change in binding energy achieved?
What is the relative size of the nuclei used as the fuel source?
How abundant is the fuel source?
What is the environmental impact of the reaction?
How safe is the technology?
How easy is it to sustain the reaction?

 

Module 8: Lesson 3 Assignment

 

Remember to submit the Module 8: Lesson 3 Assignment to your teacher.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Lesson Summary

 

In this lesson you focused on the following questions:

• Why do nuclear reactions release so much energy?
  
• What is nuclear fission?
  
• What is nuclear fusion?

In this lesson you learned that both fission and fusion nuclear reactions are processes that lead to an increase in the binding energy per nucleon, increasing the stability of the resulting nuclei. In the process of fission, a nucleus with more than 120 nucleons splits into smaller nuclei with greater binding energy per nucleon. 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 of these nuclear reactions release large amounts of energy.

 

For both fission and fusion reactions, the energy released is equal to the difference between the total binding energy of the original nucleus or nuclei and the final binding energy of the nucleus or nuclei. The energy released can also be found by calculating the total mass defect during the reaction. This mass defect was transformed into energy according to Einstein’s mass-energy equation E = mc2.

 

The product of fusion (helium) is stable and safe, which is in contrast to the unstable, dangerous daughter nuclei produced in a fission reaction.

 

In fission, a free neutron is absorbed by a large nucleus, such as uranium-235, causing it to become unstable and break apart into two smaller nuclei, accompanied by the release of several more neutrons. If the free neutrons encounter more uranium atoms they will again be absorbed, causing further fission and the production of more neutrons capable of continuing the process. Left unchecked with sufficient amounts of uranium, this chain reaction could produce a nuclear explosion. Controlling the rate of the chain reaction allows the energy to be released slowly, a strategy employed by current fission reactors.

 

In fusion, temperatures greater than 100 million Kelvin are needed to cause small nuclei, such as tritium and deuterium, to combine and form larger, more stable helium atoms while releasing an amount of energy equal to the change in the mass or difference in binding energies before and after the reaction. Advancing fusion reactor technology holds the promise of a seemingly infinite supply of clean energy.

 

Lesson Glossary

 

binding energy: the net energy required to liberate all of the protons and neutrons in a nucleus (overcome the strong nuclear force)

 

fission: when a nucleus with more than 120 nucleons splits into smaller nuclei with greater binding energy per nucleon

 

fusion: when a nucleus with fewer than 60 nucleons combines with another to form a larger nucleus with greater binding energy per nucleon

 

plasma: ionized gas in which the electrons have been separated from the nucleus

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Lesson 4—The Subatomic World

 

Get Focused

 

Sometimes you have to think big to find something really small. Deep underground, underlying the border between Switzerland and France, is a gigantic scientific instrument. The Large Hadron Collider (LHC) is the biggest machine in the world. It is nearly 27 km in circumference and contains 9300 magnets along a circular path. When it operates at full power, trillions of protons travel its circumference 11 245 times every second—nearly the speed of light!

 

Coming in the opposite direction and at the same speed, a second group of protons collide with them. All told, 600 million collisions should occur every second, with energies that will produce temperatures 100 000 times that of the Sun’s core. If it sounds impressive, that’s because it is! With these energies, never before seen on Earth, the protons will break apart, revealing the subatomic world that makes them up. The products of such a high-energy collision should help scientists answer some unresolved questions about the subatomic world, such as the following:

• What is the origin of mass? What makes up the mass in a nucleon?

• What makes up 96% of the universe? What is dark matter?

• Where is antimatter, as predicted by the standard model of the atom?

• What happened in the first few seconds of the universe?

• Are there other dimensions in the space-time continuum?

These are big, heavy questions. They will require massive amounts of energy to study. The LHC was built to provide enough energy to try to answer questions like these and to fill in the knowledge gaps that still exist in our understanding of the universe beyond our planet and reveal the fundamental make-up of the subatomic universe. These questions are beyond the scope of this course but show that, despite claims that humans understand the universe, there are still many basic concepts that we cannot explain.

 

Watch and Listen

 

Take a look at how the LHC will use hydrogen gas to investigate the quarks and particles from the inside of a proton in the video called “The Bottle to Bang.”

 

In Lesson 4 you will learn about ongoing developments that are informing our models of the structure of matter.

