AP Physics Chapter 29 The Nucleus

Chapter 29: The Nucleus 29.1Nuclear Structure and Nuclear Force 29.2Radioactivity 29.3Omitted 29.4Nuclear Binding Energy 29.5Omitted

Homework for Chapter 29 Read Chapter 29 HW 29.A: p. 922: 2-6; 8-10,12,14,15,17,20. HW 29.B: p : 58-60, 63,66,67,86.

Answer: Almost one-half of one-half-life has passed. No, there are still many carbon-14 isotopes left to count.

29.1: Nuclear Structure and the Nuclear Force

An atom consist of a nucleus and electrons in various shells around it. The nucleus contains all the positive charge of the atom and most of its mass. Each of the electrons carry a negative charge and very little mass. What constituted the nucleus was not very well known until the discovery of the neutral particle called the neutron by James Chadwick in It was then established that the nucleus contains two kinds of particles: protons and neutrons. The protons have the positive elementary charge, equal and opposite to that of an electron. A proton has almost the same mass as the hydrogen atom. James Chadwick The neutron is electrically neutral and is slightly heavier than the proton. There are as many protons in the nucleus as electrons in the orbits for a neutral atom.

The total number of protons in the nucleus is called the atomic number (Z). Different elements have different atomic numbers. The neutrons and protons are together called nucleon. The total number of nucleon is called the mass number of the nucleus (A). The number of neutrons in the nucleus is A-Z. This model places electrons outside of the nucleus. However, a problem immediately arises when it is assumed that there are protons in the nucleus. Since protons repel each other the nucleus will break apart. How are the protons held together against the repulsive forces in the nucleus? This lead to the discovery of the new fundamental force called the strong nuclear force.

The strong nuclear force is the strongest of all the known fundamental forces. The strong nuclear force, or just nuclear force, is a short range force. The distance is on the order of the size of the nucleus ( m). The nuclear force does not distinguish between protons and neutrons. It acts between any two nucleons – between two protons, a proton and a neutron, or two neutrons. Another nuclear force is called the weak nuclear force. This force is responsible for beta decay in which a neutron gives rise to a proton and electron (beta particle).

Interaction Current Theory Mediators Relative Strength [1] [1] Long-Distance Behavior Range (m) Strong Quantum chromod ynamics Quantum chromod ynamics (QCD) gluons10 38 (extremely complex expression) 10 −15 Electromagnetic Quantum electrody namics Quantum electrody namics (QED) photons10 36 ∞ Weak Electrow eak Theory W and Z bosons −18 Gravitation General Relativity General Relativity (GR) gravitons gravitons (hypothetical) 1∞

In the study of beta decay it was observed that some of the mass in the beta decay was not accounted for. In addition, linear and angular momenta were not conserved. It was thus theorized (1934) by the physicists that there must be another particle produced in the reaction but goes undetected. This particle was called the neutrino (little neutral one). They have a very small rest mass, no charge, and reacts very little with matter. These properties make it very difficult to detect. The neutrino was later detected by Reins and Cowman in 1853.

A particular nuclear species or isotope of any element is called a nuclide. For example, on the previous slide are shown three nuclides of hydrogen. In any nuclear reaction there are a number of quantities which are conserved. Two of these quantities are mass number (i.e. number of nucleon) and charge. The total of mass numbers (A) and total of atomic numbers (Z) should be balanced on the two sides for any nuclear reaction. The symbol for a nucleus can be written to indicate its mass number and atomic number. In general example: For one of the uranium isotopes, its nucleus has 92 protons and 146 neutrons. Hence the symbol for this nucleus is

ONL R Y M O T H E R A N D D A U G H T E R Z E T O E A C H W I N A N O B E L P R I

29.2: Radioactivity

In any nuclear reaction including radioactivity conserve the following quantities in order to balance the equation for reaction: 1. Nuclear charge (the total of atomic numbers) 2. Number of nucleons (the total of mass numbers) Alpha Decay An alpha particle is a helium nucleus; 2 protons and 2 neutrons. Since the parent nucleus loses two protons, the resulting daughter nucleus must be the nucleus of another element defined by the new proton number. The alpha decay process is one of nuclear transmutation, in which the nuclei of one element change into the nuclei of a lighter element.

