Chapter 28 Lecture Nuclear Physics
Nuclear Physics How are new elements created? What are the natural sources of ionizing radiation? How does carbon dating work?
Be sure you know how to: Use the right-hand rule for magnetic force to determine the direction of the force exerted by a magnetic field on a moving charged particle (Section 17.4). Relate mass to energy using the special theory of relativity (Section 25.8).
Relativistic energy
Relativistic Energy
What's new in this chapter In this chapter, we investigate several questions about the nucleus: What is the structure of the nucleus, and which processes do nuclei undergo? Do these processes occur only in stars or in huge particle accelerators, or do they happen every day and perhaps even in our bodies?
Becquerel and the emissions from uranyl crystals Becquerel found that uranium crystals that had not been exposed to sunlight formed images on photographic plates. The uranium emitted radiation without an external source of energy.
Observational experiment
Pierre and Marie Curie and the particles responsible for Becquerel's rays Chemical changes or changes in the amount of light shining on a sample did not lead to changes in the amount of radiation produced by uranium salts. These findings suggested that the electrons in the atoms were not responsible for the rays. Marie and Pierre Curie concluded that the Becquerel rays must come from the nuclei of atoms.
Rutherford and experiments investigating the charge of emitted particles Rutherford covered a uranium sample with thin aluminum sheets to investigate how metal layers affected the amount of radiation.
Testing experiment
Alpha particles, beta rays, and gamma rays Rutherford found positively charged particles with a mass-to-charge ratio twice that of a hydrogen ion; they were called alpha rays or alpha particles. Negatively charged particles had the same mass-to-charge ratio as that of the electron; they were called beta rays. Neutral radiation was thought to consist of highenergy electromagnetic waves, called gamma rays.
The early model of the nucleus The nucleus of an atom is made of positively charged alpha particles and negatively charged electrons. When a nucleus contains a large number of alpha particles, they start repelling each other more strongly than the electrons can attract them, and the alpha particles leave the nucleus. This leaves behind electrons that repel each other; thus beta rays are emitted. The nucleus is left in an excited state and emits a high-energy photon, a gamma ray.
Problem with the early model of the nucleus A hydrogen atom is lighter than an alpha particle. What, then, is the composition of its nucleus?
Size of the nucleus: Too small for an electron We can use the uncertainty principle and the size of the nucleus to show that our current models would result in atoms that rapidly lose their electrons.
The search for a neutral particle An alpha particle has the charge of two protons but four times the mass of a proton; thus it cannot be made of two protons. In 1920, Rutherford suggested a neutral particle with the approximate mass of a proton. In 1928, Bothe and Becker took the initial step in this search.
The neutral radiation is not a gamma-ray photon By comparing the energies and momenta of the particles knocked out of different atoms, Chadwick determined that the particles were uncharged particles with a mass approximately equal to that of the proton.
Revising ideas of the structure of the nucleus A new model of nuclear constituents evolved that involved protons and neutrons. The protons accounted for the electric charge of the nucleus. The uncharged neutrons accounted for the extra mass.
One atomic mass unit
Atomic Mass The atomic masses are specified in terms of the atomic mass unit u, defined such that the atomic mass of isotope 12 C is exactly 12 u. 1 u = 1.6605 10 27 kg The energy equivalent of 1 u of mass is To find the energy equivalent of any atom or particle whose mass is given in atomic mass units we can use 2015 Pearson Education, Inc.
Atomic Mass We can write 1 u in the following form as well: MeV/c 2 are units of mass. The energy equivalent of 1 MeV/c 2 is 1 MeV. 2015 Pearson Education, Inc.
Observational experiment
Isotopes Atoms of a particular element with different numbers of neutrons are called isotopes of that element. The electronic structure of an element's isotopes is the same, which means their chemical behaviors are almost identical. However, the nuclei behave quite differently.
Conceptual Exercise 28.1 Determine the number of protons and neutrons in each of the following nuclei: A. B. C. D. E. F.
Tip
Nuclear force and binding energy How can protons stay bound together when they repel each other so strongly?