 

In this lesson you will focus on answering the following essential questions:

• How is it possible to probe the subatomic world?
  
  
• What subatomic particles make up the proton and neutron?
  
  
• How does the discovery of antimatter and subatomic particles inform the latest models concerning the structure of matter?

Module 8: Lesson 4 Assignment

 

Your teacher-marked Module 8: Lesson 4 Assignment requires you to submit responses to the following:

• Assignment—A 1, A 2, A 3, A 4, and A 5
• Reflect and Connect—RC 1, RC 2, RC 3, and RC 4

After a discussion with your teacher, you must decide what to do with the questions that are not part of your assignment. For example, you may decide to submit to your teacher the responses to Try This questions that are not marked. You should record the answers to all questions in this lesson and place those answers in your course folder.

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

 

Explore

 

Probing the Subatomic World

 

When two particles such as protons collide at sufficient energy, they break down into smaller particles, which leave behind tracks as they move away from the collision. The illustration here shows the particle tracks that could occur when two particles collide. These tracks are used to deduce the nature of the subatomic particle that created them. 

 

For example, if the collision occurs in a uniform magnetic field, the direction of the curved tracks reveals the charge of the particle. The radius of curvature can also be measured to give the charge-to-mass ratio of the particle in a way similar to that of a mass spectrometer.

 

Early devices designed to capture particle tracks include the cloud chamber and bubble chamber.

 

Cloud Chamber	Bubble Chamber
A device that contains dust-free supersaturated water or ethanol vapour, which will condense along the path of a particle that moves through it.	A device that contains liquefied gas, such as hydrogen, which boils and forms bubbles along the path of a particle that moves through it.

 

Only charged particles and photons capable of ionizing the material in the chambers will produce tracks. The nature of the charge can be determined with the appropriate hand rule and the charge-to-mass ratio can be calculated based on the radius of the curvature using . To review charge-to-mass ratio, see Module 7: Lesson 1 about cathode rays and Thomson’s experiment.

 

Read

 

Read “Detecting and Measuring Subatomic Particles” on pages 830 to 835 of your physics textbook.

 

Try This

 

TR 1. Complete “Practice Problems” 1 and 2 on page 834 and “Check and Reflect” questions 2 and 5 on page 835 of the textbook.

 

Module 8: Lesson 4 Assignment

 

Remember to submit your answer to A1 to your teacher as part of your Module 8: Lesson 4 Assignment. 

 

A 1. Explain how to use the following diagram of the bubble chamber paths of an alpha particle, beta particle, beta positive particle, and a gamma ray to determine which path corresponds to which particle.

 

 

The amount of energy required to overcome the strong nuclear force and scatter the contents of the nucleus is significant. Consider the energy used in various experiments so far:

• 13.6 eV: ionizes the hydrogen atom in the study of electron energy levels
  
  
• 1.0 × 107 eV: produces Rutherford scattering, revealing the nature of the nucleus

Early particle accelerators were sometimes called atom smashers, since they could develop enough energy to scatter the contents of the nucleus. The strong nuclear force can be overcome in a particle accelerator, causing the contents of a nucleon to scatter.

• 2.0 × 109 eV: produces heavier nuclei and scatters nuclear particles in a collision

Current particle accelerators, such as the Large Hadron Collider, can generate more energy than that needed to overcome the strong nuclear force.

• 1.4 × 1013 eV: maximum energy used in the LHC to expose subatomic particles  

Read

 

Read “Probing the Structure of Matter” on pages 840 and 841 of the textbook.

 

Fundamental Particles

 

Antimatter

 

Prior to the development of quantum theory it was believed that all matter was made of three fundamental particles: electron, proton, and neutron. More recent developments in this theory predict the existence of other subatomic particles, some with very peculiar properties. For example, quantum theory predicts that every kind of particle has a corresponding antiparticle. The antiparticle of an electron is called the positron, which has an identical magnitude charge-to-mass ratio as an electron but with a positive charge. American physicist Carl Anderson identified it in particle tracks in 1932.

 

When a particle and its antiparticle collide, they are both annihilated and produce a pair of high-energy gamma ray photons. The collision of an electron and a positron are part of the nuclear process in stars. This matter-antimatter collision can be described with an equation .

 

Example Question 1. How much energy is released when an electron-positron pair annihilate? 