Beta Decay A beta particle is an electron. However, the electron emitted in beta decay is not an orbital electron, but one emitted from the nucleus, although it is not part of the original nucleus. In this type of beta decay, the neutron number of the parent nucleus decreases by one and the proton number of the daughter nucleus increases by one. The nucleon number is unchanged. A neutrino is also emitted in beta decay, but for simplicity this has not been shown in the nuclear decay equations. Another way to look at it is a neutron within the nucleus decays into a proton and an electron. n  p + e basic  - decay B - decay occurs when an isotope has too many neutrons compared to protons to be stable

A second mode of beta decay,  + or positron decay, occurs when an isotope has too many protons compared to neutrons to be stable. A positron has the same mass as an electron, but with a positive charge. The oppositely charged particle is said to be the antiparticle of the electron. As a result, the net effect of  + decay is to convert a proton into a neutron. Positron emission is also accompanied by a neutrino (although of a different type than that in  - decay). As in  - decay, the mass numbers of the parent and daughter nuclei do not change, but the proton number of the daughter nucleus in this case is one less than that of the parent nucleus.

A process related to beta decay is electron capture (EC), which involves the absorption of orbital electrons by a nucleus. The net result is a daughter nucleus the same as would have been produced by positron decay. example: e + Be  Li As in  + decay, a proton changes into a neutron, but no beta particle is emitted in electron capture. Gamma Decay In gamma decay, the nucleus emits a gamma (  ) ray, or a photon of electromagnetic energy. The emission of a gamma ray by a nucleus in an excited state is analogous to the emission of a photon by an excited atom. Nuclear energy levels are much farther apart and more complicated than those of an atom. They are on the order of kiloelectron volts and megaelectron volts apart, compared to a few electron volts between atomic levels. As a result, gamma rays are very energetic

The asterisk indicates that the nucleus is in an excited state. De-excitation results in the emission of a gamma ray. In gamma decay, the mass and proton numbers do not change. The daughter nucleus is simply the parent nucleus with less energy.

Radiation Penetration The absorption or degree of penetration of nuclear radiation is an important consideration in applications such as radioisotope treatment of cancer and nuclear shielding around a nuclear reactor or radioactive materials. Alpha particles have a large mass and are doubly charged, and generally move slowly. A few centimeters of air or a sheet of paper will usually completely stop them. Beta particles can travel a few meters in air or a few centimeters in aluminium before being stopped. Gamma rays are more penetrating. They can penetrate a centimeter or more of a dense material such as lead.

Retro Atomic Video

Summary The strong nuclear force is the short-range attractive force between nucleons that is responsible for holding the nucleus together against the repulsive electric force of its protons. Isotopes of an element are nuclides that differ only in the number of neutrons they contain. Radioactivity refers to any type of nuclear instability that results in the emission of particles and photons. Nuclei may undergo radioactive decay by the emission of an alpha particle, or helium nucleus (  decay); a beta particle, either an electron (  - decay) or a positron (  + decay); or a gamma ray, a high-energy photon of electromagnetic radiation (  decay). Nuclei can also change by capturing one of the atom’s orbital electrons (electron capture).

Check for Understanding 1.Which of the following particles are present in the nucleus of an atom? a) electrons only b) protons only c) neutrons only d) protons and neutrons only e) electrons, protons, and neutrons Answer: d 2. Which force holds the nucleons together in a nucleus? a) gravitational force b) electric force c) magnetic force d) strong nuclear force e) weak nuclear force Answer: d

Check for Understanding 3. The nucleus of Be has a) 9 neutrons and 4 protons b) 4 protons and 9 neutrons c) 5 neutrons and 4 protons d) 4 neutrons and 5 protons e) 4 neutrons, 4 protons, and one electron Answer: c 4. When a nucleus decays by emission of a gamma ray photon, a) its atomic number changes b) its mass number changes c) both the atomic number and the mass number change d) none of the two numbers change e) the mass number and the atomic number are switched around Answer: d 9494

Homework for Chapter 29 HW 29.A: p. 922: 2-6; 8-10,12,14,15,17,20.