Nuclear force Some attractive force must balance this electrical repulsive force and must attract neutrons as well; it has to be an attractive force for both protons and neutrons. We call this attractive force a nuclear force. The nuclear force must weaken to nearly zero extremely rapidly with increasing distance between nucleons. If it didn't, then nuclei of nearby atoms would be attracted to each other, clumping together into ever-larger nuclei.
Nuclear binding energy The binding energy of the nucleus is the energy that must be added to the nucleus to separate it into its component protons and neutrons. The nucleus is a bound system, so its nuclear potential energy plus electric potential energy plus kinetic energy of the protons and neutrons must be negative.
Binding energy The nuclear binding energy is computed by considering the mass difference between the atom and its separate components, Z hydrogen atoms and N neutrons:
Binding Energy 2015 Pearson Education, Inc. Slide 30-30
Example Finding the binding energy of iron What is the nuclear binding energy of 56 Fe to the nearest MeV? Atomic mass of 56 Fe as 55.934940 u. Iron has atomic number 26, so an atom of 56 Fe could be separated into 26 hydrogen atoms and 30 neutrons. The mass of the separated components is more than that of the iron nucleus; the difference gives us the binding energy. 2015 Pearson Education, Inc.
Example 30.1 Finding the binding energy of iron (cont.) SOLVE We solve for the binding energy using Equation 30.4. The masses of the hydrogen atom and the neutron are given in Table 30.2. We find 2015 Pearson Education, Inc.
Example 30.1 Finding the binding energy of iron (cont.) ASSESS The difference in mass between the nucleus and its components is a small fraction of the mass of the nucleus, so we must use several significant figures in our mass values. The mass difference is small about half that of a proton but the energy equivalent, the binding energy, is enormous. 2015 Pearson Education, Inc.
Forces and Energy in the Nucleus The strong nuclear force is the force that keeps the nucleus together. 1. It is an attractive force between any two nucleons. 2. It does not act on electrons. 3. It is a short-range force, acting only over nuclear distances. We see no evidence for the nuclear forces outside the nucleus. 4. Over the range where it acts, it is stronger than the electrostatic force that tries to push two protons apart. 2015 Pearson Education, Inc.
Forces and Energy in the Nucleus A nucleus with too many protons will be unstable because the repulsive electrostatic forces will overcome the attractive strong forces. Because neutrons participate in the strong force but exert no repulsive forces, the neutrons provide the extra glue that holds the nucleus together. 2015 Pearson Education, Inc.
Forces and Energy in the Nucleus In small nuclei, one neutron per proton is sufficient for stability, so small nuclei have N Z. As the nucleus grows, the repulsive force increases faster than the binding energy, so more neutrons are needed for stability. 2015 Pearson Education, Inc.
Forces and Energy in the Nucleus Protons and neutrons have quantized energy levels like electrons. They have spin and follow the Pauli exclusion principle. The proton and neutron energy levels are separated by a million times more energy than the energy separation of electron energy levels. 2015 Pearson Education, Inc.
Low-Z Nuclei Low-Z nuclei (Z < 8) have few protons, so we can neglect the electrostatic potential energy due to proton-proton repulsion. In this case, the energy levels of protons and neutrons are essentially identical. 2015 Pearson Education, Inc.
Low-Z Nuclei 2015 Pearson Education, Inc. Slide 30-39
Low-Z Nuclei The nuclear energy-level diagram of 12 C, which has 6 protons and 6 neutrons, shows that it is in its lowest possible energy state 2015 Pearson Education, Inc.
Low-Z Nuclei 12 B and 12 N could lower their energies in a process known as beta decay where a proton turns into a neutron or vice versa. 2015 Pearson Education, Inc.
High-Z Nuclei In a nucleus with many protons, the increasing electrostatic potential energy raises the proton energy levels but not the neutron energy levels. If there were neutrons in energy levels above vacant proton levels, the nucleus would lower its energy by changing neutrons into protons, and vice versa. The net result is that the filled levels for protons and neutrons are at just about the same height. Because neutron energy levels start at a lower energy, more neutron states are available. 2015 Pearson Education, Inc.