 

Given

 

 

Required

 

the energy released from the annihilation

 

Analysis and Solution

 

Remember that in the annihilation one electron and one positron’s worth of mass is annihilated.

 

 

Paraphrase

 

One electron positron pair annihilation releases 1.64×10–13 J.

 

Example Question 2. How much energy would be released from the annihilation of 1.00 kg of electrons in an antimatter reaction?

 

Given

 

 

Required

 

the energy released from the annihilation of 1.00 kg of electrons

 

Analysis and Solution

 

Determine the amount of energy released; remember that to annihilate 1.00 kg of electrons takes 1.00 kg of positrons.

 

 

Paraphrase

 

When 1.00 kg of electrons is annihilated it will produce 1.80 × 1017 J of energy.

 

Remember from page 820 in your physics textbook that 1.0 kg of uranium releases 7.10 × 1013 J/kg and that 1.0 kg of gasoline releases 4.4 × 107 J/kg. So, antimatter reactions are extremely energy dense.

 

Module 8: Lesson 4 Assignment

 

Remember to submit your answers to A 2 and A 3 to your teacher as part of your Module 8: Lesson 4 Assignment. 

 

A 2. Compare and contrast matter and antimatter. 

 

A 3. Give an example of a matter–antimatter pair you have already seen in Physics 30, other than electron–positron.

 

Mediating Particles

 

Quantum theory also predicts the existence of particles that produce fundamental forces like gravity and the strong nuclear force. These mediating particles are thought to carry the fundamental forces and exist for such a short time that they are undetectable. The following table summarizes the mediating particles and their relationship to the fundamental forces.

 

Mediating Particle	Fundamental Forces	Particles Observed?
photons	electromagnetic	yes
gluons	strong nuclear	indirectly
gravitrons	gravitational	no
W+.W–,Zo	weak nuclear	yes

 

Read

 

Read “Quantum Theory and the Discovery of New Particles” on pages 836 to 838 of your textbook.

 

The Subatomic Zoo

 

More than 300 more subatomic particles have been discovered using new and more powerful particle accelerators and detectors. These particles have been classified by family.

 

Leptons do not interact via the strong nuclear force and are relatively small.

 

Hadrons do interact via the strong nuclear force and are subdivided based on size (meso is Greek for “middle”; barus is Greek for “heavy”). The particles are also classified by “spin,” which is analogous to describing the rotational momentum of the spinning particle. Boson and fermion are classifications based on the spin of the particle.

 

Read

 

Read “The Subatomic Zoo” on pages 842 to 844 of your physics textbook. Take note of “Table 17.3: An Introduction to the Subatomic Zoo,” which identifies the particles, symbols, mass, and lifetime of many subatomic particles.

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

 

Try This

 

TR 2. Complete “Check and Reflect” questions 1 to 5 on page 844 of the textbook.

 

Quarks and Decay

 

Given the large number of subatomic particles that were discovered using collisions and particle accelerators, it wasn’t long before scientists suggested that a large number of these particles were, in turn, built from just three smaller particles called quarks. The first quark is called an “up” quark and has a charge of e. The second quark is called a “down” quark and has a charge of e. The third particle is called the “strange” quark and has a charge of e. Using the powerful Stanford Linear Accelerator, scientists discovered that the mass and charge of a proton are indeed concentrated in three regions within the particle, supporting the quark model.

 

Protons and neutrons are each composed of three quarks.

 

 

The up, down, and strange quarks are first-generation quarks. Subsequent research and theory has identified three other quarks named charm, beauty, and truth. 

 

Read

 

“Table 17.5: Some Properties of Quarks” on page 846 of the textbook summarizes the first-, second-, and third-generation quarks.

 

The quark model and weak electric force help explain nuclear changes, like beta and beta-positive decay. For example, during the decay process a down quark can change into an up quark, leading to the emission of an electron and an electron antineutrino. The following are both the equation and graphical representation of this process showing the conservation of mass and charge.

 

Beta Decay

 

 

 

Beta Positive Decay

 

 

 

Module 8: Lesson 4 Assignment

 

Remember to submit your answers to A4 and A5 to your teacher as part of your Module 8: Lesson 4 Assignment.

 

A 4. Which particles are involved when an up quark changes into a down quark?