29.4: Nuclear Binding Energy

The strong nuclear force is the force that holds a nucleus together. Without it, the electric repulsive force would cause it to fly apart. Although you have to add energy to bring free protons together to form a nucleus, as the nucleons get very close to each other, they will attract, and energy will be released. For a stable nucleus, more energy is released as the nucleons finally come together than had to be put in to overcome the Coulomb repulsion. The difference in the energy of the free nucleons and the bound nucleus is called the binding energy (  E) of the nucleus. The average binding energy per nucleon gives an indication of nuclear stability. The greater this number, the more tightly bound are the nucleons in a nucleus, hence the more stable it is.  E average binding energy per nucleon, where A  E is the binding energy A is the number of nucleons

example: MeV of energy is required to separate a helium nucleus into free protons and neutrons. Conversely, if two protons and two neutrons combine to form a helium nucleus, MeV of energy would be released. This is the binding energy of the nucleus.

If you know the mass of a nucleus and how many protons and neutrons is contains, you can use the Einstein mass-energy equivalence principle to determine the binding energy. This relationship tell you that mass and energy can be converted into each other.  E = (  m) c 2 where  E is the binding energy  m is the mass defect c = 3.00 x 10 8 m/s On Gold Sheet The mass defect (  m) is the mass difference between free nucleons and nucleons bound in a nucleus. The sum of the masses of the nucleons in the nucleus (bound particles) is less than that when the nucleons are separated as free particles. The mass defect has an energy equivalence called the binding energy which is the minimum amount of energy needed to separate a given nucleus apart into its constituent nucleons,  E = (  m)c 2.

Since the masses of nuclei are so small, another unit, the unified atomic mass unit (u) is used to measure nuclear masses. By definition, 1 u = x kg. It is referenced from a neutral atom of 12 C, which is taken to have an exact mass of u. If one atomic mass unit is converted to energy, energy is released:  E = (  m)c 2 = (1.66 x kg)(3.00 x 10 8 m/s) 2 = 1.49 x J = 931 MeV 1 u = 1.66 x kg = 931 MeV / c 2 If you know the change in mass in atomic mass units, you can multiply by 931 to find the energy gain or release in MeV. example: The mass defect for an atom was found to be u. The binding energy can be calculated from the energy equivalence of 1 u:  E = (  m)c 2 = ( u)(931 MeV/u) = 492 MeV On Blue Sheet

For other particles see Appendix V in text. Typically, use the hydrogen atom for the mass of the proton. Note: The mass of a hydrogen atom is slightly more than a proton. The difference is in the atomic electron. We deal with the masses of atoms, not just the nuclei, since that is what is typically measured.

Example 29.8: Which isotope of hydrogen has the smaller average binding energy per nucleon, deuterium or tritium?

Mass Defect and Nuclear Decay Imagine a nuclei at rest before emitting alpha, beta, or gamma particles. But when the nuclei decay, the alpha, beta, or gamma particles come whizzing out at an appreciable fraction of light speed. So, the daughter nucleus must recoil after decay in order to conserve momentum. Now consider energy conservation. Before decay, no kinetic energy existed. After the decay, both the daughter nucleus and the emitted particle have lots of kinetic energy. Where did this energy come from? It comes from mass. The total mass present before the decay is very slightly greater than the total mass present in both the nucleus and the decay particle after the decay. That slight difference is the mass defect. This mass is destroyed and converted into kinetic energy:  E = (  m)c 2

Example 29.9: Near high neutron areas, such as a nuclear reactor, neutrons will be absorbed by protons (hydrogen nuclei in water molecules) and will give off a characteristic energy gamma ray in the process. What is the energy of the gamma ray (to three significant figures)?

Summary The total binding energy is the minimum amount of energy needed to separate a nucleus into its constituent nucleons. The mass defect is the mass lost (converted to energy) when free nucleons are bound in a nucleus. One of most profound results of Einstein’s Theory of Relativity was the fact that mass could be converted into energy and vice versa.  E = (  m)c 2

Check for Understanding: 1.Einstein’s equation for mass-energy equivalence is given by a) E = m/c 2 b) E = mc 2 c) E = m 2 c d) E = m 2 c 2 e) E = c/m 2 Answer: b 2. In Einstein’s equation for mass-energy equivalence, “c” stands for a) Speed of sound at 0°C b) Speed of sound at 0°F c) Speed of sound at 0 K d) Speed of sound in liquid He at 4 K e) Speed of light in a vacuum Answer: e

Homework for Chapter 29 HW 29.B: p : 58-60, 63,66,67,86.