High-Z Nuclei 2015 Pearson Education, Inc. Slide 30-43
Binding Energy As A increases, the nuclear binding energy increases because there are more nuclear bonds. A useful measure for comparing one nucleus to another is the quantity B/A called the binding energy per nucleon. 2015 Pearson Education, Inc.
Binding energy per nucleon
Nuclear Stability 2015 Pearson Education, Inc. Slide 30-46
Nuclear Stability Graphically, the stable nuclei cluster very close to the line of stability. There are no stable nuclei with Z > 83 (bismuth). Heavier elements (up to Z = 92, uranium) are found in nature but they are radioactive. Unstable nuclei are in the bands along both sides of the line of stability. The lightest elements with Z < 16 are stable when N Z. As Z increases, the number of neutrons needed for stability grows increasingly larger than the number of protons.
Binding Energy The line connecting the points on this graph is called the curve of binding energy 2015 Pearson Education, Inc.
Binding Energy If two light nuclei can be joined together to make a single, larger nucleus, the final nucleus will have a higher binding energy per nucleon. Because the final nucleus is more tightly bound, energy will be released in this nuclear fusion process. Nuclear fusion of hydrogen to helium is the basic reaction that powers the sun. 2015 Pearson Education, Inc.
Binding Energy Nuclei with A > 60 become less stable as their mass increases because adding nucleons decreases the binding energy per nucleon. Alpha decay is a basic type of radioactive decay that occurs when a heavy nucleus becomes more stable by ejecting a small group of nucleons in order to decrease its mass, releasing energy in the process. Nuclear fission is when very heavy nuclei are so unstable that they can be induced to fragment into two lighter nuclei. 2015 Pearson Education, Inc.
Binding Energy The collision of a slow-moving neutron with a 235 U nucleus causes the reaction 236 U is so unstable that it immediately fragments, in this case into two nuclei and two neutrons. A great deal of energy is released in this reaction. 2015 Pearson Education, Inc.
Representing nuclear reactions The advantage of writing nuclear reactions as shown here is that atomic masses (found in atomic mass tables) can be used to analyze the energy transformations that occur during the reactions:
Observational experiment
Rules for nuclear reactions
Tip
Quantitative Exercise 28.3 Determine the missing products in the following reactions:
Testing experiment
Energy conversions in nuclear reactions
Binding energy and energy release The higher the binding energy per nucleon, the more energy needed to split the nucleus into its constituent protons and neutrons.
Binding energy and energy release The graph predicts: When two small nuclei combine, energy should be released. When a large nucleus breaks apart, energy should be released.
Fusion and chemical elements Fusion occurs naturally in stars; it requires high heat and high pressure to overcome the repulsion from the electric charges.
Fusion and chemical elements Supernova explosions contribute to the chemical composition of the universe. The elements lighter than iron that are produced in stars' cores before the explosion are ejected into space. The elements heavier than iron that are produced during the explosion are then ejected into space.
Quantitative Exercise 28.4 The energy released by the Sun comes from several sources, including the proton-proton chain of fusion reactions: Determine the energy released in this chain of reactions in MeV. Use the masses,, and to determine the rest energy converted to other forms.
Quantitative Exercise 28.4
Fission and nuclear energy
Bohr's liquid drop model of the nucleus Frisch and Meitner decided that Bohr's liquid drop model of a nucleus could explain the observation of fission. Surface tension holds a water drop together; likewise, the nuclear forces hold the nucleons together. The protons repel each other and overwhelm the effect of the "surface tension." The nucleus can then stretch itself and divide into two smaller pieces.
Alpha decay When one of the alpha particles leaves, this emission reduces the number of protons in the original nucleus as well as the electric repulsion between the remaining protons.
Nuclear decay modes Text: p. 985 2015 Pearson Education, Inc. Slide 30-68
Quantitative Exercise 28.7 Determine the kinetic energy of the product nuclei when polonium-212 undergoes alpha decay. The masses of the nuclei involved in the decay are ;, and.
Quantitative Exercise 28.7
Beta decay During beta decay, a particular element is transformed into an element with a Z number that is larger by 1.