 

A 5. Which particles are involved when a down quark changes into an up quark?

 

The Standard Model

 

The standard model summarizes the most current understanding of the atom with the following key concepts:

• All matter is composed of 12 fundamental particles and their respective anti-particles (six quarks and six leptons).
  
  
• The electromagnetic force and the weak nuclear force are both aspects of the same fundamental force (electroweak force), supplied by the W+, W–, Zo mediating particles that have been observed.
  
  
• All of the quarks have a quantum property called “colour,” which is not related to visible colour, but is used to describe the strong nuclear force. This theory is referred to as quantum chromodynamics.

Even though the standard model explains three of the fundamental forces, it cannot explain how gravity works. At the extremely small scale of the atom, gravity is so weak as to be nonexistent and, therefore, does not affect subatomic actions. However, one of the goals of physicists is to develop a single theory and set of equations that describe everything in the universe, optimistically called the grand unified theory or the theory of everything.

 

Current theoretical research is moving toward a grand unified theory that could connect the electroweak force with chromodynamics and gravity. At the same time, research continues into string theory, which may connect gravity with the other three fundamental forces. In this theory the particles are treated as tiny vibrating strings of mass-energy that are quantized similarly to standing waves. At the moment these are just theories waiting to be tested, refined, rejected, and revised in a similar way to the thousands of ideas and theories that have come before them. In many respects, the inside of the atom remains undiscovered territory. Like the furthest reaches of deep space, it can only be explored with powerful and continually evolving human technology and ingenuity.

 

Read

 

Read “Quarks and the Standard Model” on pages 845 to 849 of your textbook.

 

Self-Check

 

SC1. What are the 12 particles of the standard model?

 

SC 2. Rank the four natural forces from weakest to strongest.

 

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Reflect and Connect

 

This pixel detector on the Large Hadron Collider will track the particles emitted by the collision of protons when each proton is travelling at nearly the speed of light in opposite directions. The particle emitted in these high-energy collisions reveals the internal workings of the atom. Powerful technology is required to look deep inside the subatomic world, just as powerful technology is required to look deep into the universe.

 

The atom is as tiny as the universe is massive, so it is no wonder that vast amounts of energy and technology are required to refine the theories and ideas that describe them both! On these scales, new terminology and ideas can become so complex that it is easy to overlook all of the connections.

 

Read

 

 

Reflect and Connect

 

Read the following Reflect and Connect questions; then watch the “CERN Development Video,” which goes over the development of CERN over the past 50 years.

 

Module 8: Lesson 4 Assignment

 

Remember to submit your answers to RC 1, RC 2, RC 3, and RC 4 to your teacher as part of your Module 8: Lesson 4 Assignment.

 

RC 1. Name two famous physicists shown in the video and state why they are famous as physicists.

 

RC 2. What are two physics discoveries that have been made at CERN in the past 50 years?

 

RC 3. Why is CERN (the European Organization for Nuclear Research) significant for scientists worldwide and what does it show about cooperation in the scientific community?

 

RC 4. State two ways that the application of the work at CERN has changed life for everyday people.

 

Module 8: Lesson 4 Assignment

 

Remember to submit Module 8: Lesson 4 Assignment to your teacher.

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Lesson Summary

• How is it possible to probe the subatomic world?
  
  
• What subatomic particles make up the proton and neutron?
  
  
• How does the discovery of antimatter and subatomic particles inform the latest models concerning the structure of matter?

In this lesson you learned that particle tracks can be interpreted to identify the charge-to-mass ratio and type of charge on subatomic particles. By colliding particles, such as protons, at extremely high energies, the contents of these particles can be probed and studied. Current particle accelerators are among the most powerful machines ever built and are capable of causing particle collisions at energies never before seen on Earth.

 

Based on particle track research and theory, the subatomic world is composed of strange ideas and particles such as antimatter, mediating particles, and the quarks that make up protons and neutrons. Some evidence for up and down quarks is provided by beta decay and beta-positive decay, which is caused by the electroweak force.

 

Beta Decay

 

 

Beta Positive Decay

 

 

Current theory that relates the mediating particles to the fundamental forces of electroweak and strong nuclear force are contained in the Standard Model, which is evolving as more experimental evidence gathers. In subatomic research, theory and observation interact, one leading to the other and vice versa. Together, both theoretical and experimental physicists are working toward a grand unified theory, or theory of everything, that will bring connection to all the fundamental forces of the universe and the particles that mediate, create, and sustain them.