Problems with beta decay The problem with spin conservation: In beta decay, the spin quantum number was not conserved. The problem with energy conservation: The total energy of the products was always observed to be less than the total energy of the reactants.
Beta decay Wolfgang Pauli proposed an explanation for beta decay that did not require abandoning energy conservation or spin number conservation. He hypothesized that some unknown particle carried away the missing energy and accounted for the discrepancy in spin number. This particle had zero electric charge, zero mass, and a spin number of either +1/2 or 1/2. Enrico Fermi called the particle a neutrino, meaning "little neutral one."
Beta-minus and beta-plus decay
SYNTHESIS 30.1 Nuclear decay modes Text: p. 985 2015 Pearson Education, Inc. Slide 30-75
Gamma decay After alpha or beta decay, the nucleus can be left in an excited state from which it then emits one or more photons to return to its ground state.
Gamma Decay Gamma decay occurs when a proton or neutron undergoes a quantum jump. 2015 Pearson Education, Inc.
Gamma Decay Gamma decay occurs when a proton or neutron undergoes a quantum jump. 2015 Pearson Education, Inc.
Quantitative Exercise 28.8 The following nuclei undergo different types of radioactive decay. Determine the daughter nucleus for each and write an equation representing each decay reaction. alpha decay beta-minus decay beta-plus decay (produces a positron)
Quantitative Exercise 28.8
Half-life Using a particle detector such as a Geiger counter, we can measure the number of nuclei that decay in a short time interval and determine the number N of radioactive nuclei that remain in the sample as a function of time.
Observational experiment
Half-life
Half-lives and decay constants of some common nuclei
Determining the source of carbon in plants The photosynthesis process in plant growth may be summarized as follows: 6CO 2 + 6H 2 O + sunlight C 6 H 12 O 6 + 6O 2 Some CO 2 in the atmosphere, including the carbon-11 isotope, is synthesized by plants. The naturally occurring carbon isotope carbon-11 is radioactive, with a half-life of 20 minutes.
Decay rate (activity) A
Exponential decay
Decay rate and half-life At time t = T (one half-life), the number N of radioactive nuclei remaining is one-half the number N 0 at time zero: If the decay constant is large, then the material decays rapidly and consequently has a short half-life T.
Radioactive dating Archeologists and geologists are interested in determining the age of a radioactive sample from the known fraction N/N 0 of radioactive nuclei that remain in the sample: In this equation, T is the half-life of the radioactive material and t is the sample's age when N radioactive nuclei remain.
Tip
Carbon dating Any plant or animal that metabolizes carbon incorporates about one carbon-14 atom into its structure for every 10 12 carbon-12 atoms it metabolizes. Carbon is no longer metabolized by the organism after death, so the carbon-14 starts to transform into nitrogen-14. After 5700 years, the carbon-14 concentration decreases by one-half. A measurement of the current carbon-14 concentration indicates the age of the remains.
Example 28.11 A bone found by an archeologist contains a small amount of radioactive carbon-14. The radioactive emissions from the bone produce a measured decay rate of 3.3 decays/s. The same mass of fresh cow bone produces 30.8 decays/s. Estimate the age of the sample.
Radioactive decay series
Ionizing radiation and its measurement Ionizing radiation's effects on living organisms are classified into two categories: genetic damage and somatic damage. Genetic damage occurs when the DNA molecules in the reproductive cells are altered by the radiation. These genetic changes are passed on to future generations. Somatic damage involves cellular changes to all parts of the body except the reproductive cells.
Absorbed dose
Relative biological effectiveness (RBE)
Dose or dose equivalent
Quantitative Exercise 28.12 In a typical chest X-ray, about 10 mrem (10 x 10 3 rem) of radiation is absorbed by about 5 kg of body tissue. Each of the X-ray photons used in such exams has approximately 50,000 ev of energy. Determine about how many ions are produced by this X-ray exam.
Natural sources of ionizing radiation Radioactive elements in the Earth's crust include uranium-238, potassium-40, and radon-226. Foods may contain radioactive isotopes. Cosmic rays are elementary particles moving at almost the speed of light. The original source of cosmic rays was primarily supernova explosions of stars in our galaxy.
Human-made sources of ionizing radiation
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