 

Lesson Glossary

 

antimatter: an extension of the concept of normal matter that is made up of particles where antimatter is made up of antiparticles

 

All particles have an antiparticle.

 

bubble chamber: a device that tracks particles using bubbles in liquefied gas

 

CERN: Conseil Européen pour la Recherche Nucléaire (world’s largest particle physics laboratory)

 

CERN had the first web server and posted the first page on the World Wide Web. See CERN’s website to see that historic first page.

 

cloud chamber: a device that tracks particles using condensed gas vapours

 

fundamental particle: a particle that cannot be divided into smaller particles; an elementary particle

 

gluon: a mediating particle for the strong nuclear force

 

graviton: a hypothetical mediating particle for the gravitational force

 

mediating particle: a virtual particle that carries a fundamental force

 

quark: a fundamental particle in the hadron family

 

standard model: the current theory describing the nature of matter and the fundamental forces

 

virtual particle: a particle that exists for such a short time that it cannot be detected

 

 

Physics 30 Learn EveryWare © 2009 Alberta Education

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.

 

Analytic scoring guide.

 

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 (g)
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?

Graphing Scoring Guide

 

Physics 30 Learn EveryWare © 2009 Alberta Education

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

 

Module Glossary

 

activity or decay rate: the number of nuclei in a sample that decays in a given time interval

 

antimatter: a form of matter that has properties opposite to its normal-matter counterpart; an extension of the concept of normal matter that is made up of particles where antimatter is made up of antiparticles

 

All particles have an antiparticle.

 

antineutrino: a tiny subatomic particle with no charge emitted with  in beta decay

 

alpha particle: two protons and two neutrons bound together to form a stable particle identical to a helium nucleus

 

atomic mass: the weighted mean atomic mass number of the element’s natural isotopes

 

This number is given on the periodic table.

 

atomic mass number (A): the number of nucleons in an atom’s nucleus

 

atomic number (Z): the number of protons in the nucleus

 

The atomic number uniquely identifies the element.

 

becquerel (Bq): the unit of radioactivity equal to one decay per second

 

beta particle: an electron emitted by the nucleus when a neutron splits into a proton and electron during the beta decay process

 

binding energy: the net energy required to liberate all of the protons and neutrons in a nucleus (overcome the strong nuclear force)

 

bubble chamber: a device that tracks particles using bubbles in liquefied gas

 

CERN: Conseil Européen pour la Recherche Nucléaire (world’s largest particle physics laboratory)

 

CERN had the first web server and posted the first page on the World Wide Web. See CERN’s website to see that historic first page.

 

cloud chamber: a device that tracks particles using condensed gas vapours

 

daughter element: the element produced by a decay process

 

fission: when a nucleus with more than 120 nucleons splits into smaller nuclei with greater binding energy per nucleon

 

fundamental particle: a particle that cannot be divided into smaller particles; an elementary particle

 

fusion: when a nucleus with fewer than 60 nucleons combines with another to form a larger nucleus with greater binding energy per nucleon

 

gluon: a mediating particle for the strong nuclear force

 

graviton: a hypothetical mediating particle for the gravitational force

 

half-life: the time it takes for half the radioactive nuclei in a sample to decay

 

isotope: an atom that has the same number of protons but a different number of neutrons and, therefore, a different atomic mass number

 

mediating particle: a virtual particle that carries a fundamental force

 

nucleon: a proton or neutron

 

neutrino: a tiny subatomic particle with no charge emitted with a positron in beta-positive decay

 

neutron: a neutral particle found in the nucleus

 

parent element: the original element in a decay process

 

plasma: ionized gas in which the electrons have been separated from the nucleus

 

positron: the antimatter to an electron

 

It is the same type of particle but has an opposite charge. Unlike electrons, positrons are scarce.

 

proton: a positively charged particle found in all nuclei

 

quark: a fundamental particle in the hadron family

 

standard model: the current theory describing the nature of matter and the fundamental forces

 

transmutation: decay or change into a different element

 

virtual particle: a particle that exists for such a short time that it cannot be detected

 

 

Physics 30 Learn EveryWare © 2009 Alberta Education